Numerical Experiments with Several Variant WENO Schemes for the Compressible Viscous Flow Computations

作者：Hsieh Tsang Jen^*; Wang Ching Hua; Yang Jaw Yen

来源：Journal of the Chinese Society of Mechanical Engineers, 2009, 30(3): 209-220.

• WENO scheme
• Anti-diffusive flux corrections
• Mapped WENO scheme

Numerical experiments with several variants of the original WENO schemes, including anti-diffusive flux corrections, the mapped WENO scheme, and modified smoothness indicator are tested for the compressible Navier-Stokes equations with Spalart-Allmaras one equation turbulence model. The lower-upper symmetric-Gauss-Seidel (LU-SGS) implicit method is employed for the computation of steady state solutions. A numerical flux of the variant WENO scheme in flux limiter form is presented, which is consisted of first-order and high-order fluxes and allows for a more flexible choice of low order schemes. The Computations are performed for the two-dimensional turbulent flows over NACA 0012 and RAE2822 airfoil. Various aspects of the variant WENO methods including contact discontinuity sharpening and steady state convergence rate are examined. By using the WENO scheme with anti-diffusive flux corrections, the present solutions indicate that good convergence rate can be achieved and high order accuracy is maintained and contact discontinuities are sharpened markedly as compared with the original WENO schemes on the same meshes.

• 出版日期2009-6