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High-order finite difference and finite volume WENO schemes and discontinuous Galerkin methods for CFD. (English) Zbl 1034.76044
Summary: In recent years, high-order numerical methods have been widely used in computational fluid dynamics (CFD), to effectively resolve complex flow features using meshes which are reasonable for today’s computers. In this paper, we review and compare three types of high-order methods being used in CFD, namely the weighted essentially non-oscillatory (WENO) finite difference methods, the WENO finite volume methods, and the discontinuous Galerkin finite element methods. We summarize the main features of these methods, from a practical user’s point of view, indicate their applicability and relative strength, and show a few selected numerical examples to demonstrate their performance.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76M12 Finite volume methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
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