Comparative study of high order methods for subsonic turbulence simulation with stochastic forcing

Abstract

A class of spatially seventh-order nonlinear filter methods with adaptive dissipation control developed by Yee & Sjögreen [1, 2] is tested on three-dimensional subsonic turbulence simulations with stochastic forcing. The Euler equations are solved using the Strang operator splitting of the homogeneous part of the equations and the stochastic forcing term, with an ODE solver used to integrate the latter. Both Ducros et al. and Kennedy-Gruber skew-symmetric split formulations of the inviscid flux derivatives are considered to minimize the use of numerical dissipation. The nonlinear filter methods are shown to be numerically stable for this application at least up to an rms Mach number of 0.6. The performance and accuracy of this numerical approach are compared with those of second order TVD and fifth and seventh order WENO methods. The nonlinear filter methods are shown to be substantially more computationally efficient, delivering a superior spectral bandwidth compared to the standalone TVD and WENO methods.