Integrating discrete sub-grid filters with discretization-corrected particle strength exchange method for high Reynolds number flow simulations

Abstract

We present a discrete filter for subgrid-scale model, coupled with the discretization corrected particle strength exchange method, for the simulation of three-dimensional viscous incompressible flow at high Reynolds flows. The majority of turbulence modeling techniques, particularly in complex geometries, face significant computational challenges due to the difficulties in implementing three-dimensional (3D) convolution operations for asymmetric boundary conditions or curved domain boundaries. In this contribution, Taylor expansion is used to define differential operators corresponding to the convolution filter, so that the transfer function remains very close to the unity of sizeable displacement in wave number, making the filter a good approximation to the convolution one. A discrete Gaussian filter, in both fourth and second-order forms, was evaluated with varying ratios of particle spacing to the cutoff length. The impact of the filter's order and the ratio's value is thoroughly examined and detailed in the study. Additionally, the Brinkman penalization technique is employed to impose boundary conditions implicitly, allowing for efficient and accurate flow simulations around complex geometries without the need for modifying the numerical method or computational domain. The incompressible flow is governed by the entropically damped artificial compressibility equations allowing explicit simulation of the incompressible Navier–Stokes equations. The effectiveness of the proposed methodology is validated through several benchmark problems, including isotropic turbulence decay, turbulent channel flow, and flow around four cylinders arranged in a square in-line configuration, which are representative but not exhaustive of the full range of engineering applications. These test cases demonstrate the method's accuracy in capturing the intricate flow structures characteristic of high Reynolds number flows (up to 15k), highlighting its applicability to turbulence modeling.