SPH方法Delaunay三角刨分与自由液面重构

光滑粒子法(SPH)作为一种拉格朗日型无网格方法,兼具欧拉网格方法和拉格朗日网格方法的优势,已经成功应用于科学和工程的众多领域。SPH方法后处理一般基于无规则分布的粒子,不如网格类方法后处理简便、直接。另外,SPH方法模拟自由液面流动等问题时,通过粒子位置难以重构自由液面的准确位置。发展一种基于Delaunay三角刨分的SPH后处理方法,即先基于SPH粒子位置利用Delaunay三角刨分建立三角网格,然后将粒子信息转化成网格单元/节点信息,从而可以在三角网格上进行后处理,实现基于网格方法的后处理功能,并可以在三角网格上直接提取或重构自由液面。将本文的方法应用到液滴碰撞和溃坝流SPH模拟结果的后处理中,得到了非常好的结果,表明本文的方法有效可靠。

Delaunay triangulation and free surface extraction for SPH method

Smoothed particle hydrodynamics(SPH) is a meshfree,Lagrangian particle method,which combines the best features of Eulerian and Lagrangian grid-based methods,and has been successfully applied to different areas in sciences and engineering.The post-processing of SPH is not as straight forward and convenient as the grid-based methods since the information is based on irregularly distributed particles rather than on a grid system.Moreover,free surfaces are usually difficult to be reconstructed or extracted based simply on SPH particles.In this paper,a Delaunay triangulation is developed,in which a triangular mesh is generated form SPH particles through Delaunay triangulation,and the related information on SPH particles is converted to the triangular mesh.The SPH post-processing can then be conducted on the triangular mesh rather than on the SPH particles.Also free surfaces can be extracted from the generated Delaunay mesh.Two typical examples,the head-on collision of two liquid drops and dam collapse have been simulated.The obtained results with precisely extracted free surfaces demonstrate the effectiveness of the approach of Delaunay triangulation and free surface extraction for SPH method.