Accurate conservative remapping (rezoning) for arbitrary Lagrangian-Eulerian computations
SIAM Journal on Scientific and Statistical Computing
An efficient, accurate, simple ALE method for nonlinear finite element programs
Computer Methods in Applied Mechanics and Engineering
Momentum advection on a staggered mesh
Journal of Computational Physics
Computational methods in Lagrangian and Eulerian hydrocodes
Computer Methods in Applied Mechanics and Engineering
Computational algorithms for aerodynamic analysis and design
Applied Numerical Mathematics
MPDATA: a finite-difference solver for geophysical flows
Journal of Computational Physics
Incremental remapping as a transport&slash;advection algorithm
Journal of Computational Physics
Reference Jacobian optimization-based rezone strategies for arbitrary Lagrangian Eulerian methods
Journal of Computational Physics
Flux correction tools for finite elements
Journal of Computational Physics
Second-order sign-preserving conservative interpolation (remapping) on general grids
Journal of Computational Physics
An efficient linearity-and-bound-preserving remapping method
Journal of Computational Physics
A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian-Eulerian methods
Journal of Computational Physics
A Cell-Centered Lagrangian Scheme for Two-Dimensional Compressible Flow Problems
SIAM Journal on Scientific Computing
Explicit and implicit FEM-FCT algorithms with flux linearization
Journal of Computational Physics
ReALE: A reconnection-based arbitrary-Lagrangian-Eulerian method
Journal of Computational Physics
Journal of Computational Physics
Failsafe flux limiting and constrained data projections for equations of gas dynamics
Journal of Computational Physics
Journal of Computational Physics
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This article describes a conservative synchronized remap algorithm applicable to arbitrary Lagrangian-Eulerian computations with nodal finite elements. In the proposed approach, ideas derived from flux-corrected transport (FCT) methods are extended to conservative remap. Unique to the proposed method is the direct incorporation of the geometric conservation law (GCL) in the resulting numerical scheme. It is shown here that the geometric conservation law allows the method to inherit the positivity preserving and local extrema diminishing (LED) properties typical of FCT schemes. The proposed framework is extended to the systems of equations that typically arise in meteorological and compressible flow computations. The proposed algorithm remaps the vector fields associated with these problems by means of a synchronized strategy. The present paper also complements and extends the work of the second author on nodal-based methods for shock hydrodynamics, delivering a fully integrated suite of Lagrangian/remap algorithms for computations of compressible materials under extreme load conditions. Extensive testing in one, two, and three dimensions shows that the method is robust and accurate under typical computational scenarios.