A Non-Stiff Boundary Integral Method for 3D Porous Media Flow with Surface Tension

An efficient, non-stiff boundary integral method for 3D porous media flow with surface tension is presented. Surface tension introduces high order (i.e., high derivative) terms into the evolution equations, which leads to severe stability constraints for explicit time-integration methods. Furthermore, the high order terms appear in nonlocal operators, making the application of implicit methods difficult. Our algorithm employs a special representation of the interface which enables efficient application of implicit time-integration methods via a small-scale decomposition. The algorithm is found to be effective at eliminating the severe time-step constraint that plagues explicit time-integration methods.