Quasi-Lagrangian Acceleration of Eulerian Methods (Communications in Computational Physics, 2009)
We present a simple and efficient strategy for the acceleration of explicit Eulerianmethods for multidimensional hyperbolic systems of conservation laws. Thestrategy is based on the Galilean invariance of dynamic equations and optimization ofthe reference frame, in which the equations are numerically solved. The optimal referenceframe 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 accelerationof the numerical computations thanks to the optimal CFL condition and automaticadjustment of the computational domain to the evolving part of the solution. We showthat our quasi-Lagrangian acceleration procedure may also reduce the numerical dissipationof the underlying Eulerian method. This leads to a significantly enhancedresolution, especially in the supersonic case. We demonstrate a great potential of theproposed method on a number of numerical examples.