A High Order Finite Volume -HLLC Solver and Anisotropic Delaunay Mesh Adaptation

A high order HLLC Riemann solver is implemented within a finite volume procedure for solving the Euler equations on unstructured grids. The traditional HLLC form is modified slightly to ensure satisfactory performance on stretched meshes and an appropriate limiter is employed to ensure stability and robustness. A Delaunay anisotropic mesh adaptation strategy is introduced with the objective of improving solution accuracy with an optimum number of mesh points, a suitable points inserting algorithm is proposed as well as a Delaunay kernel modification. The electiveness of the proposed approach is demonstrated by application to a number of test examples and the results produced are compared with experiment.

[1]  Wagdi G. Habashi,et al.  EFFICIENT ANISOTROPI C MESH ADAPTATION ON WEAK AND MULTIPLE SHOCKS , 2004 .

[2]  Nigel P. Weatherill,et al.  A multigrid accelerated time‐accurate inviscid compressible fluid flow solution algorithm employing mesh movement and local remeshing , 2003 .

[3]  E. Toro.  Riemann Solvers and Numerical Methods for Fluid Dynamics , 1997 .

[4]  E. Toro,et al.  Restoration of the contact surface in the HLL-Riemann solver , 1994 .

[5]  Vivette Girault,et al.  Finite Element Methods for Navier-Stokes Equations - Theory and Algorithms , 1986, Springer Series in Computational Mathematics.

[6]  J. Peiro,et al.  Adaptive remeshing for three-dimensional compressible flow computations , 1992 .

[7]  Tao Lin,et al.  On the Accuracy of the Finite Volume Element Method Based on Piecewise Linear Polynomials , 2001, SIAM J. Numer. Anal..

[8]  Michel Fortin.  Anisotropic mesh adaptation through hierarchical error estimators , 2001 .

[9]  M. Fortin,et al.  Anisotropic mesh adaptation: towards user‐independent, mesh‐independent and solver‐independent CFD. Part I: general principles , 2000 .

[10]  LAKHDAR REMAKI,et al.  3-D Mesh Adaptation on Multiple Weak Discontinuities and Boundary Layers , 2006, SIAM J. Sci. Comput..

[11]  A. Corsini.  A FE Method for the Computational Fluid Dynamics of Turbomachinery , 2000 .

[12]  Shlomo Ta'asan,et al.  An absorbing buffer zone technique for acoustic wave propagation , 1995 .

[13]  Claire Chainais-Hillairet,et al.  Finite volume schemes for a nonlinear hyperbolic equation. Convergence towards the entropy solution and error estimate , 1999 .

[14]  Paul-Henry Cournède,et al.  A Positive MUSCL Scheme for Triangulations , 1998 .

[15]  B. G. Larwood,et al.  Aerospace simulations on parallel computers using unstructured grids , 2002 .

[16]  R. Eymard,et al.  Finite Volume Methods , 2019, Computational Methods for Fluid Dynamics.

[17]  E. F. D'Azevedo,et al.  On optimal triangular meshes for minimizing the gradient error , 1991 .