Year: 2017
Communications in Computational Physics, Vol. 22 (2017), Iss. 5 : pp. 1286–1308
Abstract
Moving mesh methods provide an efficient way of solving partial differential equations for which large, localised variations in the solution necessitate locally dense spatial meshes. In one-dimension, meshes are typically specified using the arclength mesh density function. This choice is well-justified for piecewise polynomial interpolants, but it is only justified for spectral methods when model solutions include localised steep gradients. In this paper, one-dimensional mesh density functions are presented which are based on a spatially localised measure of the bandwidth of the approximated model solution. In considering bandwidth, these mesh density functions are well-justified for spectral methods, but are not strictly tied to the error properties of any particular spatial interpolant, and are hence widely applicable. The bandwidth mesh density functions are illustrated in two ways. First, by applying them to Chebyshev polynomial approximation of two test functions, and second, through use in periodic spectral and finite-difference moving mesh methods applied to a number of model problems in acoustics. These problems include a heterogeneous advection equation, the viscous Burgers’ equation, and the Korteweg-de Vries equation. Simulation results demonstrate solution convergence rates that are up to an order of magnitude faster using the bandwidth mesh density functions than uniform meshes, and around three times faster than those using the arclength mesh density function.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2016-0246
Communications in Computational Physics, Vol. 22 (2017), Iss. 5 : pp. 1286–1308
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
-
Moving mesh finite difference solution of non-equilibrium radiation diffusion equations
Yang, Xiaobo | Huang, Weizhang | Qiu, JianxianNumerical Algorithms, Vol. 82 (2019), Iss. 4 P.1409
https://doi.org/10.1007/s11075-019-00662-5 [Citations: 1] -
A quasi-Lagrangian moving mesh discontinuous Galerkin method for hyperbolic conservation laws
Luo, Dongmi | Huang, Weizhang | Qiu, JianxianJournal of Computational Physics, Vol. 396 (2019), Iss. P.544
https://doi.org/10.1016/j.jcp.2019.06.061 [Citations: 14] -
Bandwidth-based mesh adaptation in multiple dimensions
Wise, Elliott S. | Cox, Ben T. | Treeby, Bradley E.Journal of Computational Physics, Vol. 371 (2018), Iss. P.651
https://doi.org/10.1016/j.jcp.2018.06.009 [Citations: 1] -
Moving mesh simulation of contact sets in two dimensional models of elastic–electrostatic deflection problems
DiPietro, Kelsey L. | Haynes, Ronald D. | Huang, Weizhang | Lindsay, Alan E. | Yu, YufeiJournal of Computational Physics, Vol. 375 (2018), Iss. P.763
https://doi.org/10.1016/j.jcp.2018.08.053 [Citations: 4]