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In this paper, a novel parallel algorithm is proposed to solve the problems of heavy computation and long simulation time in the field of compressible flows. In this algorithm, a third-order upwind scheme and a fourth-order central difference scheme are employed, with a third-order Runge-Kutta method for time stepping. Considering the powerful floating-point computing ability of the Graphics Processing Unit (GPU), this paper establishes the algorithm on the basis of GPU. Moreover, the direct numerical simulation method is adopted in this algorithm to improve the solution accuracy of the simulation results. To further enhance the efficiency of the algorithm, several optimization strategies are explored in the design of the algorithm as well. Both accuracy and feasibility of the algorithm are verified by a classical two-dimensional example. Compared with solving this example on the Central Processing Unit platform, the experimental results demonstrate that the maximum speedup ratio achieved by our approach is 18.03 times. [ABSTRACT FROM AUTHOR]

In this paper, we propose a modification of an acoustic-transport operator splitting Lagrange-projection method for simulating compressible flows with gravity. The original method involves two steps that respectively account for acoustic and transport effects. Our work proposes a simple modification of the transport step, and the resulting modified scheme turns out to be a flux-splitting method. This new numerical method is less computationally expensive in the low-Mach regime, more memory efficient, and easier to implement than the original one. We prove stability properties for this new scheme by showing that under classical CFL conditions, the method is positivity preserving for mass, energy and entropy satisfying. The flexible flux-splitting structure of the method enables straightforward extensions of the method to multi-dimensional problems (with respect to space) and high-order discretizations that are presented in this work. We also propose an interpretation of the flux-splitting solver as a relaxation approximation. Both the stability and the accuracy of the new method are tested against one-dimensional and two-dimensional numerical experiments that involve highly compressible flows and low-Mach regimes. • The all-regime acoustic/transport splitting solver proposed in [16] can be modified into a flux-splitting, one-step version. • The resulting method is less computationally expensive, more memory efficient, and easier to implement than the original one. • Stability properties are derived by interpreting the scheme as a convex combination of the advection/pressure steps. • This recasting allows an easy high-order extension as the new method is a standard flux-based solver. • Following the lines of [32] , we equip our scheme with the well-balanced property for gravity source terms. [ABSTRACT FROM AUTHOR]

In this paper, we propose a numerical method f or solving weakly compressible fluid flow based on a dynamical low-rank pro jector splitting. The low-rank splitting scheme is applied to the Boltzmann equation with BGK collision term, which results in a set of constant-coefficient advection equations. This procedure is numerically efficient as a small rank is sufficient to obtain the relevant dynamics (described by the Navier--Stokes equations). The resulting method can be combined with a range of different discretization strategies; in particular, it is possible to implement spectral and semi-Lagrangian methods, which allows us to design numerical schemes that are not encumbered by the sonic CFL condition. [ABSTRACT FROM AUTHOR]

In this paper, we present a fourth-order in space and time block-structured adaptive mesh refinement algorithm for the compressible multicomponent reacting Navier–Stokes equations. The algorithm uses a finite-volume approach that incorporates a fourth-order discretisation of the convective terms. The time-stepping algorithm is based on a multi-level spectral deferred corrections method that enables explicit treatment of advection and diffusion coupled with an implicit treatment of reactions. The temporal scheme is embedded in a block-structured adaptive mesh refinement algorithm that includes subcycling in time with spectral deferred correction sweeps applied on levels. Here we present the details of the multi-level scheme paying particular attention to the treatment of coarse–fine boundaries required to maintain fourth-order accuracy in time. We then demonstrate the convergence properties of the algorithm on several test cases including both non-reacting and reacting flows. Finally we present simulations of a vitiated dimethyl ether jet in 2D and a turbulent hydrogen jet in 3D, both with detailed kinetics and transport. [ABSTRACT FROM AUTHOR]

This paper introduces alternating-direction implicit (ADI) solvers of higher order of time-accuracy (orders two to six) for the compressible Navier–Stokes equations in two- and three-dimensional curvilinear domains. The higher-order accuracy in time results from 1) An application of the backward differentiation formulae time-stepping algorithm (BDF) in conjunction with 2) A BDF-like extrapolation technique for certain components of the nonlinear terms (which makes use of nonlinear solves unnecessary), as well as 3) A novel application of the Douglas–Gunn splitting (which greatly facilitates handling of boundary conditions while preserving higher-order accuracy in time). As suggested by our theoretical analysis of the algorithms for a variety of special cases, an extensive set of numerical experiments clearly indicate that all of the BDF-based ADI algorithms proposed in this paper are “quasi-unconditionally stable” in the following sense: each algorithm is stable for all couples ( h , Δ t ) of spatial and temporal mesh sizes in a problem-dependent rectangular neighborhood of the form ( 0 , M h ) × ( 0 , M t ) . In other words, for each fixed value of Δ t below a certain threshold, the Navier–Stokes solvers presented in this paper are stable for arbitrarily small spatial mesh-sizes. The second-order formulation has further been rigorously shown to be unconditionally stable for linear hyperbolic and parabolic equations in two-dimensional space. Although implicit ADI solvers for the Navier–Stokes equations with nominal second-order of temporal accuracy have been proposed in the past, the algorithms presented in this paper are the first ADI-based Navier–Stokes solvers for which second-order or better accuracy has been verified in practice under non-trivial (non-periodic) boundary conditions. [ABSTRACT FROM AUTHOR]

The work of this paper represents the first stage of a whole modeling and computational solution procedure for an on-going research on agricultural fires at the laboratory of environmental research, Assiut University. The paper presents an accurate and efficient semi-implicit pressure-based algorithm developed for solving numerically the conservation equations governing weakly compressible single-fluid flows. The algorithm uses a finite-volume technique applied to structured non-orthogonal multi - block curvilinear meshes with co-located grid arrangement. An in-house CFD code has been developed to implement the numerical solution of the present algorithm. The code is an integrated one consisting of the main elements, the pre-processor, the solver and the post-processor. This in-house CFD code undergoes a standard verification and validation process using a variety of standard test cases covering broad range of CFD applications. The results of the present code for all test cases are in good agreement with those of the well-established reference CFD codes. This insures the present code verification and validation. [ABSTRACT FROM AUTHOR]

• CWENO, MUSCL and 1st-order upwind schemes combined in one framework. • Cascade adaptive solution admissibility criteria for MOOD technique. • The MOOD augmented methods further fortifies high-order methods. • Applied to 2D and 3D compressible multicomponent flow problems. In this paper the relaxed, high-order, Multidimensional Optimal Order Detection (MOOD) framework is extended to the simulation of compressible multicomponent flows on unstructured meshes. The diffuse interface methods (DIM) paradigm is used that employs a five-equation model. The implementation is performed in the open-source high-order unstructured compressible flow solver UCNS3D. The high-order CWENO spatial discretisation is selected due to its reduced computational footprint and improved non-oscillatory behaviour compared to the original WENO variant. Fortifying the CWENO method with the relaxed MOOD technique has been necessary to further improve the robustness of the CWENO method. A series of challenging 2-D and 3-D compressible multicomponent flow problems have been investigated, such as the interaction of a shock with a helium bubble, and a water droplet, and the shock-induced collapse of 2-D and 3-D bubbles arrays. Such problems are generally very stiff due to the strong gradients present, and it has been possible to tackle them using the extended MOOD-CWENO numerical framework. [ABSTRACT FROM AUTHOR]

This paper reports on the SIMPLE-like solution algorithm that significantly improves velocity-pressure coupling, leading to the accelerated convergence. The algorithm is applicable to both incompressible and compressible flows. It is implemented within the framework of a cell centered finite volume method using colocated storage of flow variables on unstructured grids. The convergence acceleration is an outcome of the novel treatment of the pressure correction equation that accounts for two commonly neglected terms appearing in a general pressure correction equation. These terms, namely, the neighbor and nonorthogonal corrections, represent velocity corrections from neighboring cells and the cell-face pressure correction gradient associated with the grid nonorthogonality, respectively. Reminiscent of the PISO method, both neighbor and nonorthogonal corrections are taken into account by performing two or more correction steps. However, the full inclusion of neighbor velocity corrections can prevent the solution convergence. Following an analogy between time marching and a steady-state iterative approach, this problem has been resolved by introducing a pseudounsteady term into discretized velocity correction equations. Using this term, the contribution of neighbor corrections is underrelaxed, enabling a satisfactory convergence rate. The algorithm is applied to several benchmark test cases, covering laminar and turbulent, as well as incompressible and compressible, flows. For all test cases, the convergence rate can be significantly improved by performing two or more pressure correction steps. An optimal number of pressure corrections exists for which a meaningful reduction of computing time is possible. [ABSTRACT FROM AUTHOR]

This paper is concerned with a comparison of two methods of treating solid wall boundaries in the weakly compressible (SPH) method. They have been chosen because of their wide use in simulations. These methods are the boundary force particles of Monaghan and Kajtar [24] and the use of layers of fixed boundary particles. The latter was first introduced by Morris et al. [26] but has since been improved by Adami et al. [1] whose algorithm involves interpolating the pressure and velocity from the actual fluid to the boundary particles. For each method, we study the effect of the density diffusive terms proposed by Molteni and Colagrossi [19] and modified by Antuono et al. [3] . We test the methods by a series of simulations commencing with the time-dependent spin-down of fluid within a cylinder and the behaviour of fluid in a box subjected to constant acceleration at an angle to the walls of the box, and concluding with a dam break over a triangular obstacle. In the first two cases the results from the two methods can be compared to analytical solutions while, in the latter case, they can be compared with experiments and other methods. These results show that the method of Adami et al. together with density diffusion is in very satisfactory agreement with the experimental results and is, overall, the best of the methods discussed here. [ABSTRACT FROM AUTHOR]

This paper deals with the development and application of a two-dimensional weakly compressible Smoothed Particle Hydrodynamics (SPH) model to study plane jets propagating into still fluid tanks and current flows. These flow processes occurring in different water bodies are here treated through an appropriate algorithm to model inlet/outlet boundary conditions which are defined by different sets of particles. SPH equations of fluid mechanics including viscous and interface stabilization terms are adopted to determine the flow field induced by the fluid interaction. Flow phenomena induced by jet injection in a water body occur in natural and anthropic environments such as pollutant discharge into reservoirs, rivers and coasts, or in several engineering applications such as marine outfalls. Three test cases with different initial configurations are simulated: injection of a jet at the top and at the bottom of a water tank, and upstream of a channel flow (coflow jet). The proposed SPH model is validated both near the jet nozzle and far from it, comparing the obtained jet trajectories, widths and velocities with other numerical approaches, laboratory experiments and analytical solutions. [ABSTRACT FROM AUTHOR]

This paper studies the effect of compressibility on the linear stability of a two-dimensional lid-driven cavity flow in the subsonic regime. The base flow is generated by high fidelity direct numerical simulation and a biglobal mode instability analysis is carried out by a matrix forming approach. The eigenvalue problem is discretized by high-order finite differences and Arnoldi algorithm is used to reduce the size of the problem. The solution procedure uses sparse matrix techniques. Influence of Mach number on the modes known from incompressible calculations is presented, showing that compressibility has a stabilizing effect. New modes that appear only for compressible flows are presented and their relationship with duct acoustics is investigated. [ABSTRACT FROM AUTHOR]

This paper investigates a very simple method to numerically approximate the solution of the multi-dimensional Riemann problem for gas dynamics, using the literal extension of the Toro Vazquez-Harten Lax Leer (TV-HLL) scheme as its basis. Indeed, the present scheme is obtained by following the Toro–Vazquez splitting, and using the HLL algorithm with modified wave speeds for the pressure system. An essential feature of the TV-HLL scheme is its simplicity and its accuracy in computing multi-dimensional flows. The proposed scheme is carefully designed to simplify its eventual numerical implementation. It has been applied to numerical tests and its performances are demonstrated for some two-dimensional and three-dimensional test problems. [ABSTRACT FROM AUTHOR]

Usually, the temperature dependence of specific heats is neglected or the specific heats are frozen in interface computations for compressible two-material flows. In this paper, we present a practical interface treatment to faithfully capture the effect of high temperature on interface evolutions. A general technique for solving the Riemann problem equipped with a wide variety of equations of state (EOS) is established. In a unified framework for computing the interfacial states, it provides a convenient way to deal with the thermally perfect gas (PG) that considers the effect of temperature on specific heats. The algorithm of the complete and exact solution to Riemann problem with thermally PG is also designed in detail. Based on this technique, the modified ghost fluid method with an approximate Riemann solver is further extended to handle the interface of two-material flows involving thermally PG with chemical reactions. Several typical problems are selected to validate and test the present algorithm for the interaction between the thermally PG and other gases or liquids. The results indicate that the present algorithm enables an effective implementation for simulating various two-material multi-species flows with different types of EOS. As temperature increases, the behavior of the interfacial flows under the assumption of thermally PG EOS gradually differs from that under the assumption of calorically PG EOS. • Unified framework for simulating two-material multi-species flows. • Exact and approximate Riemann solvers for thermally perfect gases. • Modified ghost fluid method for high-temperature effects with chemical reactions. • Comparison of thermally/calorically perfect gases. [ABSTRACT FROM AUTHOR]