×

zbMATH — the first resource for mathematics

WENO schemes on arbitrary mixed-element unstructured meshes in three space dimensions. (English) Zbl 1210.65160
Summary: The paper extends weighted essentially non-oscillatory (WENO) methods to three dimensional mixed-element unstructured meshes, comprising tetrahedral, hexahedral, prismatic and pyramidal elements. Numerical results illustrate the convergence rates and non-oscillatory properties of the schemes for various smooth and discontinuous solutions test cases and the compressible Euler equations on various types of grids. Schemes of up to fifth order of spatial accuracy are considered.

MSC:
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Balsara, D.; Shu, C.-W., Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy, J. comput. phys., 160, 405-452, (2000) · Zbl 0961.65078
[2] T. Barth, P. Frederickson, Higher order solution of the Euler equations on unstructured grids using quadratic reconstruction, in: 28th Aerospace Sciences Meeting, AIAA paper no. 90-0013, 1990.
[3] Dumbser, M.; Käser, M., Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems, J. comput. phys., 221, 2, 693-723, (2007) · Zbl 1110.65077
[4] Dumbser, M.; Käser, M.; Titarev, V.; Toro, E., Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems, J. comput. phys., 226, 204-243, (2007) · Zbl 1124.65074
[5] Friedrichs, O., Weighted essentially non-oscillatory schemes for the interpolation of Mean values on unstructured grids, J. comput. phys., 144, 1, 194-212, (1998) · Zbl 1392.76048
[6] Godunov, S., A finite difference method for the computation of discontinuous solutions of the equations of fluid dynamics, Mat. sbornik, 47, 357-393, (1959)
[7] J.D. Gray, Summary Report on Aerodynamic Characteristics of Standard Models HB-1 and HB-2, Technical Report, AEDC-TDR-64-137, 1964.
[8] Hahn, M.; Drikakis, D., Assessment of large-eddy simulation of internal separated flow, J. fluids eng., 131, 7, 071201, (2009)
[9] Jiang, G.; Shu, C., Efficient implementation of weighted ENO schemes, J. comput. phys., 126, 202-212, (1996) · Zbl 0877.65065
[10] Karypis, G.; Kumar, V., Multilevel k-way partitioning scheme for irregular graphs, J. parallel distrib. comput., 48, 96-129, (1998)
[11] Käser, M.; Iske, A., ADER schemes for the solution of conservation laws on adaptive triangulations, () · Zbl 1072.65116
[12] Kulikovskii, A.; Pogorelov, N.; Semenov, A., Mathematical aspects of numerical solution of hyperbolic systems, Monographs and surveys in pure and applied mathematics, vol. 118, (2002), Chapman and Hall
[13] Liu, X.; Osher, S.; Chan, T., Weighted essentially non-oscillatory schemes, J. comput. phys., 115, 200-212, (1994) · Zbl 0811.65076
[14] Shi, J.; Hu, C.; Shu, C.-W., A technique for treating negative weights in WENO schemes, J. comput. phys., 175, 108-127, (2002) · Zbl 0992.65094
[15] Taube, A.; Dumbser, M.; Balsara, D.; Munz, C.-D., Arbitrary high-order discontinuous Galerkin schemes for the magnetohydrodynamic equations, J. sci. comput., 30, 3, 441-464, (2007) · Zbl 1176.76075
[16] Thornber, B.; Mosedale, A.; Drikakis, D., On the implicit large eddy simulations of homogeneous decaying turbulence, J. comput. phys., 226, 1902-1929, (2007) · Zbl 1219.76027
[17] Titarev, V.A.; Drikakis, D., Uniformly high-order schemes on arbitrary unstructured meshes for advection-diffusion equations, Comput fluids, (2010) · Zbl 1433.65178
[18] Titarev, V.; Toro, E., Finite-volume WENO schemes for three-dimensional conservation laws, J. comput. phys., 201, 1, 238-260, (2004) · Zbl 1059.65078
[19] Toro, E., Riemann solvers and numerical methods for fluid dynamics, (2009), Springer-Verlag
[20] Toro, E.; Millington, R.; Nejad, L., Towards very high order Godunov schemes, (), 907-940 · Zbl 0989.65094
[21] Toro, E.; Titarev, V., Derivative Riemann solvers for systems of conservation laws and ADER methods, J. comput. phys., 212, 1, 150-165, (2006) · Zbl 1087.65590
[22] van der Vegt, J.; van der Ven, H., Space – time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows: I. general formulation, J. comput. phys., 182, 2, 546-585, (2002) · Zbl 1057.76553
[23] Zhang, Y.-T.; Shu, C.-W., Third order WENO scheme on three dimensional tetrahedral meshes, Commun. comput. phys., 5, 2-4, 836-848, (2009) · Zbl 1364.65177
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.