An efficient method for two-fluid incompressible flows appropriate for the immersed boundary method

The accuracy, robustness, and performance of the proposed method is demonstrated by several validations against conventional approaches and experiments. The results verify that the pressure BCs are properly recovered along the IB solid interface, while a non-smooth pressure field is also allowed across the solid obstacle. The accuracy of the method was found to be 2nd-order, both in time and space. The performance of the proposed method is compared against the conventional approach using a multigrid iterative solver. The impact of the time-step on the accuracy of the constant coefficient approach is examined. Results show that the final speed-up strongly depends on the specific physical and numerical parameters such as the density ratio or the Reynolds number. It is demonstrated that for the range of parameters examined, speed-up factors of 100-10 can be achieved for density ratios of 10-1000 respectively.