Computation of free-surface flows and fluid-object interactions with the CIP method based on adaptive meshless soroban grids

The CIP Method [J comput phys 61:261-268 1985; J comput phys 70:355-372, 1987; Comput phys commun 66:219-232 1991; J comput phys 169:556-593, 2001] and adaptive Soroban grid [J comput phys 194:57-77, 2004] are combined for computation of three- dimensional fluid-object and fluid-structure interactions, while maintaining high-order accuracy. For the robust computation of free-surface and multi-fluid flows, we adopt the CCUP method [Phys Soc Japan J 60:2105-2108 1991]. In most of the earlier computations, the CCUP method was used with a staggered-grid approach. Here, because of the meshless nature of the Soroban grid, we use the CCUP method with a collocated-grid approach. We propose an algorithm that is stable, robust and accurate even with such collocated grids. By adopting the CIP interpolation, the accuracy is largely enhanced compared to linear interpolation. Although this grid system is unstructured, it still has a very simple data structure.