WENO scheme with subcell resolution for computing nonconservative Euler equations with applications to one-dimensional compressible two-medium flows. (English) Zbl 1383.76359
Summary: High order path-conservative schemes have been developed for solving nonconservative hyperbolic systems in [C. Parés, SIAM J. Numer. Anal. 44, No. 1, 300–321 (2006; Zbl 1130.65089); M. Castro et al., Math. Comput. 75, No. 255, 1103–1134 (2006; Zbl 1096.65082); J. Sci. Comput. 39, No. 1, 67–114 (2009; Zbl 1203.65131)]. Recently, it has been observed in [R. Abgrall and S. Karni, J. Comput. Phys. 229, No. 8, 2759–2763 (2010; Zbl 1188.65134)] that this approach may have some computational issues and shortcomings. In this paper, a modification to the high order path-conservative scheme in [M. Castro et al., Math. Comput. 75, No. 255, 1103–1134 (2006; Zbl 1096.65082)] is proposed to improve its computational performance and to overcome some of the shortcomings. This modification is based on the high order finite volume WENO scheme with subcell resolution and it uses an exact Riemann solver to catch the right paths at the discontinuities. An application to one-dimensional compressible two-medium flows of nonconservative or primitive Euler equations is carried out to show the effectiveness of this new approach.
MSC:
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 76M28 | Particle methods and lattice-gas methods |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
path-conservative schemes; high-order finite volume WENO scheme; subcell resolution; nonconservative hyperbolic systems; primitive Euler equations; two-medium flows; exact Riemann solverReferences:
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