A Nonlocal Formulation for Weakly Compressible Fluid

Abstract

In this paper, we propose a nonlocal formulation for both solid and weakly compressible fluid. The nonlocal fluid formulation is based on the nonlocal interaction of each material point with its neighbors, which is analogous to the peridynamic theory, a nonlocal formulation for solid. By considering the direction of the interaction, the horizon and dual-horizon are defined, and the dual property between horizon and dual-horizon is proved. The nonlocal divergence is introduced, which enables to derive the nonlocal interaction with the local formulation. The formulations allow the varying horizon size and satisfy the conservation of linear momentum, angular momentum, and energy at the same time. Two numerical examples are tested to verify the accuracy of the current method.