Toward a Simple, Accurate Lagrangian Hydrocode.

Abstract

Lagrangian hydrocodes play an important role in the computation of transient, compressible, multi-material flows. This research was aimed at developing a simply constructed cell-centered Lagrangian method for the Euler equations that respects multidimensional physics while achieving second-order accuracy. Algorithms that can account for the multidimensional physics associated with acoustic wave propagation and vorticity transport are needed in order to increase accuracy and prevent mesh imprinting. Many of the building blocks of traditional finite volume schemes, such as Riemann solvers and spatial gradient limiters, have their foundations in one-dimensional ideas and so were not used here. Instead, multidimensional point estimates of the fluxes were computed with a Lax-Wendroff type procedure and then nonlinearly modified using a temporal flux limiting mechanism.

The linear acoustic equations were used as a simplified test environment for the Lagrangian Euler system. Here Lax-Wendroff methods that exactly preserve vorticity were investigated and found to resist mesh imprinting. However, the dispersion properties of the schemes were poor and so third-order accurate vorticity preserving methods were developed to remedy the problem. The third-order methods guided the construction of a temporal limiting mechanism, which was then used in a vorticity preserving flux-corrected transport scheme. While the acoustic work was interesting in its own right, it also proved to be a useful stepping stone to Lagrangian hydrodynamics. The acoustics algorithms were extended to produce the Simple Lagrangian Method (SLaM). Standard test problems have shown that a first-order accurate version of the method is able to resist mesh imprinting and spurious vorticity despite its minimalistic structure. SLaM is capable of second-order accuracy with a simple parameter change and some preliminary work was done to extend the temporal flux limiting ideas from acoustics to the Lagrangian case. The limited SLaM method converges at second-order for smooth data and is able to capture shocks without producing large unphysical oscillations.