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Designing an efficient solution strategy for fluid flows. I: A stable high order finite difference scheme and sharp shock resolution for the Euler equations. (English) Zbl 0899.76281
A possible strategy for solving the compressible Euler or Navier- Stokes equations is presented. As parts of the strategy, the authors introduce high-order centered approximations applied to the symmetrized governing system of equations and ensuring the stability of the resulting schemes. To remove spurious oscillations near shocks, artificial dissipation is added in shock regions. For detection those regions and subsequent refining local meshes, the wavelet technique is suggested and described in detail. Numerical results illustrating good resolution properties of the method are presented.

76M20 Finite difference methods applied to problems in fluid mechanics
76L05 Shock waves and blast waves in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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