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Appropriate mesh refinement plays a vital role in the accuracy and convergence of computational fluid dynamics solvers. This work is an extension of the previous work that further demonstrates the accuracy of the 3D adaptive mesh refinement method by comparing the accuracy measures between the ones derived from the analytical fields and those identified by the refined meshes. The adaptive mesh refinement method presented in this study is based on the law of mass conservation for three-dimensional incompressible or compressible steady fluid flows. The assessment of the performance of the adaptive mesh refinement method considers its key features such as drawing closed streamline and identification of singular points, asymptotic planes, and vortex axis. Several illustrative examples of the applications of the 3D mesh refinement method with a multi-level refinement confirm the accuracy and efficiency of the proposed method. Furthermore, the results demonstrate that the adaptive mesh refinement method can provide accurate and reliable qualitative measures of 3D computational fluid dynamics problems. [ABSTRACT FROM AUTHOR]

The phase‐field formulation for fracture propagation is widely adopted due to its capability of naturally treating complex crack geometries. The challenges of the phase‐field crack simulation include the non‐convexity of the underlying energy functional and the expensive computational cost associated with the fine mesh required to resolve the phase‐field length‐scale around the crack region. We present a novel phase‐field monolithic scheme based on the limited‐memory Broyden–Fletcher–Goldfarb–Shanno (BFGS) method, or the L‐BFGS method, to address the convergence difficulties usually encountered by a Newton‐based approach because of the non‐convex energy functional. Comparing with the conventional BFGS method, the L‐BFGS monolithic scheme avoids to store the fully dense Hessian approximation matrix. This feature is critical in the context of finite element simulations. To alleviate the expensive computational cost, we integrate the proposed L‐BFGS monolithic scheme with an adaptive mesh refinement (AMR) technique. We provide the algorithmic details about the proposed L‐BFGS monolithic scheme, especially about how to handle the hanging‐node constraints generated during the AMR process as extra linear constraints. Several two‐dimensional (2D) and three‐dimensional (3D) numerical examples are provided to demonstrate the capabilities of the proposed monolithic scheme, including the accuracy, the robustness, and the computational efficiency regarding the memory consumption and the wall‐clock time. Particularly, we emphasize the importance of the appropriately chosen convergence criteria for brute crack propagation. The proposed L‐BFGS phase‐field monolithic scheme combined with the AMR technique offers an accurate, robust, and efficient approach to model brittle crack propagation in both 2D and 3D problems. [ABSTRACT FROM AUTHOR]

ABSTRACT In this work, we improve the traditional adaptive mesh refinement (AMR) by combining it with the finite analytical method (FAM) to solve the multiphase flow in heterogeneous porous media numerically. The FAM can provide rather accurate internodal transmissibility, and it is employed to improve the accuracy of coarsening and refining processes in AMR. The high performance of the proposed AMR‐FAM is indicated through numerical tests for solving the two‐phase flow in 2D heterogeneous media. The numerical simulation results indicate that the proposed AMR‐FAM is more accurate than the traditional AMR‐FAM. Compared with the simulation in the original fine grids, the proposed AMR‐FAM can provide nearly the same results. Moreover, the computational cost in the AMR grids is only approximately one‐third of the cost in the original fine grids according to our numerical tests. [ABSTRACT FROM AUTHOR]

AMReX is a software framework for the development of block-structured mesh applications with adaptive mesh refinement (AMR). AMReX was initially developed and supported by the AMReX Co-Design Center as part of the U.S. DOE Exascale Computing Project (ECP), and is continuing to grow post-ECP. In addition to adding new functionality and performance improvements to the core AMReX framework, we have also developed a Python binding, pyAMReX, that provides a bridge between AMReX-based application codes and the data science ecosystem. pyAMReX provides zero-copy application GPU data access for AI/ML, in situ analysis and application coupling, and enables rapid, massively parallel prototyping. In this paper we review the overall functionality of AMReX and pyAMReX, focusing on new developments, new functionality, and optimizations of key operations. We also summarize capabilities of ECP projects that used AMReX and provide an overview of new, non-ECP applications. [ABSTRACT FROM AUTHOR]

Digital terrain models (DTMs) are created using elevation data collected in geological surveys using varied sampling techniques like airborne lidar and depth soundings. This often leads to large data sets with different distribution patterns, which may require smooth data approximations in irregular domains with complex boundaries. The thin plate spline (TPS) interpolates scattered data and produces visually pleasing surfaces, but it is too computationally expensive for large data sizes. The finite element thin plate spline (TPSFEM) possesses smoothing properties similar to those of the TPS and interpolates large data sets efficiently. This article investigated the performance of the TPSFEM and adaptive mesh refinement in irregular domains. Boundary conditions are critical for the accuracy of the solution in domains with arbitrary-shaped boundaries and were approximated using the TPS with a subset of sampled points. Numerical experiments were conducted on aerial, terrestrial, and bathymetric surveys. It was shown that the TPSFEM works well in square and irregular domains for modeling terrain surfaces and adaptive refinement significantly improves its efficiency. A comparison of the TPSFEM, TPS, and compactly supported radial basis functions indicates its competitiveness in terms of accuracy and cost. [ABSTRACT FROM AUTHOR]

The convergence analysis for least-squares finite element methods led to various adaptive mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteriori error estimator or an alternative explicit residual-based error estimator as well as a separate marking strategy based on the alternative error estimator and an optimal data approximation algorithm. This paper reviews and discusses available convergence results. In addition, all three strategies are investigated empirically for a set of benchmarks examples of second-order elliptic partial differential equations in two spatial dimensions. Particular interest is on the choice of the marking and refinement parameters and the approximation of the given data. The numerical experiments are reproducible using the author's software package octAFEM available on the platform Code Ocean. [ABSTRACT FROM AUTHOR]

Digital terrain models (DTMs) are created using elevation data collected in geological surveys using varied sampling techniques like airborne lidar and depth soundings. This often leads to large data sets with different distribution patterns, which may require smooth data approximations in irregular domains with complex boundaries. The thin plate spline (TPS) interpolates scattered data and produces visually pleasing surfaces, but it is too computationally expensive for large data sizes. The finite element thin plate spline (TPSFEM) possesses smoothing properties similar to those of the TPS and interpolates large data sets efficiently. This article investigated the performance of the TPSFEM and adaptive mesh refinement in irregular domains. Boundary conditions are critical for the accuracy of the solution in domains with arbitrary-shaped boundaries and were approximated using the TPS with a subset of sampled points. Numerical experiments were conducted on aerial, terrestrial, and bathymetric surveys. It was shown that the TPSFEM works well in square and irregular domains for modeling terrain surfaces and adaptive refinement significantly improves its efficiency. A comparison of the TPSFEM, TPS, and compactly supported radial basis functions indicates its competitiveness in terms of accuracy and cost.

Current tetrahedral adaptive mesh refinement techniques have primarily focused on the 3D reconstruction and analysis of simple stratified geological bodies. When applying adaptive mesh refinement to complex geological structures, such as those containing intersecting faults with discontinuous data, excessive refinement can easily lead to compromised mesh structures in the fault zones. To improve the accuracy of tetrahedral mesh models for such complex fault systems, this study proposed a tetrahedral adaptive mesh grading refinement method specifically for intersecting faults. Initially, the refinement range around the fault was adaptively determined based on a fault influence formula. Subdivision formulas were then developed for tetrahedrons and tetrahedral edges to grade both the tetrahedrons and their edges within the refinement range. To address the various scenarios that arose during tetrahedral mesh subdivision, the eight types of subdivisions were unified into three types by upgrading the edge treatments. Finally, new vertices were introduced, and existing vertices were reconnected to tetrahedrons within the refined area, adjusting mesh element sizes to generate a high-quality mesh model. A case study was conducted on a tetrahedral mesh model from an open-pit coal mine in Inner Mongolia. The mesh model was analyzed before and after refinement using a 3D mesh quality evaluation algorithm and FLAC3D simulation software. Results showed that the distortion value of the refined mesh model decreased from 0.3317 to 0.3061, indicating an improvement in mesh quality. Under the same parameters, the unrefined model exhibited a maximum displacement of 1.16 m with a stability coefficient of 1.27, while the refined model showed a maximum displacement of 1.29 m and a stability coefficient of 1.23. The displacement cloud map of the refined model was aligned with the fault, accurately reflecting the fault distribution and its impact on the slope. In contrast, the displacement cloud map of the unrefined model was misaligned with the fault center, demonstrating a less pronounced effect of the fault on the slope.

The lid-driven cavity flow problem stands as a widely recognized benchmark in fluid dynamics, serving to validate CFD algorithms. Despite its geometric simplicity, the lid-driven cavity flow problem exhibits a complex flow regime primarily characterized by the formation of vortices at the centre and corners of the square domain. This study evaluates the accuracy of the 2D velocity-driven adaptive mesh refinement (2D VDAMR) method in estimating vortex centres in a steady incompressible flow within a 2D square cavity. The VDAMR algorithm allows for an arbitrary number of finite mesh refinements. Increasing the number of successive mesh refinements results in more accurate outcomes. In this paper, the initial coarse uniform grid mesh was refined ten times for Reynolds numbers 100 ≤ R e ≤ 7500 . Results show that VDAMR accurately identifies vortex centres, with its findings closely aligning with benchmark data from six literature sources. [ABSTRACT FROM AUTHOR]

This document describes the reasoning and trade studies used to evaluate tools for constructing the aerodynamic lineload databases for the liftoff and transition phases of flight for the Space Launch System. Three computational fluid dynamics codes (USM3D, FUN3D, and Kestrel) were investigated with various turbulence models as well as detached eddy simulation variants for the launch vehicle in free air and in proximity to the tower. Decisions were made mostly based on results from brief developmental studies performed in response to specific, unforeseen challenges that were encountered in the analysis of a given configuration. The need to develop databases in a timely manner, as well as to accurately capture the expected leeward-wake flowfield characteristics, led to the selection of the Kestrel flow solver with its delayed detached eddy simulation method, the Spalart-Allmaras turbulence model, and the adaptive mesh refinement capability in the off-body Cartesian grid region. [ABSTRACT FROM AUTHOR]

Numerical simulation of high‐speed flows often needs a fine grid for capturing detailed structures of shock or contact wave, which makes high‐order discontinuous Galerkin methods (DGMs) extremely costly. In this work, a characteristic‐compression based adaptive mesh refinement (AMR, h‐adaptive) method is proposed for efficiently improving resolution of the high‐speed flows. In order to allocate computational resources to needed regions, a characteristic‐compression embedded shock wave indicator is developed on incompatible grids and employed as the criterion for AMR. This indicator applies the admissible jumps of eigenvalues to measure the local compression of homogeneous characteristic curves, and theoretically can capture regions of characteristic‐compression which contain structures of shock, contact waves and vortices. Numerical results show that the proposed h‐adaptive DGM is robust, efficient and high‐resolution, it can capture dissipative shock, contact waves of different strengths and vortices with low noise on a rather coarse grid, and can significantly improve resolution of these structures through mild increase of computational resources as compared with the residual‐based h‐adaptive method. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Mine Automation is the property of Industry & Mine Automation Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Transactions of Nanjing University of Aeronautics & Astronautics is the property of Editorial Department of Journal of Nanjing University of Aeronautics & Astronautics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We present an algorithm to solve the dispersive depth-averaged Serre--Green--Naghdi equations using patch-based adaptive mesh refinement. These equations require adding additional higher derivative terms to the nonlinear shallow water equations. This has been implemented as a new component of the open source GeoClaw software that is widely used for modeling tsunamis, storm surge, and related hazards, improving its accuracy on shorter wavelength phenomena. We use a formulation that requires solving an elliptic system of equations at each time step, making the method implicit. The adaptive algorithm allows different time steps on different refinement levels and solves the implicit equations level by level. Computational examples are presented to illustrate the stability and accuracy on a radially symmetric test case and two realistic tsunami modeling problems, including a hypothetical asteroid impact creating a short wavelength tsunami for which dispersive terms are necessary. [ABSTRACT FROM AUTHOR]

Summary: The fluid‐structure interaction is simulated using the boundary data immersion method. As the fluid‐structure interface is smeared in the smoothing region, deviations are incurred in fluid simulations. For compressible flow, high order difference schemes with more mesh cells for the stencils are usually employed to achieve high overall accuracy, but near interfaces it requires wider smoothing region of several mesh cells for computational stability and hence lowers its accuracy significantly. To address this issue, the proposed algorithm switches to lower order difference schemes near the interfaces and applies adaptive mesh refining there to compensate the accuracy loss. Implemented with Structured Adaptive Mesh Refinement Application Infrastructure (SAMRAI), the algorithm shows notable improvement in the overall accuracy and efficiency in cases such as channel flow and flow past a cylinder. The algorithm is used to simulate the shock wave past a fixed or free cylinder with Ma =2.67$$ =2.67 $$ and Re =1482$$ =1482 $$, which reveals the relaxation process and the temporal evolution of the drag coefficient, it goes through a valley and maintains at relatively high value for the fixed cylinder, while that of the free cylinder tends to decrease in fluctuation which is found to be caused by the interaction between the forward moving cylinder and vortexes in the unsteady wake. [ABSTRACT FROM AUTHOR]

Numerous studies of rotating detonation engines (RDEs) have noted the appearance of weaker secondary waves which travel with or counter to the primary wave system. These secondary waves can affect the speed, strength, multiplicity, and directional preference of the primary wave system, all of which have implications for engine performance and operability. As such, understanding the formation and stabilization of different wave modes is critical for developing practical RDE systems. To this end, the present work uses an adaptive mesh refinement framework to simulate two-dimensional unwrapped RDEs at high spatial resolution. Four injection configurations are considered, including a simplified continuous injection boundary, as well as three discrete injection setups with varying injector diameter and spacing. In the discrete injection cases, the effects of mass flow rate and near-wave grid resolution are also investigated. Continuous injection is found to produce a single wave, while discrete injection yields increasing numbers of co- and counter-propagating waves when the number of injectors or the reactant flow rate increases. The generation of secondary waves is linked to acoustic reflections associated with wave passage over the discrete injectors, as well as successive “micro-explosions” that occur when a reaction zone recouples to a shock wave traversing a reactant jet. These secondary waves can then coalesce in the presence of fresh reactants, providing a mechanism for new primary waves to form and the directional preference of the wave system to switch. The diameter and spacing of the injectors directly impact the sustained propagation of the primary waves, as well as the availability of reactants needed to form a strong counter-propagating wave system. The unsteadiness induced by the different injection schemes is manifested in conditional statistics for heat release and heat release rate, which show enhanced deflagrative combustion in discrete injection configurations.

In this work, numerical simulations are performed to predict two-phase annular flow of refrigerant R245fa inside a 3.4 mm diameter vertical channel. The VOF (Volume of Fluid) method implemented in an OpenFOAM solver is used to accurately track the vapor-liquid interface. A 2D axisymmetric domain is considered and the Adaptive Mesh Refinement (AMR) method is applied to the cells near the liquid/vapor interface. The Reynolds-Averaged Navier Stokes (RANS) equations are solved and the k-ω SST model is adopted for turbulence modelling in both the liquid and vapor phase. Simulations are used to calculate instantaneous and mean values of the liquid film thickness at mass flux G = 100 kg m-2 s-1 and vapor quality ranging between 0.2 and 0.85. Numerical results are compared against measurements of the liquid film thickness taken during vertical annular downflow. Previous works from the literature and the deviations observed between present numerical and experimental results suggest the need for turbulence damping at the vapor-liquid interface by adding a source term in the ω equation. The simulations show that a low value of the turbulence damping parameter (e.g. 1) causes the average liquid film thickness to increase by 25 %–52 % compared to the non-damped scenario. The interface presents large amplitude disturbance waves in the non-damped case, whereas small ripple waves are predicted when turbulence damping is introduced. Furthermore, the difference between the application of a symmetric and asymmetric treatment for the source term is analysed. From the comparison between experimental data and numerical simulations, it emerges that the value of the correct damping source term to be applied is strictly dependent on the vapor quality.

A new adaptive clipping-and-redistribution method is presented which provides bounds-preservation for multidimensional interpolation in the context of high-order finite-volume discretizations with adaptive mesh refinement (AMR). The underlying finite-volume method (FVM) for the computational fluid dynamics applications is fourth-order accurate for smooth solutions and utilizes AMR for computational efficiency in solving multiscale problems involving turbulence and combustion. High-order interpolation between different AMR levels is required. However, this operation often leads to numerical issues because combustion species must have physical bounds preserved. The present study overcomes two major challenges in the development of the high-order interpolation method. First, the method needs to be bound-preserving near extrema or discontinuities to prevent the emergence of unphysical oscillations while maintaining fourth-order accuracy in smooth flows. Second, the method needs to satisfy the conservation requirement in multiple dimensions, particularly in the context of curvilinear coordinate transformations. Additionally, the method is designed to be localized and computationally inexpensive. The new interpolation scheme is demonstrated by solving reacting flows, which are extremely sensitive to unphysical overshoots in conserved quantities. The test problems are shock-induced (Formula presented.) - (Formula presented.) combustion and a (Formula presented.) -air flame in a practical bluff-body combustor. Results show the method prevents new extrema near discontinuities while maintaining high-order accuracy in smooth regions. In particular, the method is extremely beneficial for combustion with stiff chemistry. With the proposed new method, even if flame fronts cross AMR interfaces or new grids are created in the vicinity of the flame, solution stability is retained.

Reacting flow simulations for combustion applications require extensive computing capabilities. Leveraging the AMReX library, the Pele suite of combustion simulation tools targets the largest supercomputers available and future exascale machines. We introduce PeleC, the compressible solver in the Pele suite, and detail its capabilities, including complex geometry representation, chemistry integration, and discretization. We present a comparison of development efforts using both OpenACC and AMReX’s C++ performance portability framework for execution on multiple GPU architectures. We discuss relevant details that have allowed PeleC to achieve high performance and scalability. PeleC’s performance characteristics are measured through relevant simulations on multiple supercomputers. The success of PeleC’s design for exascale is exhibited through demonstration of a 160 billion cell simulation and weak scaling onto 100% of Summit, an NVIDIA-based GPU supercomputer at Oak Ridge National Laboratory. Our results provide confidence that PeleC will enable future combustion science simulations with unprecedented fidelity.

Summary: The Oak Ridge Leadership Computing Facility (OLCF) has been preparing the nation's first exascale system, Frontier, for production and end users. Frontier is based on HPE Cray's new EX architecture and Slingshot interconnect and features 74 cabinets of optimized 3rd Gen AMD EPYC CPUs for HPC and AI and AMD Instinct 250X accelerators. As a part of this preparation, "real‐world" user codes have been selected to help assess the functionality, performance, and usability of the system. This article describes early experiences using the system in collaboration with the Hamburg Observatory for two selected codes, which have since been adopted in the OLCF test harness. Experiences discussed include efforts to resolve performance variability and per‐cycle slowdowns. Results are shown for a performance portable astrophysical magnetohydronamics code, AthenaPK, and a mini‐application stressing the core functionality of a performance portable block‐structured adaptive mesh refinement framework, Parthenon‐Hydro. These results show good scaling characteristics to the full system. At the largest scale, the Parthenon‐Hydro miniapp reaches a total of 1.7×1013 zone‐cycles/s on 9216 nodes (73,728 logical GPUs) at ≈92% weak scaling parallel efficiency (starting from a single node using a second‐order, finite‐volume method). [ABSTRACT FROM AUTHOR]

In this paper, a kind of immersed boundary method, the discretized force with ghost cell method, is introduced to study compressible flow. Meanwhile, an adaptive mesh refinement scheme and a wall treatment for turbulent flow are proposed. With the help of in-house code, the accuracy of the method is verified based on several classic tests. [ABSTRACT FROM AUTHOR]

We discuss refinement criteria for the Berger–Rigoutsos (block-based) refinement algorithm in our numerical relativity code GR-Athena++ in the context of binary black hole (BBH) merger simulations. We compare three different strategies: the 'box-in-box' approach, the 'sphere-in-sphere' approach and a local criterion for refinement based on the estimation of truncation error of the finite difference scheme. We extract and compare gravitational waveforms using the three different mesh refinement methods and compare their accuracy against a calibration waveform and demonstrate that the sphere-in-sphere approach provides the best strategy overall when considering computational cost and the waveform accuracy. Ultimately, we demonstrate the capability of each mesh refinement method in accurately simulating gravitational waves from BBH systems—a crucial aspect for their application in next-generation detectors. We quantify the mismatch achievable with the different strategies by extrapolating the gravitational wave mismatch to higher resolution. [ABSTRACT FROM AUTHOR]

As the need for handling complex geometries in computational fluid dynamics (CFD) grows, efficient and accurate mesh generation techniques become paramount. This study presents an adaptive mesh refinement (AMR) technology based on cell-based Cartesian grids, employing a distance-weighted least squares interpolation for finite difference discretization and utilizing immersed boundary methods for wall boundaries. This facilitates effective management of both transient and steady flow problems. Validation through supersonic flow over a forward-facing step, subsonic flow around a high Reynolds number NHLP airfoil, and supersonic flow past a sphere demonstrated AMR's efficacy in capturing essential flow characteristics while wisely refining and coarsening meshes, thus optimizing resource utilization without compromising accuracy. Importantly, AMR simplified the capture of complex flows, obviating manual mesh densification and significantly improving the efficiency and reliability of CFD simulations. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Chongqing University of Technology (Natural Science) is the property of Chongqing University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The JPEG algorithm is a defacto standard for image compression. We investigate whether adaptive mesh refinement can be used to optimize the compression ratio and propose a new adaptive image compression algorithm. We prove that it produces a quasi-optimal subdivision grid for a given error norm with high probability. This subdivision can be stored with very little overhead and thus leads to an efficient compression algorithm. We demonstrate experimentally, that the new algorithm can achieve better compression ratios than standard JPEG compression with no visible loss of quality on many images. The mathematical core of this work shows that Binev's optimal tree approximation algorithm is applicable to image compression with high probability, when we assume small additive Gaussian noise on the pixels of the image. [ABSTRACT FROM AUTHOR]

This paper deals with the efficient implementation of the finite element method with continuous piecewise linear functions (P1-FEM) in R d ( d ∈ N ). Although at present there does not seem to be a very high practical demand for finite element methods that use higher-dimensional simplicial partitions, there are some advantages in studying the efficient implementation of the method independent of the dimension. For instance, it provides additional insights into necessary data structures and the complexity of implementations. Throughout, the focus is on an efficient realization using Matlab built-in functions and vectorization. The fast and vectorized Matlab function can be easily implemented in many other vector languages and is provided in Julia, too. The complete implementation of the adaptive FEM is given, including assembling stiffness matrix, building load vector, error estimation, and adaptive mesh-refinement. Numerical experiments underline the efficiency of our freely available code which is observed to be of a slightly more than linear complexity with respect to the number of elements when memory limits are not exceeded. [ABSTRACT FROM AUTHOR]

This paper presents a feature-based adaptive mesh refinement (AMR) method for Large Eddy Simulation of propagating deflagrations, using massive-scale parallel unstructured AMR libraries. The proposed method, named turbulent flame propagation-AMR (TFP-AMR), is able to track the transient dynamics of both the turbulent flame and the vortical structures in the flow. To handle the interaction of the turbulent flame brush with the vortical structures of the flow, a vortex selection criterion is derived from flame/vortex interaction theory. The method is built with the general intent to prioritise conservatively estimated parameters, rather than to rely on user-dependent parameters. In particular, a specific mesh adaptation triggering strategy is constructed, adapted to the strongly transient physics found in deflagrations, to guarantee that the physics of interest consistently reside within a region of high accuracy throughout the transient process. The methodology is applied and validated on several elementary cases representing fundamental bricks of the full problem: (1) a laminar flame propagation, (2) the advection of a pair of non-reacting vortices, (3) a flame/vortex interaction. The method is then applied to three different configurations of a three-dimensional complex explosion scenario in an obstructed chamber. All cases demonstrate the TFP-AMR capability to recover accurate results at reduced computational cost without requiring any ad hoc tuning of the AMR method or its parameters, thus demonstrating its genericity and robustness. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel staggered least squares method for elliptic equations on polygonal meshes. Our new method can be flexibly applied to rough grids and allows hanging nodes, which is of particular interest in practical applications. Moreover, it offers the advantage of not having to deal with inf-sup conditions and yielding positive definite discrete problems. Optimal a priori error estimates in energy norm are derived. In addition, a superconvergent estimates in energy norm are also developed by employing variational error expansion. The main difficulty involved here is to show the $ L^2 $ norm error estimates for the potential variable, where duality argument and the superconvergent estimates are the key ingredients. The single valued flux over the outer boundary of the dual partition enables us to construct a locally conservative flux. Numerical experiments confirm the theoretical findings and the performance of the adaptive mesh refinement guided by the least squares functional estimator are also displayed.

Detonation-based engines have a higher thermal efficiency than deflagration-based engines and are therefore widely studied. In this study, the effect of initiation conditions on the detonation wave propagation and the performance of a pulse detonation engine, one type of detonationbased engine, was numerically investigated. Hydrogen-oxygen mixtures with equivalence ratios of φ=0.8, 1.0, and 1.2 were defined as initiation conditions with constant pressure and temperature. The numerical simulations were conducted using the transient explicit density-based solver in the ANSYS Fluent commercial software. The adaptability of the adaptive mesh refinement method in detonation-based engines was explored in the numerical studies, reducing the average total cell count by a factor of 2.617, and obtaining consistent results according to validation studies. The adaptive mesh refinement method was also used in numerical simulations where different equivalence ratios were defined. It was determined that an increase in the equivalence ratio resulted in an increase in the detonation wave velocity. Also, an increase in thrust distribution at the nozzle exit was observed before the blowdown stage, and the calculated thrust values for φ=0.8, φ=1.0, and φ=1.2 were 248.28 N, 264.5 N, and 270.83 N, respectively.

In this paper, we propose a novel staggered least squares method for elliptic equations on polygonal meshes. Our new method can be flexibly applied to rough grids and allows hanging nodes, which is of particular interest in practical applications. Moreover, it offers the advantage of not having to deal with inf-sup conditions and yielding positive definite discrete problems. Optimal a priori error estimates in energy norm are derived. In addition, a superconvergent estimates in energy norm are also developed by employing variational error expansion. The main difficulty involved here is to show the L 2 norm error estimates for the potential variable, where duality argument and the superconvergent estimates are the key ingredients. The single valued flux over the outer boundary of the dual partition enables us to construct a locally conservative flux. Numerical experiments confirm the theoretical findings and the performance of the adaptive mesh refinement guided by the least squares functional estimator are also displayed. In this paper, we propose a novel staggered least squares method for elliptic equations on polygonal meshes. Our new method can be flexibly applied to rough grids and allows hanging nodes, which is of particular interest in practical applications. Moreover, it offers the advantage of not having to deal with inf-sup conditions and yielding positive definite discrete problems. Optimal a priori error estimates in energy norm are derived. In addition, a superconvergent estimates in energy norm are also developed by employing variational error expansion. The main difficulty involved here is to show the norm error estimates for the potential variable, where duality argument and the superconvergent estimates are the key ingredients. The single valued flux over the outer boundary of the dual partition enables us to construct a locally conservative flux. Numerical experiments confirm the theoretical findings and the performance of the adaptive mesh refinement guided by the least squares functional estimator are also displayed. [ABSTRACT FROM AUTHOR]

Detonation-based engines have a higher thermal efficiency than deflagration-based engines and are therefore widely studied. In this study, the effect of initiation conditions on the detonation wave propagation and the performance of a pulse detonation engine, one type of detonationbased engine, was numerically investigated. Hydrogen-oxygen mixtures with equivalence ratios of φ=0.8, 1.0, and 1.2 were defined as initiation conditions with constant pressure and temperature. The numerical simulations were conducted using the transient explicit density-based solver in the ANSYS Fluent commercial software. The adaptability of the adaptive mesh refinement method in detonation-based engines was explored in the numerical studies, reducing the average total cell count by a factor of 2.617, and obtaining consistent results according to validation studies. The adaptive mesh refinement method was also used in numerical simulations where different equivalence ratios were defined. It was determined that an increase in the equivalence ratio resulted in an increase in the detonation wave velocity. Also, an increase in thrust distribution at the nozzle exit was observed before the blowdown stage, and the calculated thrust values for φ=0.8, φ=1.0, and φ=1.2 were 248.28 N, 264.5 N, and 270.83 N, respectively. [ABSTRACT FROM AUTHOR]

A novel formulation of the vortex particle method (VPM) is developed for large-eddy simulation (LES) in a meshless scheme that is numerically stable. A new set of VPM governing equations are derived from the LES-filtered Navier-Stokes equations. The new equations reinforce the conservation of angular momentum by resizing vortex elements subject to vortex stretching. In addition to the VPM reformulation, a new anisotropic dynamic model of subfilter-scale (SFS) vortex stretching is developed. This SFS model is well suited for turbulent flows with coherent vortical structures, where the predominant cascade mechanism is vortex stretching. The mean and fluctuating components of turbulent flow and Reynolds stresses are validated through the simulation of a turbulent round jet. The computational efficiency of the scheme is showcased in the simulation of an aircraft rotor in hover, showing our meshless LES to be 100 times faster than a mesh-based LES with similar fidelity. The implementation of our meshless LES scheme is released as open-source software, called FLOWVPM. [ABSTRACT FROM AUTHOR]

To understand the actual operation of detonation engines, it is of great significance to simulate the detonation characteristics after being affected by unsteady supersonic flow. Adaptive mesh refinement method and single-step chemical reaction model were used for simulation calculations. The Navier–Stokes equations and hybrid sixth-order weighted essentially non-oscillatory centered difference scheme was adopted in this study. Three different amplitudes of disturbances (0.1, 0.2, and 0.3) and two hot jet injection times were analyzed. The results showed that a moderate disturbance can improve the stability of detonation wave under the ideal hot jet injection time. It allows detonation wave to stay in the combustion chamber for a longer time, which is beneficial for the release of thrust performance. Although the stability of detonation wave is significantly different between the low and high-amplitude disturbances, the residence time of detonation wave is close to the steady flow case under ideal initiation conditions. When the ignition time is insufficient, successful detonation can occur with low and medium-amplitude disturbances. However, the ignition delay was significantly prolonged with medium-amplitude disturbance. There was also greater instability, which is detrimental to the thrust release. When the inflow has a high-amplitude disturbance, the detonation wave fails to ignite due to insufficient energy. • This article considers the influence of unsteady inflow characteristics on detonation. • The presence of disturbances can delay the initiation of detonation waves. • Proper disturbance can enhance the stability of detonation waves under the ideal initiation conditions. • The disturbance causes a significant increase in pressure behind the wave under the non-ideal initiation conditions. [ABSTRACT FROM AUTHOR]

When a submarine encounters an emergency situation, it should take emergency-surfacing actions by moving upward with a large angle of attack in the vertical plane. Previous research has often neglected the effect of vertical plane motion on the lateral force (Fy), rolling moment (Mx), and yawing moment (Mz). To examine the flow characteristics of submarines at high angles of attack on the vertical plane, the SST-DDES method is adopted in conjunction with adaptive mesh refinement (AMR) technology, and the new Omega vortex detection method is employed as the AMR criterion for numerical calculations. The obtained results are then appropriately verified by conducting water tank experiments, and the effects of different angles of attack and heel angles on Fy, Mx, and Mz are methodically examined. The results reveal that, in the flow around the vertical plane of a submarine, the influence of Fy and Mz cannot be ignored. In addition, when the vertical velocity of the hull is greater than 0.6 m/s, the influence of Mx cannot be overlooked either. When the angle of attack on the vertical plane of the submarine is greater than 25°, the effects of Fy, Mx, and Mz cannot be neglected, and the effect of Mz is particularly prominent, with its amplitude close to or greater than the average value of the pitch moment (My). The obtained results reveal that the presence of the heel angle (θ) intensifies the forces on the hull for Fy, Mx, and Mz, and the forces caused by the vertical velocity at Fy, Mx, and Mz cannot be neglected. These findings can provide a mechanical analysis basis for the analysis of nonlinear motion phenomena during submarine surfacing. [ABSTRACT FROM AUTHOR]

In this paper, we locally construct a conservative flux for finite element solutions of elliptic interface problems with discontinuous coefficients. Since the Discontinuous Galerkin method has built-in conservative flux, we consider in this paper the conforming finite element method and a special type of nonconforming method with arbitrary orders. We also perform our analysis based on Nitsche’s method, which imposes the Dirichlet boundary condition weakly. The construction method is derived based on a mixed problem with one solution coinciding with the finite element solution and with the other solution being naturally used to obtain a conservative flux. We then apply the recovered flux to the a posteriori error estimation and prove the robust reliability and efficiency for conforming elements, under the assumption that the diffusion coefficient is quasi-monotone. Numerical experiments are provided to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Relativistic jets are major sources of radio-frequency radiation in the Universe. Their study is complicated by the fact that the relativistic gas flows interact with interstellar space, with the formation of complex flows that are smaller than the jets but can affect the evolution of the entire jets. Adaptive grids have traditionally been used to simulate such multi-scale phenomena with high spatial resolution in the zone of complex jets and low resolution to reproduce the unperturbed gas flows. In this paper, a Patch-Block-Structured Adaptive-Mesh-Refinement technique is proposed for modeling multi-scale relativistic jets. To use this technique, mathematical tools for numerically solving the equations of special relativistic hydrodynamics are updated in a particular manner. The approach is applied to the evolution of a jet in interstellar space. [ABSTRACT FROM AUTHOR]

Based on the time-fractional Black-Scholes pricing model, the evaluation of an American-style option problem can be formulated as a free boundary problem. It is equivalent to a time-fractional parabolic variational inequality. Due to the time-fractional derivative involved in the problem, increasing the computational cost for large final times has been expected in the numerical solution for this problem. In this paper, we want to propose a new adaptive numerical method to solve this problem accurately, with low computational cost. The presented method is based on interpolating wavelets family. An adaptive scheme in time discretization with an adaptive wavelet collocation method for space discretization has been used for the given problem. We show that combination of interpolating wavelet basis and finite difference method, makes an accurate structure to design an optimal adaptive mesh for this problem. The presented computational mesh by this method can prevent growing of computational cost by time. The performance of the proposed method has been tested by means of some numerical experiments. We show that, in comparison with the full grid algorithms, the presented adaptive algorithm can capture the priori unknown free boundary and is able to find the value of American put option price with high accuracy and reasonable CPU time. [ABSTRACT FROM AUTHOR]

Aerodynamics is one of the main areas of development in vehicle design. One of the most efficient ways of testing the aerodynamic design of a vehicle is to use Computational Fluid Dynamics (CFD), which allows for faster and more accurate aerodynamic simulations, which in turn helps increase the fuel economy and electric vehicle's range. Resource optimization is one of the most important aspects of CFD, and one of its main aspects is the spatial discretization of the fluid domain. This study discusses the use of Adaptive Mesh Refinement (AMR) for the aerodynamic design of private vehicles. This paper compares the results obtained with the use of AMR based on different fluid dynamic criteria for the DrivAer model and correlates the results with experimental data and computational results provided by various authors in previous publications. Four different optimization functions are defined and compared. The results for the drag coefficient, pressure coefficient, and total pressure wake have been correlated, showing great accuracy. This study has proven that the use of AMR highly optimizes computational resources by optimizing the mesh in the desired areas, thereby reducing the number of cells needed elsewhere. The use of these criteria has proven useful for drag coefficient prediction simulations because these criteria make use of the AMR to optimize the wake region.

Hot cylinders within the cavity can find diverse thermal applications, ranging from electronic devices and heat exchangers to solar systems, nuclear reactors, and the thermal design of passive cooling systems. Consequently, considering the use of phase change materials (PCM) close to hot cylinders emerges as a viable method for both cooling and storing thermal energy. In this work, two hot cylinders are arranged vertically and horizontally in the nano-enhanced phase change material (NePCM) trapezoidal enclosure with varying angles. The novelty of the current study lies in the fact that no prior research has explored the impact of hot cylinders arrangement on the melting process of a NePCM within a trapezoidal cavity, considering various inclination angles. The fixed grid, adaptive mesh refinement, and enthalpy-porosity method are used to model the melting flow. The numerical results indicate that the trapezoidal enclosure with vertically arranged hot cylinders exhibits better thermal performance than the other configuration. It is also found that the full melting time for both arrangements is minimum when the angle of the trapezoidal enclosure is γ=+40°. The reduction in full melting times for the vertical and horizontal arrangements of this angle are 25.3% and 29.6%, respectively, compared to the trapezoidal enclosure with γ=0.0°. Moreover, the NePCM with the graphite nanoplatelets (GNPs) of φ=1.0% has the shortest melting time for 0.0%≤φ≤3.0%. As future research, further exploration into the complexities of non-Newtonian NePCM flow can be pursued. Additionally, there is potential to explore modifying the cylinders' geometry into elliptical forms, encompassing a range of aspect ratios.

We address the numerical solution of the Dirichlet problem for the two-dimensional elliptic Monge–Ampère equation using a least-squares/relaxation approach. The relaxation algorithm allows the decoupling of the differential operators from the nonlinearities of the equation, within a splitting approach. The approximation relies on mixed low order finite element methods with regularization techniques. In order to account for data singularities in non-smooth cases, we introduce an adaptive mesh refinement technique. The error indicator is based an independent formulation of the Monge–Ampère equation under divergence form, which allows to explicit a residual term. We show that the error is bounded from above by an a posteriori error indicator plus an extra term that remains to be estimated. This indicator is then used within the existing least-squares framework. The results of numerical experiments support the convergence of our relaxation method to a convex classical solution, if such a solution exists. Otherwise they support convergence to a generalized solution in a least-squares sense. Adaptive mesh refinement proves to be efficient, robust, and accurate to tackle test cases with singularities.

The lid-driven cavity flow problem stands as a widely recognized benchmark in fluid dynamics, serving to validate CFD algorithms. Despite its geometric simplicity, the lid-driven cavity flow problem exhibits a complex flow regime primarily characterized by the formation of vortices at the centre and corners of the square domain. This study evaluates the accuracy of the 2D velocity-driven adaptive mesh refinement (2D VDAMR) method in estimating vortex centres in a steady incompressible flow within a 2D square cavity. The VDAMR algorithm allows for an arbitrary number of finite mesh refinements. Increasing the number of successive mesh refinements results in more accurate outcomes. In this paper, the initial coarse uniform grid mesh was refined ten times for Reynolds numbers 100≤Re≤7500. Results show that VDAMR accurately identifies vortex centres, with its findings closely aligning with benchmark data from six literature sources.

We introduce several spatially adaptive model order reduction approaches tailored to non-coercive elliptic boundary value problems, specifically, parametric-in-frequency Helmholtz problems. The offline information is computed by means of adaptive finite elements, so that each snapshot lives in a different discrete space that resolves the local singularities of the analytical solution and is adjusted to the considered frequency value. A rational surrogate is then assembled adopting either a least-squares or an interpolatory approach, yielding a function-valued version of the the standard rational interpolation method ($ \mathcal{V} $-SRI) and the minimal rational interpolation method (MRI). In the context of building an approximation for linear or quadratic functionals of the Helmholtz solution, we perform several numerical experiments to compare the proposed methodologies. Our simulations show that, for interior resonant problems (whose singularities are encoded by poles on the real axis), the spatially adaptive $ \mathcal{V} $-SRI and MRI work comparably well. Instead, when dealing with exterior scattering problems, whose frequency response is mostly smooth, the $ \mathcal{V} $-SRI method seems to be the best-performing one.

Wavelet-based grid resolution adaptation driven by the ‘multiresolution analysis’ (MRA) of the Haar wavelet (HW) allows to devise an adaptive first-order finite volume (FV1) model (HWFV1) that can readily preserve the modelling fidelity of its reference uniform-grid FV1 counterpart. However, the MRA entails an enormous computational effort as it involves ‘encoding’ (coarsening), ‘decoding’ (refining), analysing and traversing modelled data across a deep hierarchy of nested, uniform grids. GPU-parallelisation of the MRA is needed to handle its computational effort, but its algorithmic structure (1) hinders coalesced memory access on the GPU and (2) involves an inherently sequential tree traversal problem. This work redesigns the algorithmic structure of the MRA in order to parallelise it on the GPU, addressing (1) by applying Z-order space-filling curves and (2) by adopting a parallel tree traversal algorithm. This results in a GPU-parallelised HWFV1 model (GPU-HWFV1). GPU-HWFV1 is verified against its CPU predecessor (CPU-HWFV1) and its GPU-parallelised reference uniform-grid counterpart (GPU-FV1) over five shallow water flow test cases. GPU-HWFV1 preserves the modelling fidelity of GPU-FV1 while being up to 30 times faster. Compared to CPU-HWFV1, it is up to 200 times faster, suggesting that the GPU-parallelised MRA could be used to speed up other FV1 models. HIGHLIGHTS Wavelet-based grid adaptation is parallelised on the GPU via a Z-order space-filling curve and a parallel tree traversal algorithm.; An adaptive Haar wavelet first-order finite volume shallow water model running on the GPU is developed (GPU-HWFV1).; GPU-HWFV1 is 20–300 times faster than its single-core serial CPU version 4.; GPU-HWFV1 is 1.3–30 times faster than its GPU-parallelised reference uniform-grid counterpart.;

In tsunami inundations or slope disasters of heavy rain, a lot of floating debris or driftwood logs are included in the flows. The damage to structures from solid body impacts is more severe than the damage from the water pressure. In order to study free-surface flows that include floating debris, developing a high-accurate simulation code of free-surface flows with high performance for large-scale computations is desired. We propose the single-phase free-surface flow model based on the cumulant lattice Boltzmann method coupled with a particle-based rigid body simulation. The discrete element method calculates the contact interaction between solids. An octree-based AMR (Adaptive Mesh Refinement) method is introduced to improve computational accuracy and time-to-solution. High-resolution grids are assigned near the free surfaces and solid boundaries. We conducted two kinds of tsunami flow experiments in the 15 and 70m water tanks at Hachinohe Institute of Technology and Kobe University to validate the accuracy of the proposed model. The simulation results have shown good agreement with the experiments for the drifting speed, the number of trapped wood pieces, and the stacked angles. [ABSTRACT FROM AUTHOR]