| Summary: | Computational fluid dynamics has been widely used in the design and analysis of various fluid systems. The proper treatment of boundary conditions is crucial for the accurate simulation of fluid flow. However, in particle methods, such as smoothed particle hydrodynamics method and moving particle semi-implicit method, the treatment of boundary conditions has been a challenging problem. In this paper, starting from the incompressibility condition, we present a new theory for the unified treatment of both rigid bodies and wall boundaries, which allows the strong coupling of rigid bodies and incompressible fluids. Because the boundary models are based on signed distance functions and do not use particles, these models can avoid several problems, such as resolution dependence of particle representations, and unavoidable unevenness of surfaces. We also provide a way to efficiently handle rigid-body boundaries and wall boundaries without particles by finding the fundamental boundary weight function that does not change with time. Several numerical examples are presented to demonstrate the capability of our models and to compare them with theoretical and experimental results.
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