Seminario de Matemática Aplicada: Invariant domain preserving ALE approximation of Euler equations

Conferenciante: Laura Saavedra Lago. Universidad Politécnica de Madrid Arbitrary Lagrangian Eulerian (ALE) techniques mix the advantages of classical Lagrangian hydrodynamics methods while minimizing their shortcomings. We have developed ALE methods to solve nonlinear hyperbolic systems while preserving invariant domains. Our ALE methods are based on continuous finite elements and explicit time stepping and are stabilized by means of graph-based artificial viscosity. First, we propose a first-order artificial viscosity that does not require any ad hoc parameters and results in precise invariant domain properties and entropy inequalities. Second, we describe a high-order method that preserves the invariant domains by combining the first-order method with an entropy-consistent high-order method via a convex limiting process. In the first part of this talk, I will describe a version of the second-order ALE scheme for the Euler equations, focusing on computational and ALE motion aspects. In the second part of the talk, building upon the previously established discretization framework, I will introduce an explicit Lagrangian approximation technique for the compressible Euler equations. This method is invariant domain preserving and exactly mass conserving. I will illustrate numerically the robustness of those methods on various benchmark problems. https://www.usc.gal/gl/departamento/matematica-aplicada/eventos/conferencia-laura-saavedra-lago