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Multidimensional slope limiters for MUSCL-type finite volume schemes on unstructured grids. (English) Zbl 0934.65109
The improvement of existing limiters in MUSCL-type numerical methods for the numerical solution of two-dimensional hyperbolic conservation laws is the central theme of the present paper. The framework of MUSCL-type schemes on triangular grids is exploited. Local constraints on the linear reconstruction of the solution are imposed so that an appropriate maximum principle is satisfied. This opens way to the development of new MUSCL-type schemes. Numerical results are given for a scalar problem as well as for the shallow water equation.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76M20 Finite difference methods applied to problems in fluid mechanics
35L65 Hyperbolic conservation laws
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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