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Resolution of high order WENO schemes for complicated flow structures. (English) Zbl 1047.76081
Summary: In this short note we address the issue of numerical resolution and efficiency of high order weighted essentially non-oscillatory (WENO) schemes for computing solutions containing both discontinuities and complex solution features, through two representative numerical examples: the double Mach reflection problem and the Rayleigh–Taylor instability problem. We conclude that for such solutions with both discontinuities and complex solution features, it is more economical in CPU time to use higher order WENO schemes to obtain comparable numerical resolution.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76L05 Shock waves and blast waves in fluid mechanics
76E17 Interfacial stability and instability in hydrodynamic stability
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[1] Balsara, D; Shu, C.-W, Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy, Journal of computational physics, 160, 405-452, (2000) · Zbl 0961.65078
[2] Berger, M; Colella, A, Local adaptive mesh refinement for shock hydrodynamics, Journal of computational physics, 82, 64-84, (1989) · Zbl 0665.76070
[3] Cockburn, B; Shu, C.-W, The runge – kutta discontinuous Galerkin method for conservation laws V: multidimensional systems, Journal of computational physics, 141, 199-224, (1998) · Zbl 0920.65059
[4] Colella, P; Woodward, P.R, The piecewise parabolic method (PPM) for gas dynamical simulations, Journal of computational physics, 54, 174-201, (1984) · Zbl 0531.76082
[5] Glimm, J; Grove, J; Li, X; Oh, W; Tan, D.C, The dynamics of bubble growth for rayleigh – taylor unstable interfaces, Physics of fluids, 31, 447-465, (1988) · Zbl 0641.76099
[6] Harten, A, High resolution schemes for hyperbolic conservation laws, Journal of computational physics, 49, 357-393, (1983) · Zbl 0565.65050
[7] Jiang, G; Shu, C.-W, Efficient implementation of weighted ENO schemes, Journal of computational physics, 126, 202-228, (1996) · Zbl 0877.65065
[8] J.-F. Remacle, J.E. Flaherty, M.S. Shephard, An adaptive discontinuous Galerkin technique with an orthogonal basis applied to compressible flow problems, SIAM Journal on Scientific Computing (to appear) · Zbl 1127.65323
[9] Samtaney, R; Pullin, D.I, Initial-value and self-similar solutions of the compressible Euler equations, Physics of fluids, 8, 2650-2655, (1996) · Zbl 1027.76642
[10] Shu, C.-W, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, (), 325-432 · Zbl 0927.65111
[11] Shu, C.-W; Osher, S, Efficient implementation of essentially non-oscillatory shock capturing schemes, Journal of computational physics, 77, 439-471, (1988) · Zbl 0653.65072
[12] Woodward, P; Colella, P, The numerical simulation of two-dimensional fluid flow with strong shocks, Journal of computational physics, 54, 115-173, (1984) · Zbl 0573.76057
[13] Young, Y.-N; Tufo, H; Dubey, A; Rosner, R, On the miscible rayleigh – taylor instability: two and three dimensions, Journal of fluid mechanics, 447, 377-408, (2001) · Zbl 0999.76056
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