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A TVD principle and conservative TVD schemes for adaptive Cartesian grids. (English) Zbl 1106.65075
From the conclusion: With the total-variation-diminishing (TVD) principle generalized for the case of a Cartesian adaptive grid, formulate the limited reconstruction procedure at refinement interfaces. This procedure provides stable and accurate numerical solutions when combined with a Godunov-type scheme. The limited reconstruction procedure presented here has been utilized already in the magnetohydrodynamical code BATSRUS at the University of Michigan.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L45 Initial value problems for first-order hyperbolic systems
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
76W05 Magnetohydrodynamics and electrohydrodynamics
76M20 Finite difference methods applied to problems in fluid mechanics
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