Remap for ALE Hydrodynamics via Direct Interpolation and Constraint Optimization

Abstract

This work presents an optimization-based remap approach for arbitrary Lagrangian-Eulerian (ALE) hydrodynamics that preserves sharp features and physical bounds while conserving global quantities such as volume, mass, momentum, and total energy. Achieving these properties is the main challenge in remap methods. The presented approach is well-suited for high-order finite element (FE) discretizations and ALE methods that allow for large, purely Lagrangian displacements between successive remeshing and remapping steps. Recent advances in parallel, GPU-capable interpolation routines enable the initial transfer of all fields via direct physical-space interpolation, avoiding computationally costly and diffusive pseudo-transient PDE-based advection. The interpolation produces bounded fields with minimal numerical diffusion. However, it may violate the desired conservation of global properties. Thus, a subsequent optimization step restores conservation while preserving physical bounds. The presented method provides minimally diffusive remapping of finite element fields of arbitrary order. Moreover, it directly remaps quantities defined at integration points, eliminating the need for projection onto finite element spaces. The approach also mitigates typical challenges associated with synchronizing primal variables and conserved quantities in advection-based remap methods. The proposed optimization-based remap method is evaluated using standard two- and three-dimensional remap benchmarks and full ALE hydrodynamics simulations.