A modified volume-of-fluid/hybrid Cartesian immersed boundary method for simulating free-surface undulation over moving topographies

An accurate numerical model, coupled with the modified volume-of-fluid method and the hybrid Cartesian immersed boundary method, has been developed to investigate the evolution of undulation of free surface influenced by moving topographies. The dynamic processes comprise topology changes of moving boundaries, at which the air-liquid interface and the solid-liquid interface are both involved. To accurately predict the topology changes along the air-liquid interface, a modified volume-of-fluid method is proposed. The resulting features of evolving surface wave and its possible amplitude amplification are mainly concerned. An optimal local advection scheme associated with the sub-grid resolution of interface tracking technique is developed in a semi-Lagrangian description. Additionally, the hybrid Cartesian immersed boundary method with bilinear interpolation enables to place solid bodies of arbitrary shape in fluid flows, while referring to the ease of mesh generation and its inherent simplicity to implement moving bodies on Cartesian grids. A second-order spatial accuracy is maintained as the two combined method is conducted. To show the accuracy and capability of the proposed model, a number of examples with increasing complexity of bottom boundary are well validated with the existing experimental data and numerical results. (C) 2018 Elsevier Ltd. All rights reserved.