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Compact accurately boundary-adjusting high-resolution technique for fluid dynamics. (English) Zbl 1172.76034
Summary: A novel high-resolution numerical method is presented for one-dimensional hyperbolic problems based on the extension of the original upwind leapfrog scheme to quasi-linear conservation laws. The method is second-order accurate on non-uniform grids in space and time, has a very small dispersion error and computational stencil defined within one space-time cell. For shock-capturing, the scheme is equipped with a conservative nonlinear correction procedure which is directly based on the maximum principle. Plentiful numerical examples are provided for linear advection, quasi-linear scalar hyperbolic conservation laws and gas dynamics, and comparisons with other computational methods in the literature are discussed.

76M20 Finite difference methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
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