Abstract
In this paper, the solution of a generalized system of hyperbolic equations by means of upwind, limited, second-order accurate fluxes including a new sonic fix is presented. The new sonic fix introduced here utilizes a dissipation term embedded directly in the fluxes and it is totally based on physical grounds producing the correct decay rate of sonic gradients. In addition to the sonic fix, the effects of the source term on the flux limiters are also introduced. The resulting scheme is applied to a variety of test problems resulting from the solutions of Euler's and magneto-hydrodynamic (MHD) equations. To eliminate the divergence problem, a new implementation of a recently introduced scheme for the MHD equations which includes a divergence wave and a source related to ∇·Bis introduced. The numerical test results obtained with this new scheme are in excellent agreement with previous results and they show that the scheme presented here is robust, accurate, and entropy satisfying by producing very sharp contact discontinuities and shocks without postshock oscillations and divergence errors.
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