An Eulerian formulation of immersed method for moving interfaces with tangential stretching

The forces generated by moving interfaces usually include the parts due to tangential stretching. We derive the evolution equation for the tangential stretching, which then forms the basis for an Eulerian formulation based on level set functions. The jump conditions are then derived using the level set and stretch functions. The derived jump conditions under this Eulerian formulation are clean. This makes possible a local level set method for immersed interface method to simulate membranes or vesicles where the tangential forces are present. This is a continuation of one piece of my work during my Ph.D. study.