On Godunov-type methods for gas dynamics
SIAM Journal on Numerical Analysis
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Local piecewise hyperbolic reconstruction of numerical fluxes for nonlinear scalar conservation laws
SIAM Journal on Scientific Computing
Convergence Rates for Relaxation Schemes Approximating Conservation Laws
SIAM Journal on Numerical Analysis
Nonlinear stability of the relaxing schemes for scalar conservation laws
Applied Numerical Mathematics
Relaxed High Resolution Schemes for Hyperbolic Conservation Laws
Journal of Scientific Computing
Variants of relaxed schemes and two-dimensional gas dynamics
ICCMSE '03 Proceedings of the international conference on Computational methods in sciences and engineering
Relaxed High Resolution Schemes for Hyperbolic Conservation Laws
Journal of Scientific Computing
Variants of relaxed schemes and two-dimensional gas dynamics
Journal of Computational and Applied Mathematics - Special issue: Selected papers of the international conference on computational methods in sciences and engineering (ICCMSE-2003)
Variants of relaxed schemes and two-dimensional gas dynamics
Journal of Computational and Applied Mathematics - Special issue: Selected papers of the international conference on computational methods in sciences and engineering (ICCMSE-2003)
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Numerical schemes based on relaxation are typically central difference schemes. In the case of supersonic flows, however, central differences are unphysical approximations. Introducing a shift in the relaxation approximation relaxed upwind schemes are constructed. Similar as central relaxed schemes, the new upwind versions also avoid the nonlinear Riemann problem and staggered grids. In addition, they simulate the physical domain of dependence correctly even in transonic flow regimes. The performance of the methods is illustrated by an acoustic shock interaction in gas dynamics.