Volume 1, Issue 3
Two-Dimensional Multi-Domain Hybrid Spectral-WENO Methods for Conservation Laws

B. Costa, W. S. Don, D. Gottlieb & R. Sendersky

DOI:

Commun. Comput. Phys., 1 (2006), pp. 548-574.

Published online: 2006-01

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  • Abstract

The multi-domain hybrid Spectral-WENO method (Hybrid) is introduced for the numerical solution of two-dimensional nonlinear hyperbolic systems in a Cartesian physical domain which is partitioned into a grid of rectangular subdomains. The main idea of the Hybrid scheme is to conjugate the spectral and WENO methods for solving problems with shock or high gradients such that the scheme adapts its solver spatially and temporally depending on the smoothness of the solution in a given subdomain. Built as a multi-domain method, an adaptive algorithm is used to keep the solutions parts exhibiting high gradients and discontinuities always inside WENO subdomains while the smooth parts of the solution are kept inside spectral ones, avoiding oscillations related to the well-known Gibbs phenomenon and increasing the numerical efficiency of the overall scheme. A higher order version of the multi-resolution analysis proposed by Harten is used to determine the smoothness of the solution in each subdomain. We also discuss interface conditions for the two-dimensional problem and the switching procedure between WENO and spectral subdomains. The Hybrid method is applied to the two-dimensional Shock-Vortex Interaction and the Richtmyer-Meshkov Instability (RMI) problems.

  • Keywords

Porous media nearly-analytic discretization three-component seismic wavefield anisotropy numerical dispersion.

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@Article{CiCP-1-548, author = {}, title = {Two-Dimensional Multi-Domain Hybrid Spectral-WENO Methods for Conservation Laws}, journal = {Communications in Computational Physics}, year = {2006}, volume = {1}, number = {3}, pages = {548--574}, abstract = {

The multi-domain hybrid Spectral-WENO method (Hybrid) is introduced for the numerical solution of two-dimensional nonlinear hyperbolic systems in a Cartesian physical domain which is partitioned into a grid of rectangular subdomains. The main idea of the Hybrid scheme is to conjugate the spectral and WENO methods for solving problems with shock or high gradients such that the scheme adapts its solver spatially and temporally depending on the smoothness of the solution in a given subdomain. Built as a multi-domain method, an adaptive algorithm is used to keep the solutions parts exhibiting high gradients and discontinuities always inside WENO subdomains while the smooth parts of the solution are kept inside spectral ones, avoiding oscillations related to the well-known Gibbs phenomenon and increasing the numerical efficiency of the overall scheme. A higher order version of the multi-resolution analysis proposed by Harten is used to determine the smoothness of the solution in each subdomain. We also discuss interface conditions for the two-dimensional problem and the switching procedure between WENO and spectral subdomains. The Hybrid method is applied to the two-dimensional Shock-Vortex Interaction and the Richtmyer-Meshkov Instability (RMI) problems.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7970.html} }
TY - JOUR T1 - Two-Dimensional Multi-Domain Hybrid Spectral-WENO Methods for Conservation Laws JO - Communications in Computational Physics VL - 3 SP - 548 EP - 574 PY - 2006 DA - 2006/01 SN - 1 DO - http://dor.org/ UR - https://global-sci.org/intro/article_detail/cicp/7970.html KW - Porous media KW - nearly-analytic discretization KW - three-component seismic wavefield KW - anisotropy KW - numerical dispersion. AB -

The multi-domain hybrid Spectral-WENO method (Hybrid) is introduced for the numerical solution of two-dimensional nonlinear hyperbolic systems in a Cartesian physical domain which is partitioned into a grid of rectangular subdomains. The main idea of the Hybrid scheme is to conjugate the spectral and WENO methods for solving problems with shock or high gradients such that the scheme adapts its solver spatially and temporally depending on the smoothness of the solution in a given subdomain. Built as a multi-domain method, an adaptive algorithm is used to keep the solutions parts exhibiting high gradients and discontinuities always inside WENO subdomains while the smooth parts of the solution are kept inside spectral ones, avoiding oscillations related to the well-known Gibbs phenomenon and increasing the numerical efficiency of the overall scheme. A higher order version of the multi-resolution analysis proposed by Harten is used to determine the smoothness of the solution in each subdomain. We also discuss interface conditions for the two-dimensional problem and the switching procedure between WENO and spectral subdomains. The Hybrid method is applied to the two-dimensional Shock-Vortex Interaction and the Richtmyer-Meshkov Instability (RMI) problems.

B. Costa, W. S. Don, D. Gottlieb & R. Sendersky. (2020). Two-Dimensional Multi-Domain Hybrid Spectral-WENO Methods for Conservation Laws. Communications in Computational Physics. 1 (3). 548-574. doi:
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