Abstract: 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.

Key words: compressible multifluids, finite point method, interface tracking, meshfree method