An efficient fluid-solid coupling algorithm for single-phase flows

We present a simple and efficient fluid/solid coupling algorithm in two-spatial dimensions. In particular, we consider the numerical approximation of the Navier-Stokes equations on irregular domains and propose a novel approach for solving the projection step with Neumann boundary conditions on arbitrary shaped objects. This method is straightforward to implement and leads to a symmetric positive definite linear system for both the Projection step and for the implicit treatment of the viscosity. Both the density and the viscosity can be varying in space, which can serve as a basis for two-phase flows simulations. We demonstrate the accuracy of our method in in the L and L∞ norms. We apply this method to the simulation of a flow past a cylinder and show that our method can reproduce the known stable and unstable regimes as well as correct lift and drag forces. We also apply this algorithm to the coupling of flows with moving rigid bodies.