Implicit WENO Scheme and High Order Viscous Formulas for Compressible Flows

Yiqing Shen, Baoyuan Wang, Gecheng Zha
2007 25th AIAA Applied Aerodynamics Conference   unpublished
The purpose of this paper is to develop a robust and efficient high order fully conservative finite difference scheme for compressible Navier-Stokes equations. The 5th order WENO scheme is used for the inviscid fluxes. A conservative fourth order accuracy finite central differencing scheme is developed for the viscous terms. An improved ε value of 10 −2 is suggested for the WENO smooth factors calculation, which removes the weight oscillation and significantly improves the convergence rate and
more » ... nvergence rate and level. The wall surface is taken as half-point mesh so that the no slip wall boundary condition can be accurately imposed. A 3th order accurate finite difference scheme is given to treat wall boundary condition. The implicit time marching method with unfactored Gauss-Seidel line relaxation is used with the high order scheme to achieve steady state solutions with high convergence rate.
doi:10.2514/6.2007-4431 fatcat:a7pys4obbvax3hvrtllmi2ej6m