A wall-modeled immersed boundary/large eddy simulation method and its application to simulating heart valve flows

Abstract

In this work, a wall-modeled immersed boundary (IB)/large eddy simulation (LES) method is extended to the simulation of moving-boundary flows. The used non-equilibrium algebraic wall model is based on an assumed velocity profile, the coefficients of which are determined from physical constraints provided by the full turbulent-boundary-layer equations. To implement the wall model in an IB method named the local domain-free discretization (DFD) method, a local coordinate system fixed on the moving body is introduced. Thus, wall modeling is transformed into a local two-dimensional problem and the complexity of implementation of the wall model is reduced. In the present LES-DFD method, the tangential velocity at an exterior dependent node is determined via wall shear stress prescribed by the wall model. To reduce computational cost for simulating an internal flow with moving boundaries, the stationary boundaries are handled by the body-fitted-grid method and the moving boundaries by the local DFD method. There is no need of an auxiliary grid for solving the non-equilibrium algebraic wall model. Therefore, the inbuilt advantage of an IB method can be retained when simulating moving-boundary problems, and the economy of equilibrium wall models can also be preserved. The present method is applied to simulating the pulsatile flows through a bileaflet mechanical heart valve implanted in a model aorta. The predicted results show an acceptable agreement with the referenced experimental measurements or numerical results at much higher resolution and the applicability of the non-equilibrium wall model to LES of complex moving-boundary flows is verified.