A New Boundary Condition Framework for Particle Method by Using Local Regular-Distributed Background Particles—The Special Case for Poisson Equation

Abstract

To improve the accuracy of solving the Poisson equation and the efficiency of handling complex boundary shapes in the particle method, this paper proposes a Local Regular-distributed Background Particles (LRBP) as an alternative to traditional boundary handling methods. This method avoids the trouble of arranging virtual particles by introducing background particles, making it suitable for problems with complex boundary shapes. In addition, based on the framework of the weak form Poisson equation, the boundary conditions are easily applied, and the calculations are more accurate. Furthermore, this method allows for different interpolation methods inside and outside the boundary, providing flexibility and versatility. These characteristics are well demonstrated in the validation examples, which indicate its potential to solve complex flow problems.