Accurate compact flowfield-dependent variation method for compressible euler equations

Abstract

Numerical simulations of compressible inviscid flows using fully implicit high order compact flowfielddependent variation (HOC-FDV) method has been developed. The third-order accurate in time flowfield-dependent variation (FDV) scheme is used for time discritization and the fourthorder compact Pade scheme is used to approximate the first and second spatial derivatives. The solution procedure consists of a number of tri-diagonal matrix operations with considerable saving in computing time, and produces an efficient solver. The method has been tested and verified for two numerical examples, a flow over a channel flow with compression/expansion and a flow past NACA0012 airfoil. Good agreement with the analytical and other numerical solutions has been obtained in both cases. Numerical results show the validity and accuracy of the proposed method.