Direct Arbitrary-Lagrangian-Eulerian ADER-MOOD finite volume schemes for multidimensional hyperbolic conservation laws

JOURNAL OF COMPUTATIONAL PHYSICS

卷:292

Article

Boscheri, Walter¹  Loubere, Raphael^2,3  Dumbser, Michael¹ 

[1] Univ Trento, Dept Civil Environm & Mech Engn, Lab Appl Math, I-38123 Trento, Italy

[2] Univ Toulouse 3, CNRS, F-31062 Toulouse, France

[3] Univ Toulouse 3, IMT, F-31062 Toulouse, France

关键词: Arbitrary-Lagrangian-Eulerian;    A posteriori limiter;    MOOD paradigm;    ADER schemes;    Moving unstructured triangular and tetrahedral meshes;    High order of accuracy in space and time;    High performance computing (HPC);    Hyperbolic conservation laws;   

DOI  :  10.1016/j.jcp.2015.03.015

来源: Elsevier

【 摘 要 】

In this paper we present a new family of efficient high order accurate direct Arbitrary-Lagrangian-Eulerian (ALE) one-step ADER-MOOD finite volume schemes for the solution of nonlinear hyperbolic systems of conservation laws for moving unstructured triangular and tetrahedral meshes. This family is the next generation of the ALE ADER-WENO schemes presented in [16,20]. Here, we use again an element-local space-time Galerkin finite element predictor method to achieve a high order accurate one-step time discretization, while the somewhat expensive WENO approach on moving meshes, used to obtain high order of accuracy in space, is replaced by an a posteriori MOOD loop which is shown to be less expensive but still as accurate. This a posteriori MOOD loop ensures the numerical solution in each cell at any discrete time level to fulfill a set of user-defined detection criteria. If a cell average does not satisfy the detection criteria, then the solution is locally re-computed by progressively decrementing the order of the polynomial reconstruction, following a so-called cascade of predefined schemes with decreasing approximation order. A so-called parachute scheme, typically a very robust first order Godunov-type finite volume method, is employed as a last resort for highly problematic cells. The cascade of schemes defines how the decrementing process is carried out, i.e. how many schemes are tried and which orders are adopted for the polynomial reconstructions. The cascade and the parachute scheme are choices of the user or the code developer. Consequently the iterative MOOD loop allows the numerical solution to maintain some interesting properties such as positivity, mesh validity, etc., which are otherwise difficult to ensure. We have applied our new high order unstructured direct ALE ADER-MOOD schemes to the multidimensional Euler equations of compressible gas dynamics. A large set of test problems has been simulated and analyzed to assess the validity of our approach in terms of both accuracy and efficiency (CPU time and memory consumption). (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free