Local time stepping applied to implicit-explicit methods for hyperbolic systems.

*(English)*Zbl 1204.35017Several algorithms are described in detail to compute the solution of a one-dimensional multiphase flow, in the framework of a Lagrange-Euler projection formulation of the equations. The equations constitute highly nonlinear conservation laws and address physical problems where slow kinetic waves coexist with fast acoustic ones. Both explicit and semi-implicit adaptive finite volume schemes (on nonuniform, moving or fixed meshes) are presented, and for each one, two adaptive enhancement methods are described. The first one is the standard multiresolution method already implemented in more complicated cases. The second technique is a further enhancement to the first one: the local time stepping (LTS), which is the main goal of the paper. The robustness and efficiency of both is checked by performing a parameter study. The benefits of the LTS enhancement in terms of computing time are very encouraging for both the explicit and implicit case.

Reviewer: Argiris I. Delis (Chania)

##### MSC:

35A35 | Theoretical approximation in context of PDEs |

35L65 | Hyperbolic conservation laws |

65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |