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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).

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
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References:
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