Higher-order bounded differencing schemes for compressible and incompressible flows

In recent years, three higher-order (HO) bounded differencing schemes, namely AVLSMART, CUBISTA and HOAB that were derived by adopting the normalized variable formulation (NVF), have been proposed. In this paper, a comparative study is performed on these schemes to assess their numerical accuracy, computational cost as well as iterative convergence property. All the schemes are formulated on the basis of a new dual-formulation in order to facilitate their implementations on unstructured meshes. Based on the proposed dual-formulation, the net effective blending factor (NEBF) of a high-resolution (HR) scheme can now be measured and its relevance on the accuracy and computational cost of a HR scheme is revealed on three test problems: (1) advection of a scalar step-profile; (2) 2D transonic flow past a circular arc bump: and (3) 3D lid-driven incompressible cavity flow. Both density-based and pressure-based methods are used for the computations of compressible and incompressible flow, respectively. Computed results show that all the schemes produce solutions which are nearly as accurate as the third-order QUICK scheme; however, without the unphysical oscillations which are commonly inherited from the HO linear differencing scheme. Generally, it is shown that at higher value of NEBF, a HR scheme can attain better accuracy at the expense of computational cost. Copyright (c) 2006 John Wiley & Sons, Ltd.