Multidimensional upwind schemes based on fluctuation-splitting for systems of conservation laws. (English) Zbl 0771.76048

Summary: A class of truly multidimensional upwind schemes for the computation of inviscid compressible flows is presented, applicable to unstructured cell-vertex grids. These methods use very compact stencils and produce sharp resolution of discontinuities with no overshoots.


76M20 Finite difference methods applied to problems in fluid mechanics
35L65 Hyperbolic conservation laws
Full Text: DOI


[1] Barth, T. J. (1990): On unstructured grids and solvers. VKI LS 1990-04
[2] Bourgois, G.; Deconinck, H.; Roe, P. L.; Struijs, R. (1992): Multidimensional upwind schemes for scalar advection on tetrahedral meshes. First European Computational Fluid Dynamics Conference, Brussels
[3] Deconinck, H.; Roe, P. L.; Struijs, R. (1991): A multidimensional generalization of Roe’s flux difference splitter for the Euler equations. 4th ISCFD Conference, U.C. Davis · Zbl 0790.76054
[4] De Palma, P.; Deconinck, H.; Struijs, R. (1990): Investigation of Roe’s 2D wave models for the Euler equations. VKI TN 172
[5] Roe, P. L. (1981): The use of the Riemann problem in finite differences. In: Reynolds, W. C.; MacCormac, R. W. (eds): 7th Int. Conf. Numerical Meth. in Fluid Dynamics. Berlin, Heidelberg, New York: Springer · Zbl 0474.65066
[6] Roe, P. L. (1981): Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comp. Phys. 43, No. 2, 357 · Zbl 0474.65066
[7] Roe, P. L. (1982): Fluctuations and signals?A framework for numerical evolution problems. In: Mortan, K. W.; Baines, M. J. (eds): Numerical Methods for Fluid Dynamics: New York: Academic Press · Zbl 0569.76072
[8] Roe, P. L. (1986): Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics. J. Comp. Phys. 63, 458-476 · Zbl 0587.76126
[9] Roe, P. L. (1987): Linear advection schemes on triangular meshes. CoA Report No. 8720, Cranfield, November
[10] Roe, P. L. (1991): Beyond the Riemann problem I. ICASE-NASA Langley workshop. September
[11] Roe, P. L.; Beard, L. (1992): An improved wave model for multidimensional upwinding of the Euler equations. 13th International Conference on Numerical Methods in Fluid Dynamics. Rome
[12] Roe, P. L.; Struijs, R.; Deconinck, H. (1993): A conservative linearization for the multidimensional Euler equations. To appear in J. Comp. Phys. · Zbl 0790.76054
[13] Sidilkover, D. (1990): Numerical solution to steady-state problems with discontinuities. Ph.D. thesis; Wiezmann Institute, Israel
[14] Struijs, R.; Deconinck, H.; Roe, P. L. (1991): Fluctuation splitting schemes for the 2D Euler equations. VKI lecture series 1991-01
[15] Struijs, R.; Deconinck, H.; dePalma, P.; Roe, P. L.; Powell, K. G. (1991): Progress on multidimensional upwind Euler solvers for unstructured grids. AIAA 91-1550
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.