Improving the staggered grid Lagrangian hydrodynamics for modeling multi-material flows

TL;DR

This paper enhances the staggered grid Lagrangian hydrodynamics method for multi-material flow modeling by introducing dynamic remeshing around interfaces and an Euler-like flow to reduce oscillations, enabling more accurate simulations of complex deformations.

Contribution

It presents novel remeshing techniques for multi-material interfaces and an Euler-like flow correction to improve stability and accuracy in Lagrangian hydrodynamics simulations.

Findings

Effective prevention of mesh distortion during extreme deformations

Reduction of checkerboard oscillations in triangular mesh simulations

Successful modeling of complex multi-material interactions

Abstract

In this work, we make two improvements on the staggered grid hydrodynamics (SGH) Lagrangian scheme for modeling 2-dimensional compressible multi-material flows on triangular mesh. The first improvement is the construction of a dynamic local remeshing scheme for preventing mesh distortion. The remeshing scheme is similar to many published algorithms except that it introduces some special operations for treating grids around multi-material interfaces. This makes the simulation of extremely deforming and topology-variable multi-material processes possible, such as the complete process of a heavy fluid dipping into a light fluid. The second improvement is the construction of an Euler-like flow on each edge of the mesh to count for the "edge-bending" effect, so as to mitigate the "checkerboard" oscillation that commonly exists in Lagrangian simulations, especially the triangular mesh based simulations. Several typical hydrodynamic problems are simulated by the improved staggered grid Lagrangian hydrodynamic method to test its performance.