TY - JOUR
T1 - Quasi-Lagrangian Acceleration of Eulerian Methods
AU - Igor Kliakhandler & Alexander Kurganov
JO - Communications in Computational Physics
VL - 4
SP - 743
EP - 757
PY - 2009
DA - 2009/06
SN - 6
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cicp/7703.html
KW - 
AB - <p style="text-align: justify;">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.</p>