A universal solver for hyperbolic equations by cubic-polynomial interpolation. II: Two- and three-dimensional solvers. (English) Zbl 0991.65522
Summary: A new numerical method is proposed for multidimensional hyperbolic equations. The scheme uses a cubic spatial profile within grids, and is described in an explicit finite-difference form by assuming that both the physical quantity and its spatial derivative obey the master equation. The method gives a stable and less diffusive result than the old methods without any flux limiter. Extension to nonlinear equations with nonadvection terms is straightforward.
For Part I see Comput. Phys. Commun. 66, No. 2-3, 219–232 (1991; Zbl 0991.65521).
For Part I see Comput. Phys. Commun. 66, No. 2-3, 219–232 (1991; Zbl 0991.65521).
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 35L45 | Initial value problems for first-order hyperbolic systems |
| 76L05 | Shock waves and blast waves in fluid mechanics |
| 35L67 | Shocks and singularities for hyperbolic equations |
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 65D05 | Numerical interpolation |
Keywords:
cubic-polynomial interpolation; multidimensional hyperbolic equations; cubic-interpolated; pseudo-particle method; finite-difference method; hyperbolic equations; KdV equation; shock-tube problem; shock wave; cubic-interpolated pseudo-particle methodCitations:
Zbl 0991.65521References:
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