This paper presents robust discontinuous Galerkin methods for the incompressible Navier-Stokes equations on moving meshes. High-order accurate arbitrary Lagrangian-Eulerian formulations are proposed in a unified framework both monolithic as well projection or splitting-type solvers. The is flexible, allows implicit and explicit of convective term, adaptive time-stepping. with ALE transport term...

This paper develops the structure-preserving finite volume weighted essentially non-oscillatory (WENO) hybrid schemes for shallow water equations under arbitrary Lagrangian-Eulerian (ALE) framework, dubbed as ALE-WENO schemes. The WENO reconstruction is adopted on moving meshes, which distinguishes smooth, non-smooth, and transition stencils by a simple smoothness detector. To maintain positivi...

In this work we present a high-accurate discretization to solve the compressible Navier-Stokes equations using an Arbitrary Lagrangian-Eulerian meshless method (SPH-MLS), which can be seen as general formulation that includes some well-known meshfree methods particular case. The is based on use of Moving Least Squares (MLS) approximants weight functions Galerkin and accurate discretize convecti...

The Eulerian and Lagrangian second-order perturbation theories are solved explicitly in closed forms in 6= 1 and 6= 0 Friedmann-Lemâ tre models. I explicitly write the secondorder theories in terms of closed one-dimensional integrals. In cosmologically interested cases ( = 0 or + = 1), they reduce to elementary functions or hypergeometric functions. For arbitrary and , I present accurate tting ...

Abstract. This work is concerned with the simulation of compressible flow in time dependent domains. We present an ALE (Arbitrary Lagrangian-Eulerian) formulation of the Navier-Stokes equations describing compressible flow, discretize them in space by the discontinous Galerkin method and introduce a semi-implicit linearized time stepping for the numerical solution of the complete problem. We pr...