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arXiv · 1912.09559

PDE-Based Multidimensional Extrapolation of Scalar Fields over Interfaces with Kinks and High Curvatures

Daniil Bochkov·Frederic Gibou
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Abstract

We present a PDE-based approach for the multidimensional extrapolation of smooth scalar quantities across interfaces with kinks and regions of high curvature. Unlike the commonly used method of [2] in which normal derivatives are extrapolated, the proposed approach is based on the extrapolation and weighting of Cartesian derivatives. As a result, second- and third-order accurate extensions in the $L^\infty$ norm are obtained with linear and quadratic extrapolations, respectively, even in the presence of sharp geometric features. The accuracy of the method is demonstrated on a number of examples in two and three spatial dimensions and compared to the approach of [2]. The importance of accurate extrapolation near sharp geometric features is highlighted on an example of solving the diffusion equation on evolving domains.

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Daniil Bochkov, Frederic Gibou. 2019-12-19. PDE-Based Multidimensional Extrapolation of Scalar Fields over Interfaces with Kinks and High Curvatures. https://doi.org/10.1137/19m1307883

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