Large eddy simulations of wall-bounded flows using a simplified immersed boundary method and high-order compact schemes

This paper presents a solution algorithm based on an immersed boundary (IB) method that can be easily implemented in high-order codes for incompressible flows. The time integration is performed using a predictor-corrector approach, and the projection method is used for pressure-velocity coupling. Spatial discretization is based on compact difference schemes and is performed on half-staggered meshes. A basic algorithm for body-fitted meshes using the aforementioned solution method was developed by A. Tyliszczak (see article A high-order compact difference algorithm for half-staggered grids for laminar and turbulent incompressible flows in Journal of Computational Physics) and proved to be very accurate. In this paper, the formulated algorithm is adapted for use with the IB method in the framework of large eddy simulations. The IB method is implemented using its simplified variant without the interpolation (stepwise approach). The computations are performed for a laminar flow around a 2D cylinder, a turbulent flow in a channel with a wavy wall, and around a sphere. Comparisons with literature data confirm that the proposed method can be successfully applied for complex flow problems. The results are verified using the classical approach with body-fitted meshes and show very good agreement both in laminar and turbulent regimes. The mean (velocity and turbulent kinetic energy profiles and drag coefficients) and time-dependent (Strouhal number based on the drag coefficient) quantities are analyzed, and they agree well with reference solutions. Two subfilter models are compared, ie, the model of Vreman (see article An eddy-viscosity subgrid-scale model for turbulent shear flow: algebraic theory and applications in Physics and Fluids) and sigma model (Nicoudet al, see article Using singular values to build a subgrid-scale model for large eddy simulations in Physics and Fluids). The tests did not reveal evident advantages of any of these models, and from the point of view of solution accuracy, the quality of the computational meshes turned out to be much more important than the subfilter modeling.