The Immersed Interface Method for Non-Smooth Rigid Objects in Incompressible Viscous Flows (Communications in Computational Physics, 2020)
In the immersed interface method, an object in a flow is formulated as a singular force, and jump conditions caused by the singular force are incorporated into numerical schemes to compute the flow. Previous development of the method consideredonly smooth objects. We here extend the method to handle non-smooth rigid objectswith sharp corners in 2D incompressible viscous flows. We represent the boundary ofan object as a polygonal curve moving through a fixed Cartesian grid. We computenecessary jump conditions to achieve boundary condition capturing on the object. Weincorporate the jump conditions into finite difference schemes to solve the flow on theCartesian grid. The accuracy, efficiency and robustness of our method are tested usingcanonical flow problems. The results demonstrate that the method has second-orderaccuracy for the velocity and first-order accuracy for the pressure in the infinity norm,and is extremely efficient and robust to simulate flows around non-smooth complexobjects.
Keywords: The immersed interface method; boundary condition capturing; non-smooth complex rigid objects; jump conditions.