| Abstract: | We develop the immersed interface method (IIM) to simulate a two-fluid flow of two immiscible fluidswith different density and viscosity. Due to the surface tension and the discontinuous fluid properties,the two-fluid flow has nonsmooth velocity and discontinuous pressure across the moving sharp interfaceseparating the two fluids. The IIM computes the flow on a fixed Cartesian grid by incorporatinginto numerical schemes the necessary jump conditions induced by the interface.We present how to compute these necessary jump conditions from the analytical principal jumpconditions derived in [Xu, DCDS, Supplement 2009, pp. 838-845]. We test our method on some canonicaltwo-fluid flows. The results demonstrate that the method can handle large density and viscosity ratios,is second-order accurate in the infinity norm, and conserves mass inside a closed interface. |
