报告地点：行健楼学术活动室526
邀请人：陈金如教授
摘要： We develop the structure-preserving Lagrangian-Eulerian discontinuous Galerkin (ALE-DG) methods for a class of hyperbolic conservation laws with source term, which can preserve a general hydrostatic equilibrium state and positivity-preserving property under a suitable time step at the same time. Such equations mainly include the shallow water equations with non-flat bottom topography and the Euler equations with gravitation. By introducing well-balanced numerical fluxes and corresponding source term approximations, we established well-balanced schemes. We also discuss about the weak positivity property of the proposed schemes, and how the positivity-preserving limiter can be applied to enforce the positivity-preserving property effectively. Numerical examples have been provided not only to demonstrate the good properties but also to show the advantages on moving mesh.
