Two-Dimensional RBF-ENO Method on Unstructured Grids

Essentially non-oscillatory (ENO) and weighted ENO (WENO) methods on equidistant Cartesian grids are widely used to solve partial differential equations with discontinuous solutions. However, stable ENO/WENO methods on unstructured grids are less well studied. We propose a high-order ENO method based on radial basis function (RBF) to solve hyperbolic conservation laws on general two-dimensional grids. The radial basis function reconstruction offers a flexible way to deal with ill-conditioned cell constellations. We introduce a smoothness indicator based on RBFs and a stencil selection algorithm suitable for general meshes. Furthermore, we develop a stable method to evaluate the RBF reconstruction in the finite volume setting which circumvents the stagnation of the error and keeps the condition number of the reconstruction bounded. We conclude with several challenging numerical examples in two dimensions to show the robustness of the method.


Published in:
Journal Of Scientific Computing, 82, 3, 76
Year:
Mar 11 2020
Publisher:
New York, SPRINGER/PLENUM PUBLISHERS
ISSN:
0885-7474
1573-7691
Keywords:
Laboratories:




 Record created 2020-03-26, last modified 2020-05-10


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