×

zbMATH — the first resource for mathematics

On essentially non-oscillatory schemes on unstructured meshes: Analysis and implementation. (English) Zbl 0822.65062
Author’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.

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
PDF BibTeX XML Cite
Full Text: DOI