On Hybrid High Resolution Upwind Methods for Multicomponent Flows

Abstract

AbstractShock capturing numerical methods expressed in terms of conservative variables produce erroneous solutions when applied to multicomponent flows. Numerical schemes expressed in terms of primitive variables are able to provide accurate results for non‐shocked multicomponent flows. An assessment of four hybrid primitive‐conservative upwind schemes is presented for the solution of multicomponent flows involving strong shock waves. The schemes used are the MUSCL‐Hancock scheme, the Weighted Average Flux scheme, and modified versions of the Generalised Riemann Problem, and Piecewise Linear Methods. These four hybrid schemes provide accurate solutions to such problems, and numerical experiments suggest that they converge. It is also shown that conservative methods may often provide satisfactory results when applied to multicomponent problems when the flow is dominated by strong shocks.