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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]

Purpose: To present the detailed implementation processes of the IDEAL algorithm for two-dimensional compressible flows based on Delaunay triangular mesh, and compare the performance of the SIMPLE and IDEAL algorithms for solving compressible problems. What's more, the implementation processes of Delaunay mesh generation and derivation of the pressure correction equation are also introduced. Design/methodology/approach: Programming completely in C++. Findings: Five compressible examples are used to test the SIMPLE and IDEAL algorithms, and the comparison with measurement data shows good agreement. The IDEAL algorithm has much better performance in both convergence rate and stability over the SIMPLE algorithm. Originality/value: The detail solution procedure of implementing the IDEAL algorithm for compressible flows based on Delaunay triangular mesh is presented in this work, seemingly first in the literature. [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]

• 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]

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]

In this work, we present a new monolithic finite element strategy for solving fluid–structure interaction problems involving a compressible fluid and a hyperelastic structure. In the Lagrangian limit, the time‐stepping strategy that we propose conserves the total energy, and linear and angular momenta. Detailed proofs with numerical validations are provided. We use a displacement‐based Lagrangian formulation for the structure, and a velocity‐based arbitrary Lagrangian–Eulerian mixed formulation with appropriately chosen interpolations for the various field variables to ensure stability of the resulting numerical procedure. A hybrid formulation is used to prevent locking of thin structures. Apart from physical variables such as displacement, velocity, and so forth, no new variables are introduced in the formulation. The use of the exact tangent stiffness matrix ensures that the algorithm converges quadratically within each time step. A number of benchmark examples have been solved to illustrate the good performance of the proposed method. [ABSTRACT FROM AUTHOR]

Motivated by the enlightenment that diminishing the jump at the cell boundary can effectively reduce numerical dissipation near the critical region, and a novel constrained interpolation profile conservative semi-Lagrangian method is proposed based on a newly designed boundary variation diminishing algorithm. First, a constrained interpolation profile conservative semi-Lagrangian scheme with the piecewise tangent of hyperbola for interface capturing scheme is proposed as one candidate to represent jump-like discontinuities. Second, the constrained interpolation profile conservative semi-Lagrangian scheme with a fourth-order weighted essentially non-oscillatory limiter is used as another candidate to keep the high-order and non-oscillatory reconstruction for smooth solutions. The selection criterion of these two candidates is designed by minimizing the total variations of the first derivative at cell boundaries. A unified pressure-based projection formulation with a fractional step procedure is implemented with the proposed scheme to simulate both compressible and incompressible flows. A variety of numerical tests are studied, including linear and nonlinear scalar wave transport problems and compressible and incompressible flow problems. Results show that the proposed method can effectively eliminate numerical oscillation and diffusion, suggesting it has great potential to be applied to various types of engineering problems including both compressible and incompressible flows. [ABSTRACT FROM AUTHOR]

This work proposes a new topology optimization formulation to subsonic compressible flows. Compressible flows can be seen in many aerodynamic problems and optimization techniques can be used to improve designs of wings, diffusers, and other applications. In this work, the compressible Navier-Stokes equations are used coupled with a density-based material model. The effects of the material model are shown for both the momentum and energy equations. Two objective functions are considered, the entropy variation in a control volume and the entropy generation. The algorithm is implemented by a finite element model to solve the state equations. The pyadjoint libraries are used to perform the automatic sensitivity derivation and an internal point optimizer is used to update the design variable. The algorithm is evaluated by performing the optimization of 2D domains and a 3D diffuser. The results show optimized designs with reduced entropy generation. [ABSTRACT FROM AUTHOR]