High-Order Immersed-Boundary Simulation and Error Analysis for Flow Around a Porous Structure

In this study, a two-dimensional cylinder or a three-dimensional sphere is used as an example for a porous structure in the flow field. Immersed-boundary (IB) methods have been used to simulate flow around a cylinder/sphere, which is a typical problem to verify the effectiveness and accuracy of the methods. The flow was previously simulated by modeling the solid obstacles as a porous medium with flow resistivity. The current study makes an extension of the previous IB method. The fifth order WENO-Z scheme and third order Runge-Kutta method are used for space and time discretization, respectively. The Navier–Stokes equation is used for the fluids region and a ZK type of source term is applied in place of the forcing term for the porous domain. These two equations are solved simultaneously. Thus, there is no need to specify the interface conditions directly. In addition, the errors are estimated in terms of the flow resistivity that is zero for fluid, finite for porous, and infinite for non-porous solid. The aim of this paper is to establish estimates of the error induced by such an IB method. Numerical tests are performed to confirm the improvement of this method.