A frame-invariant vector limiter for flux corrected nodal remap in arbitrary Lagrangian–Eulerian flow computations

Abstract

This article describes a frame-invariant vector limiter for Flux-Corrected Transport (FCT) numerical methods. Our approach relies on an objective vector projection, and, because of its intrinsic structure, the proposed approach can be generalized with ease to higher-order tensor fields.The proposed concept is applied to nodal finite element formulations and the so-called algebraic FCT paradigm, but the ideas pursued here are very general and also apply to more general instantiations of flux-corrected transport.Specifically, we consider the arbitrary Lagrangian–Eulerian (ALE) equations of compressible inviscid flows. In addition to the geometric conservation law (GCL) and the local extreme diminishing (LED) property of the original scalar limiters, the proposed approach ensures frame invariance (objectivity) for vectors. Particularly, we use an ALE strategy based on a two-stage, Lagrangian plus mesh remap (data transfer based on conservative interpolation), in which remap and limiting are performed in a synchronized way. The proposed approach is however of general applicability, is not limited to a specific ALE implementation, and can easily be generalized to computations with standard (monolithic) ALE or Eulerian reference frames.The significance of the frame-invariant limiter for vectors is demonstrated in computations of compressible materials under extreme load conditions. Extensive testing in two and three dimensions demonstrates that the proposed limiter greatly enhances the robustness and reliability of the existing methods under typical computational scenarios.