High-order semi-Lagrangian kinetic scheme for compressible turbulence

TL;DR

This paper introduces a novel semi-Lagrangian lattice Boltzmann method for 3D compressible turbulence that allows larger time steps without stability issues, enabling more efficient simulations of turbulent flows.

Contribution

The paper presents a 3D semi-Lagrangian lattice Boltzmann method using only 45 velocities, overcoming previous dimensional and stability limitations.

Findings

Accurately captures shocks and turbulence in 3D without additional stabilization.

Allows time steps up to two orders of magnitude larger than existing methods.

Enables fully explicit simulations of compressible turbulence constrained only by physics.

Abstract

Turbulent compressible flows are traditionally simulated using explicit time integrators applied to discretized versions of the Navier-Stokes equations. However, the associated Courant-Friedrichs-Lewy condition severely restricts the maximum time step size. Exploiting the Lagrangian nature of the Boltzmann equation's material derivative, we now introduce a feasible three-dimensional semi-Lagrangian lattice Boltzmann method (SLLBM), which circumvents this restriction. While many lattice Boltzmann methods for compressible flows were restricted to two dimensions due to the enormous number of discrete velocities in three dimensions, the SLLBM uses only 45 discrete velocities. Based on compressible Taylor-Green vortex simulations we show that the new method accurately captures shocks or shocklets as well as turbulence in 3D without utilizing additional filtering or stabilizing techniques, even when the time step sizes are up to two orders of magnitude larger compared to simulations in the literature. Our new method therefore enables researchers for the first time to study compressible turbulent flows by a fully explicit scheme, whose range of admissible time step sizes is only dictated by physics, while being decoupled from the spatial discretization.