A cartesian grid method for modeling multiple moving objects in 2D incompressible viscous flow

We present an efficient method for solving 2D incompressible viscous flows around multiple moving objects. Our method employs an underlying regular Cartesian grid to solve the system using a streamfunction–vorticity formulation and with discontinuities representing the embedded objects. The no-penentration condition for the moving geometry is satisfied by superposing a homogenous solution to the Poisson’s equation for the streamfunction. The no-slip condition is satisfied by generating vorticity on the surfaces of the objects. Both the initial Poisson solution and the evaluation of the homogenous solution require embedding irregular discontinuities in a fast Poisson solver. Computation time is dictated by the time required to do a fast Poisson solution plus solve an integral form of Laplace’s equation. There is no significant increase in computational cost if the geometry of the embedded objects is variable and moving relative to the underlying grid. We test the method against the canonical example of flow past a cylinder, and obtained new results on the flow and forces of two cylinders moving relative to each other.