We combine an Eulerian–Lagrangian approach and multiresolution analysis to develop unconditionally stable, explicit, multilevel methods for multidimensional linear hyperbolic equations. The derived schemes generate accurate numerical solutions even if large time steps are used. Furthermore, these schemes have the capability of carrying out adaptive compression without introducing mass balance error. Computational results are presented to show the strong potential of the numerical methods developed.
Published in Siam Journal on Scientific Computing, Volume 23, Issue 4, 2001, pages 1418-1438.
© Siam Journal on Scientific Computing 2001, Society for Industrial and Applied Mathematics
Wang, H., & Liu, J. (2001). Development of CFL-Free, Explicit Schemes for Multidimensional Advection-Reaction Equations. SIAM Journal On Scientific Computing, 23(4), 1418-1438. doi: 10.1137/s1064827500376181