Numerical methods for problems with moving interfaces and irregular geometries

In this article, we present a unified approach to identify an interface and model the associated interface conditions. Interface includes but is not limited to (1) fluid-fluid interface, (2) fluid-solid interface and (3) physical boundaries and/or internal interfaces. We identify an interface using the distance function. The continuum surface force model is used to model surface tension forces at fluidfluid interfaces. This model is then extended to model surface conditions at fluidsolid interfaces and physical boundaries. Capabilities of the current approach are demonstrated using a few test cases. Comparisons with available solutions show that the current approach produces accurate solutions.