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High order accurate schemes for Euler and Navier-Stokes equations on staggered Cartesian grids. (English) Zbl 1436.65124
Summary: We present here a new class of staggered schemes for solving the compressible 1D Euler equations in internal energy formulation on uniform grids. The schemes are applicable to arbitrary equation of states and can be extended to high order of accuracy in both time and space on smooth flows. High order accuracy in time is reached thanks to Cauchy-Kovalevskaya procedure. Modifications on the initial schemes are performed to give sufficient conditions for stability on 1D wave equations. Results obtained for wave equations are extended to 1D Euler equations and then to 2D compressible Navier-Stokes equations using directional splitting methods. Results on the conservation of total energy are given, proper shock capturing is observed experimentally. Numerical results are provided up to 4th-order accuracy in 1D and 2D.
MSC:
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
76N06 Compressible Navier-Stokes equations
35Q31 Euler equations
76M12 Finite volume methods applied to problems in fluid mechanics
Software:
KRAKEN
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