Physics-driven complex relaxation for multi-body systems of SPH method

Abstract

In the smoothed particle dynamics (SPH) method, the characteristics of a target particle are interpolated based on the information from its neighboring particles. Consequently, a uniform initial distribution of particles significantly enhances the accuracy of SPH calculations. This aspect is particularly critical in Eulerian SPH, where particles are stationary throughout the simulation. To address this, we introduce a physics-driven complex relaxation method for multi-body systems. Through a series of two-dimensional and three-dimensional case studies, we demonstrate that this method is capable of achieving a globally uniform particle distribution, especially at the interfaces between contacting bodies, and ensuring improved zero-order consistency. Moreover, the effectiveness and reliability of the complex relaxation method in enhancing the accuracy of physical simulations are further validated.

Figures (25)

• Figure 1: Geometric boundary analysis after importing airfoil and its external flow field with the same boundary into the SPH solver. In the CAD stage, the airfoil and its external fluid field shares the same boundary. Although the same higher resolution $\Delta x = L/1000$ is used for discretization, due to the discrete origin points of the airfoil (the leading edge) and the discrete origin point of the external flow field (lower left corner of the calculation domain ) are different, resulting in a small gap at the trailing edge of the airfoil between the solid body and the fluid body. Note that the solid line is the geometric boundary of the inner solid body, while the dashed line is that of the outer fluid body.
• Figure 2: An illustration of surface bounding method zhu2021cad.
• Figure 3: ‘Static confinement’ boundary condition for completing kernel support of surface particles. The blue and white cells with yellow stars have partial or full volume contributing to level-set kernel support for the target red particle.
• Figure 4: Surface profiles of the airfoil with $\Delta x = L/1000$. The orange line is the geometric boundary of the inner body, while the blue line is that of the outer body. It can be seen that there is a distinct gap at the trailing edge after the two bodies are parsed.
• Figure 5: The illustration of Boolean operations on geometry: the orange line in the left picture is the geometric boundary of the inner body, while the blue line is that of the outer boundary of the outer body. Through the subtract operation, the complete geometric boundary of the outer body can be obtained as the right picture.