Utilization of high order DRP-type schemes and large eddy simulation based on relaxation filtering for turbulent gas flow computations in the case of Taylor-Green vortex breakdown

The paper considers Large Eddy Simulation based on the relaxation filtering technique (LES-RF) and implemented by high order DRP-type schemes. This technique is an alternative to the classical eddy-viscosity-type methods. It can be expressed as the composition of a high-order and high-resolution numerical scheme and an explicit selective filtering, which dissipates the energy from small scales poorly resolved by the scheme. With this technique, simulations of the Taylor-Green vortex breakdown problem have been performed for Reynolds numbers 1600 and 3000 and different computational meshes varying from 64 3 to 256 3 cells. The problem of periodic three-dimensional flow decaying to small-scale turbulent structures because of the inherent instability has been studied. The simulation employs a compressible formulation at small Mach number (Ma = 0.09) for minimization of compressibility effects. Filter strength, the only free parameter in the scheme, is varied as well. The obtained results are in good agreement with the Direct Numerical Simulations performed by other authors. It has been found that the filter strength, if taken sufficiently high and at a fixed time step size chosen from the condition CFL ~ 0.45, has no marked effect on the results. However, the quality of the results begins to degrade if the time step size decreases significantly. This indicates the need for modification of the scheme for practical applications.