ACCURACY ANALYSIS AND IMPROVEMENT OF VISCOUS FLUX SCHEMES IN UNSTRUCTURED SECOND-ORDER FINITE-VOLUME DISCRETIZATION

Due to the widespread applications of unstructured second-order finite volume schemes in computational fluid dynamics (CFD) simulations, studying the discretization accuracy of second-order finite volume schemes is of practical value. Two primary factors that affecting accuracy of viscous flow simulation, including cell gradient reconstruction and interface gradient calculation method, are considered in this paper. Firstly, the odd-even decoupling problem in the discretization of viscous flux is analyzed theoretically and verified by the method of manufactured solutions (MMS) based on the scalar diffusion equation. Modification of interface gradient is proposed to eliminate the decoupling problem and the computational accuracy of the diffusion equation is improved greatly as a result. Then, the effects of cell gradient reconstruction and interface gradient method on the accuracy of viscous flow simulation are studied by the MMS method based on the diffusion equation. Results of MMS grid convergence tests show that cell gradient reconstruction and interface gradient method determine the accuracy of viscous flow simulation together. Finally, grid convergence tests are carried out for three realistic viscous flow cases, i.e., the laminar flat plate, the turbulent flat plate and the 2D airfoil near wake in NASA Turbulence Modeling Resource website. The numerical results verify the conclusions obtained by MMS tests, and the viscous flux discretization schemes are obtained with better performance in accuracy and grid convergence property.