Large eddy simulation of Rayleigh-Taylor instability using the arbitrary Lagrangian-Eulerian method

Abstract

This research addresses the application of a large eddy simulation (LES) to Arbitrary Lagrangian Eulerian (ALE) simulations of Rayleigh-Taylor instability.-First, ALE simulations of simplified Rayleigh-Taylor instability are studied. The advantages of ALE over Eulerian simulations are shown. Next, the behavior of the LES is examined in a more complicated ALE simulation of Rayleigh-Taylor instability. The effects of eddy viscosity and stochastic backscatter are examined. The LES is also coupled with ALE to increase grid resolution in areas where it is needed. Finally, the methods studied above are applied to two sets of experimental simulations. In these simulations, ALE allows the mesh to follow expanding experimental targets, while LES can be used to mimic the effect of unresolved instability modes.

A tensor artificial viscosity using a finite element approach

“…The numerical shock hydro experiments were conducted in the framework of an existing ALE hydro code, cf. [18,19], in order to showcase the plug-in character of the proposed tensor artificial viscosity. Therefore, the quality of the full simulation results below is limited by the inaccuracies of the existing staggered-grid method, such as the HEMP operator for computing the pressure gradient and the approach for computing nodal momentum using simple nodal masses.…”

“…The variational approximation of the generalized viscous force term in (16)- (18) requires the gradients of the basis functions. These are given in Table 4.…”

“…Given the previous definitions, we can discretize the variational form of the generalized viscous force term from (16)- (18). For every zone in our computational mesh, we calculate a finite element ''stiffness" matrix of the form…”

“…Most modern hydro codes are of the arbitrary Lagrangian-Eulerian (ALE) [18] variety; where severe grid distortion is corrected by a mesh relaxation algorithm followed by a remapping of the state variables onto the new grid. However, such mesh relaxation approaches will not address the issue of symmetry preservation if the underlying methods used in the Lagrange step do not respect the symmetry.…”