On essentially non-oscillatory schemes on unstructured meshes: Analysis and implementation.

*(English)*Zbl 0822.65062Author’s abstract: During the past few years, the class of essentially non-oscillatory schemes for the numerical simulation of hyperbolic equations and systems has been constructed. Since then, a few extensions have been made to multidimensional simulations of compressible flows, mainly in the context of very regular structured meshes. In this paper, we first recall and improve the results of an earlier paper about non- oscillatory reconstruction on unstructured meshes. We put much emphasis on the effective calculation of the reconstruction. Then, we describe a class of numerical schemes on unstructured meshes. We give some applications for its third-order version. They demonstrate that a higher order of accuracy is indeed obtained, even on very irregular meshes.

Reviewer: U.GĂ¶hner (Leonberg)

##### MSC:

65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |

65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |

35L15 | Initial value problems for second-order hyperbolic equations |

76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |