Multidimensional Extrapolation over Interfaces with Kinks and Regions of High Curvatures

12/19/2019

∙

by   Daniil Bochkov, et al.

∙

0

∙

share

We present a PDE-based approach for the multidimensional extrapolation of smooth scalar quantities across interfaces with kinks and regions of high curvature. Second- and third-order accurate extensions in the L^∞ norm are obtained with linear and quadratic extrapolations, respectively. The accuracy of the method is demonstrated on a number of examples in two and three spatial dimensions and compared to the commonly used approach of [2]. Application of the method in the context of adaptive Quad-/Oc-tree grids is briefly discussed.