High resolution schemes for steady flow computation

Abstract

With the introduction of the concept of total variation diminishing scheme (TVD), a variety of numerical schemes using this approach have emerged. For steady state calculations, two particular TVD schemes have proved popular, i.e., the Yee symmetric and the Osher-Chakravarthy upwind TVD schemes. When applied to Euler equations, these two schemes give almost identical results. However, when they are employed to solve Navier-Stokes equations, the authors found dramatic differences especially when high Reynolds number viscous flow is tackled. In one viscous flow calculation, the Yee scheme gave an “unrepresentative” result while Osher-Chakravarthy scheme gave the “physical” result. The paper demonstrates that the numerical dissipation embedded in the schemes may be the cause. Modifications, therefore, are suggested to make Yee's scheme less dissipative so that it is much more suitable for viscous flow calculations. The numerical experiments do favor the modified scheme. Osher-Chakravarthy TVD scheme and the modified Yee scheme are recommended for viscous flow calculation at high Reynolds number.