DNS of square-cylinder flow using hybrid wavelet-collocation/volume-penalization method

The direct numerical simulation (DNS) of unsteady flow past a square-cylinder has a very high computational cost, even at moderately low Reynolds-numbers (Re), where the transition to a complex 3D wake occurs. In fact, the cylinder wake is unstable to two main spanwise disturbances that are referred to as “Mode A” and “Mode B” in the literature, similarly to what happens for circular cylinders. For the long-wavelengthMode A, the critical Re has been observed to be around 160, while the short-wavelengthMode B has been found to become unstable for Re≈ 190. The spanwise wavelengths of the above two modes are about 5.2 and 1.2 times the side length of the cross section, respectively [1]. In order to numerically predict the essential features of the transitional shedding flow past the cylinder, the extent of the computational domain in the homogeneous spanwise direction, where periodic boundary conditions are applied, must be sufficiently high to capture the evolution of the 3D disturbances. Furthermore, the numerical grid must be properly refined close to the body surface, to resolve the boundary layer, as well as in the wake region. The degrees of freedom of the solution and, thus, the associated computational cost can be drastically reduced by using adaptive numerical methods, where the spatially non-uniform grid is not prescribed a-priori but dynamically adapted following the flow evolution. In this study, the mesh adaptation is based on the wavelet decomposition of the velocity field, by automatically refining the grid where high gradients in the solution exist. The wavelet-based eddy-capturing approach [2] is extended to nonhomogeneous bluff-body flow, where the presence of the obstacle is mimicked by using the Brinkman volume-penalization method [3].