Artificial Force Free Boundaries: Particle-Based Fluid Simulation with Implicit Surfaces

Abstract

We develop improved boundary conditions for particle-based fluid simulation with implicit surfaces. The implicit surfaces are well suited to represent complex obstacles, specifically, when the shape of the obstacles is smooth or varies with time. In existing particle-based fluid simulation with implicit surfaces, an artificially defined force is applied. Although this artificial force successfully enforces non-penetration boundary conditions to the obstacles, some stability and low-accuracy issues remain. The instability of stacking and clustering, and low-accuracy pressure fields occur because of the artificially defined force and incompatibility of the effective radius when using particle methods. This study presents an improved boundary treatment for implicit surfaces. The proposed boundary conditions follow only the formulation of particle-based methods and do not require any artificial force. When we apply the discretization techniques of particle-based methods, the governing equations are also considered on implicit surfaces. Given that the proposed treatment of boundary conditions is applicable to any particle-based method, we adapted our formulation to both explicit and implicit schemes. The results of the test show that our method does not suffer from instability near the boundary in comparison with existing methods. Moreover, the proposed method can also produce better pressure fields than the existing ones.