This paper reviews recent developments in Arbitrary Lagrangian Eulerian (ALE) methods for
modeling high speed compressible multimaterial flows in complex geometry on general …

The paper presents a detailed review of the smooth particle hydrodynamics (SPH) method
with particular focus on its astrophysical applications. We start by introducing the basic ideas …

The purpose of this work is to propose a novel a posteriori finite volume subcell limiter
technique for the Discontinuous Galerkin finite element method for nonlinear systems of …

Computer simulation was first pioneered as a scientific tool in meteorology and nuclear
physics in the period following World War II, but it has grown rapidly to become …

This book describes the theoretical and computational aspects of the mimetic finite
difference method for a wide class of multidimensional elliptic problems, which includes …

The mimetic finite difference (MFD) method mimics fundamental properties of mathematical
and physical systems including conservation laws, symmetry and positivity of solutions …

This monograph provides an accessible introduction to the theory, and the large-scale
simulation methods currently used in radiation hydrodynamics, the study of the dynamics of …

The principal goal of all numerical algorithms is to represent as faithfully and accurately as
possible the underlying continuum equations to which a numerical solution is sought …

We present a new Lagrangian cell-centered scheme for two-dimensional compressible
flows. The primary variables in this new scheme are cell-centered, ie, density, momentum …

The numerical approximation of the Euler equations of gas dynamics in a
movingLagrangian frame is at the heart of many multiphysics simulation algorithms. In this …