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Higher‐order bounded differencing schemes for compressible and incompressible flows
Author(s) -
Ng K. C.,
Yusoff M. Z.,
Ng E. Y. K.
Publication year - 2006
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1248
Subject(s) - transonic , polygon mesh , mathematics , scalar (mathematics) , compressibility , incompressible flow , bounded function , compressible flow , computation , mathematical optimization , convergence (economics) , numerical diffusion , flow (mathematics) , algorithm , mathematical analysis , geometry , aerodynamics , mechanics , physics , economics , economic growth
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 © 2006 John Wiley & Sons, Ltd.