An enthalpy‐preserving shock‐capturing term for residual distribution schemes

Abstract

Summary In this contribution, we investigate strategies to perform shock‐capturing computation of steady hypersonic flow fields by means of residual distribution schemes. The ultimate objective is the computation of flow solutions for which the correct upstream enthalpy value is recovered in the postshock region. To this end, the parallelism existing between the classical Bx scheme and the stabilized finite element techniques is exploited. The simple Lax‐Friedrichs dissipation term is leveraged to build two new residual distribution schemes. Upon testing on both inviscid and viscous steady problems, solutions obtained with one of the two schemes are shown to recover the correct upstream total enthalpy level in the postshock region. This last scheme provides also improved wall pressure and skin friction predictions; heat transfer predictions are, unfortunately, similar to those offered by the Bx scheme. A conjecture for explaining this behavior is exposed.

On the well-posedness of the multi-dimensional Roe–Liu–Vinokur linearization for residual distribution schemes

“…Research is undergoing to improve the regularization techniques for RD schemes: e.g. [26] describes an enthalpy-preserving shock capturing term which can be extended in a straightforward manner to the complex thermochemical non-equilibrium model considered in this work. Alternative, supplementary dissipative terms are described in [27,28].…”