中文摘要：

为探索高维多介质流体力学散乱点集上的Lagrange有限点方法,首先对相应一维问题进行研究,提出一种Lagrange有限点方法：在计算区域内（包括物质界面）设置任意离散点集,所有力学量都设在该点集上,在内点和界面点上分别建立离散格式.内点算法为基于Taylor展开的差分方法.界面点算法为显式追踪算法,从定解条件出发,利用Rankine-Hugoniot关系和特征差分方法,计算界面点位置及相应的状态量变化.通过追踪界面点的运动得到物质界面是方法的最大特色.典型算例计算结果与精确解符合很好,验证了算法的合理和有效性.

英文摘要：

A Lagrangian finite point method for one-dimensional compressible multifluids is presented.The proposed method is a meshfree numerical procedure based on a combination of interior point scheme and interface point tracking algorithm.The discretization of unknown function and its derivatives are defined only by position of the so called Lagrangian points.The interior point formulation is based on Taylor series expansion in continuous regions on both sides of a interface.Unlike most current meshfree method,a point is settled at the interface position initially.State of interface point is updated using Rankine-Hugoniot conditions at interface together with characteristics difference computation.The interface tracking algorithm is the main feature of the method.Numerical tests show that the algorithm is oscillation-free at material interfaces and accuracy of the method is demonstrated.