An upwind finite difference scheme for meshless solvers.

*(English)*Zbl 1023.76034Summary: We present an upwind finite difference scheme for meshless solvers. This new scheme, capable of working on any type of grid (structure, unstructured or even a random distribution of points) produces superior results. A means to construct schemes of specified order of accuracy is discussed. Numerical computations for different types of flow over a wide range of Mach numbers are presented. Also, these results are compared with those obtained using a cell vertex finite volume code on the same grids, and with theoretical values wherever possible. The present framework has the flexibility to choose between various upwind flux formulas.

##### MSC:

76M20 | Finite difference methods applied to problems in fluid mechanics |

76N15 | Gas dynamics (general theory) |

##### Keywords:

meshless solvers; upwind finite difference scheme; two-dimensional compressible Euler equations; least squares
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\textit{D. Sridar} and \textit{N. Balakrishnan}, J. Comput. Phys. 189, No. 1, 1--29 (2003; Zbl 1023.76034)

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