Application of Level Set / Immersed-Boundary Method to Simulate Fluid-Fluid and Fluid-Solid Problems

Free surface generated by a complex structure will be predicted in Cartesian grids by our proposed approach, which combines the immersed boundary and level set methods to model the solid-fluid and fluid-fluid interface, respectively. For accurately predicting the level set value, the spatial derivative terms in the pure advection equation are approximated by the seventh-order accurate upwinding combined compact difference scheme. For ensuring that the predicted interface has a finite thickness all the time, the re-initialization equation is used. In the immersed boundary method we proposed a differential based interpolation scheme at points near the solid boundaries. The discretized linear system of Poisson pressure equation is solved using the DFC (Divergence free compensated) method. Dam-break flow at the Reynolds number Re = 42792 is modeled to get the results that agree well with the experiment data. For the verification of the level set / immersed boundary method, water column collapsed over a submerged structure is also investigated.