Implicit WENO Scheme and High Order Viscous Formulas for Compressible Flows

Abstract

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 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.

High Order Boundary Conditions for High Order Finite Difference Schemes on Curvilinear Coordinates Solving Compressible Flows

“…∂F v ∂ξ can be discretized by a simple and straightforward central difference scheme while ∂F v ∂ξ must be treated more carefully to achieve grid level coupling and eliminate possible odd-even decoupling [25,31] problem. However, both of them can be written into conservative form.…”

“…The use of the Euler equations in primitive-variable form makes the formulas of the characteristic variables very simple. (2) A conservative, high order discretization for the viscous fluxes proposed in [25] is improved to make the computation more efficient, and the corresponding extrapolation procedures for computing the physical and numerical viscous fluxes at the boundary are also proposed. (3) The present boundary treatment procedure is designed for the curvilinear coordinates, which can be used together with finite difference schemes to solve problems on general geometries.…”

Comparison of Drag Prediction Using RANS models and DDES for the DLR-F6 Configuration Using High Order Schemes

“…This term vanishes at the end of each physical time step, and has no influence on the accuracy of the solution. An implicit pseudo time marching scheme using Gauss-Seidel line relaxation is employed to achieve high convergence rate instead of using the explicit scheme [27]. The pseudo temporal term is discretized with first order Euler scheme.…”

Boundary closures for fourth-order energy stable weighted essentially non-oscillatory finite-difference schemes

“…3 The nonlinear weight functionsw (r) j+1/2 , r = {L, C, R} used in equation (13), are constructed such that the interface fluxf j+ 1 2 is a convex combination of the three candidate second-order fluxes. The weight functions are constructed using the expressions…”