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Spectral (finite) volume method for conservation laws on unstructured grids. IV: Extension to two-dimensional systems. (English) Zbl 1039.65072
Summary: The fourth in a series [cf. Z. J. Wang, ibid. 178, No. 1, 210–251 (2002; Zbl 0997.65115); Z. J. Wang and Y. Liu, ibid. 179, No. 2, 665–697 (2002; Zbl 1006.65113) and J. Sci. Comput. 20, 137–157 (2004; Zbl 1097.65100)], the spectral volume (SV) method is extended to multi-dimensional systems – the 2D Euler equations. The focus of this paper is to study the performance of the SV method on multidimensional non-linear systems, and to verify that high order solution accuracy up to fourth-order can be achieved for the systems of conservation laws. Implementation details including total variation diminishing (TVD) and total variation bounded (TVB) limiters are presented. An accuracy study is performed first to numerically verify that the designed order of accuracy can be obtained for smooth flow solutions. Then, solutions with both smooth features and discontinuities are utilized to demonstrate the overall capability of the SV method.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
76M22 Spectral methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
Software:
Mathematica
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