Artificial viscosity (Q) and artificial heat flux (H) errors for spherically divergent shocks

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Abstract
An extremely simple infinite shock benchmark problem, in spherical geometry, is used as a basis of comparison of various shock following techniques. The purpose of this paper is to determine the source of the large numerical errors encountered in this benchmark calculation, and to further evaluate (i.e., in spherical geometry) the new shock following procedure Q and H which utilizes both an artificial viscosity Q and an artificial heat flux term H. It is found that the Q and H method is the most accurate of all the methods tested, excluding the use of mesh refinement. Accurate results are hard to obtain. This is surprising, in as much as this benchmark problem (of an infinite divergent shock) has the simplest possible solution; namely, constant post-shock states. The best results are obtained with the new Q and H shock following method with errors on the order of a few percent at the shock and ten percent at the origin. Here the use of the artificial heat flux term H permits a more natural representation of shocks and reduces overheating at the origin.

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