A balanced-force algorithm for two-phase flows

Numerical methods for imposing body forces in two-phase flow simulations are discussed. Numerical schemes are presented to avoid the inaccurate solutions that result from inconsistent implementation of forces. First, the momentum equations are discretized so that they accurately accommodate the discontinuity in fluid properties at an interface. Consistent numerical estimations for different body forces such as interfacial (including Marangoni), gravity and electromagnetic forces are discussed. Then, it is shown that the standard pressure–velocity coupling scheme for collocated algorithms is not sufficient for multiphase flows, and therefore a new pressure–velocity coupling is devised and tested for both single and two-phase flows. Finally, to advect the level set function, a cost effective fifth-order WENO method is developed. These formulations are accurate and efficient both for uniform and non-uniform meshes. Several test cases are presented and compared with a standard implementation of body forces to demonstrate the efficiency of the proposed algorithm.