负压梯度下自由 动模拟的无网格粒 法Dirichlet (边界

Dirichlet boundary conditions for the free-surface are normally imposed through direct assignment in meshless particle methods. The discretization error caused by the disordered particle distribution is generally ignored. Since it is especially difficult to calculate convergence under the negative pressure gradient, to improve the calculation accuracy and stability near the free surface, this paper proposes a Dirichlet boundary condition assignment method based on the virtual boundary. Using the moving particle semi-implicit method, polynomial fitting is carried out for free-surface particles with the least square method. The fitting curve is taken as the virtual boundary, and the deviation vector from the free-surface particle to the virtual boundary is used to correct the assignment. The validity and accuracy of the algorithm are proved through the case of a rotating square patch of fluid. This paper also further studies the influence of the key parameters on the accuracy and manifestation of the boundary conditions. When the search radius for fitting is four times the initial interparticle distance, fitting errors can be reduced and boundary deformation can be prevented. The proposed method can enhance the accuracy and stability in the kernel truncation region of the free surface, and can significantly suppress the particle drift caused by gradient force deviation on the free surface, in case of large deformation and under a negative pressure gradient. This paper provides new thoughts for improving the flow calculation of complex interfaces with large deformation.