CONVECTION TREATMENT AND PRESSURE SPLITTING FOR SEQUENTIAL SOLUTION PROCEDURES, PART I: THEORY AND ONE-DIMENSIONAL TEST CASES

Abstract

Treatment ofconvective and pressure fluxes in the Euler and Navier-Stokes equations using splitting formulas for convective velocity and pressure, with a view to incorporate them in sequential pressure-based methods, is investigated. Two schemes—a controlled variation scheme (CVS) and an advection upstream splitting method (AUSM)—are explored for their accuracy in resolving sharp gradients. In Part I, basic concepts and the derivation of the CVS, along with its comparison to the AUSM scheme, are presented. To demonstrate the performance of the CVS and AUSM, flows involving moving or reflecting shock waves, as well as a one-dimensional combusting flow with a strong heat release source term, are investigated