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

We present a new approach for multi-material arbitrary Lagrangian--Eulerian (ALE)
hydrodynamics simulations based on high-order finite elements posed on high-order …

The remap phase in arbitrary Lagrangian–Eulerian (ALE) hydrodynamics involves the
transfer of field quantities defined on a post‐Lagrangian mesh to some new mesh, usually …

Abstract Three-temperature (3T), unstructured-mesh, non-equilibrium radiation
hydrodynamics (RHD) code have been developed for the simulation of intense thermal …

This paper is concerned with the development of general-purpose algebraic flux correction
schemes for continuous (linear and multilinear) finite elements. In order to enforce the …

This book focuses on the interplay between Eulerian and Lagrangian conservation laws for
systems that admit physical motivation and originate from continuum mechanics. Ultimately …

We present a new optimization-based property-preserving algorithm for passive tracer
transport. The algorithm utilizes a semi-Lagrangian approach based on incremental …

Strongly coupled nonlinear phenomena such as those described by Earth system models
(ESMs) are composed of multiple component models with independent mesh topologies …

We develop a fast, efficient and accurate optimization-based algorithm for the high-order
conservative and local-bound preserving remap (constrained interpolation) of a scalar …

This work introduces a single-stage, single-step method for the compressible Euler
equations that is provably positivity-preserving and can be applied on both Cartesian and …