2019/04/08 by Giacomo Albi, Giacomo Dimarco, Albi, Giacomo +3
Mathematics · Engineering · #Numerical methods for differential equations #Advanced Numerical Methods in Computational Mathematics #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1904.03865
We consider the development of high order space and time numerical methods\nbased on Implicit-Explicit (IMEX) multistep time integrators for hyperbolic\nsystems with relaxation. More specifically, we consider hyperbolic balance laws\nin which the convection and the source term may have very different time and\nspace scales. As a consequence the nature of the asymptotic limit changes\ncompletely, passing from a hyperbolic to a parabolic system. From the\ncomputational point of view, standard numerical methods designed for the\nfluid-dynamic scaling of hyperbolic systems with relaxation present several\ndrawbacks and typically lose efficiency in describing the parabolic limit\nregime. In this work, in the context of Implicit-Explicit linear multistep\nmethods we construct high order space-time discretizations which are able to\nhandle all the different scales and to capture the correct asymptotic behavior,\nindependently from its nature, without time step restrictions imposed by the\nfast scales. Several numerical examples confirm the theoretical analysis.\n