A Rotated Characteristic Decomposition Technique for High-Order Reconstructions in Multi-dimensions
KAUST DepartmentApplied Mathematics and Computational Science Program
Extreme Computing Research Center
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Embargo End Date2022-08-11
Permanent link to this recordhttp://hdl.handle.net/10754/669249
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AbstractWhen constructing high-order schemes for solving hyperbolic conservation laws, the corresponding high-order reconstructions are commonly performed in characteristic spaces to eliminate spurious oscillations as much as possible. For multi-dimensional finite volume (FV) schemes, we need to perform the characteristic decomposition several times in different normal directions of the target cell, which is very time-consuming. In this paper, we propose a rotated characteristic decomposition technique which requires only one-time decomposition for multi-dimensional reconstructions. The rotated direction depends only on the gradient of a specific physical quantity which is cheap to calculate. This technique not only reduces the computational cost remarkably, but also controls spurious oscillations effectively. We take a third-order weighted essentially non-oscillatory finite volume (WENO-FV) scheme for solving the Euler equations as an example to demonstrate the efficiency of the proposed technique.
CitationShen, H., & Parsani, M. (2021). A Rotated Characteristic Decomposition Technique for High-Order Reconstructions in Multi-dimensions. Journal of Scientific Computing, 88(3). doi:10.1007/s10915-021-01602-z
SponsorsH.S. acknowledges the financial support of National Natural Science Foundation of China (Contract No. 11901602).
PublisherSpringer Science and Business Media LLC
JournalJournal of Scientific Computing