Two-dimensional Lagrangian Simulation Study Of Large Deformation Motion Of Multi-medium Compressible Fluid

In the numerical simulation of multi-material fluids,due to the simplicity of the governing equations and the capacity of capturing the movement of the interface sharply,lagrangian methods have been widely used.However,the consistency between the grid and the material would result in distortive and tangled grids when simulating the movements with large deformation.It would decrease the accuracy and terminate the simulation in advance.Under this circumstance,grid dynamical local remeshing would be an efficient method to handle the distortive grids.In this paper,a grid remeshing operation,"hat-trick",is proposed based on the triangular mesh in lagrangian method.This operation,along with the "diagonal-swapping","edge-splitting"and " edge-merging",constitute a new grid dynamical local remeshing scheme.The later three ones are adopted not only in the single material but also on the multi-material interface while the "hat-trick" operations is only applied on the multi-material interface.Each operation has its own corresponding criterion,which involves the angle or the length of a side.After the remeshing,the quantities on the old mesh would be projected to the new mesh.This process is called remapping.Remapping in the dynamical local remeshing is easy to operate.It just copes with the four operations.In this paper,the conservative remapping with first-order and second-order accuracy would be presented.In the first-order remapping,the quantities are assumed piecewise constant in the grid cells while the piecewise linearity is used in the second-order remapping.These two remapping methods can guarantee the conservation of the mass,momentum and energy.Based on this scheme,three tests with large deformation have been simulated,namely the R-T instability,the interaction between shock and bubble,and the triple points problem.The results verify the effectiveness and accuracy of the scheme.This paper also discusses the application of virtual mesh method in hypervelocity impact problems.In simulating hypervelocity impact problems,the topology transformation that interfaces contact each other and materials facture should be worked out.In this paper,when using lagrangian methods to simulate the hypervelocity impact problems,the vaccum area around the real material would be occupied by the virtual material,which is meshed along with the real material.Interface contact is finally achieved by the dynamic local remeshing on the multi-material interfaces.Besides,material facture would be simulated in a way where a virtual mesh cell replaces the fracturing area based on failure model.In this paper,aluminum ball impacting aluminum target would be simulated.The results show the entire process from collision to fracture of the ball and target.In addition,it is also compared to the simulation by HDS program.The result proves the effectiveness of virtual mesh in hypervelocity impact problems.In this paper,a resolution to the non-physical oscillations in triangular mesh is also proposed.The resolution is called Compensatory Material Flow method.In the method,the stiffness of a triangle is considered as the reason for the oscillations.Specifically,the sides of a triangle can not bend.Compensatory Material Flow method uses an extra material flow between mesh cells to compensate for the edge-bending effect and the oscillations are mitigated to some extent,which is verified in the K-H instability and shock tube simulation.