A High-Order Shifted Interface Method for Lagrangian Shock Hydrodynamics

TL;DR

This paper introduces a high-order shifted interface method for Lagrangian shock hydrodynamics that accurately tracks curved material interfaces using level-set functions, improving stability and precision in multi-dimensional simulations.

Contribution

It combines the Shifted Interface Method with high-order finite elements to precisely represent moving interfaces without cut cell issues in Lagrangian hydrodynamics.

Findings

Accurate interface tracking in multi-dimensional simulations.

Improved numerical stability and matrix conditioning.

Validated performance on standard benchmarks.

Abstract

We present a new method for two-material Lagrangian hydrodynamics, which combines the Shifted Interface Method (SIM) with a high-order Finite Element Method. Our approach relies on an exact (or sharp) material interface representation, that is, it uses the precise location of the material interface. The interface is represented by the zero level-set of a continuous high-order finite element function that moves with the material velocity. This strategy allows to evolve curved material interfaces inside curved elements. By reformulating the original interface problem over a surrogate (approximate) interface, located in proximity of the true interface, the SIM avoids cut cells and the associated problematic issues regarding implementation, numerical stability, and matrix conditioning. Accuracy is maintained by modifying the original interface conditions using Taylor expansions. We demonstrate the performance of the proposed algorithms on established numerical benchmarks in one, two and three dimensions.