Quasi-Lagrangian acceleration of Eeulerian methods
Document Type
Article
Publication Date
1-1-2009
Department
Department of Mathematical Sciences
Abstract
We present a simple and efficient strategy for the acceleration of explicit Eulerian methods for multidimensional hyperbolic systems of conservation laws. The strategy is based on the Galilean invariance of dynamic equations and optimization of the reference frame, in which the equations are numerically solved. The optimal reference frame moves (locally in time) with the average characteristic speed of the system, and, in this sense, the resulting method is quasi-Lagrangian. This leads to the acceleration of the numerical computations thanks to the optimal CFL condition and automatic adjustment of the computational domain to the evolving part of the solution. We show that our quasi-Lagrangian acceleration procedure may also reduce the numerical dissipation of the underlying Eulerian method. This leads to a significantly enhanced resolution, especially in the supersonic case. We demonstrate a great potential of the proposed method on a number of numerical examples.
Publication Title
Communications in Computational Physics
Recommended Citation
Kliakhandler, I.,
&
Kurganov, A.
(2009).
Quasi-Lagrangian acceleration of Eeulerian methods.
Communications in Computational Physics,
6(4), 743-757.
http://doi.org/10.4208/cicp.2009.v6.p743
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/14243
Publisher's Statement
© 2009 Global-Science Press. Publisher’s version of record: https://doi.org/10.4208/cicp.2009.v6.p743