Grid Subdivision Algorithm Based on the Young’s Interface Reconstruction Algorithm

Abstract

Spatial discretization using either finite difference or finite element techniques can be carried out in a Lagrangian or Eulerian method. For the reason that the Eulerian method can eliminate the problems associated with a distorted grid that are encountered with a Lagrangian method, it is much suitable to treat the flows with large distortions such as explosion problems. But the disadvantages of the Eulerian method are the difficulty in the identification of material interface and calculation of the material transportation between the neighboring grids. This paper describes a 2-D multi-material Eulerian finite difference method for explosion problems and presents a grid subdivision algorithm based on the Young’s interface reconstruction algorithm to treat the transportation of the mixed grids. The operator splitting method is employed here, that is to say that the calculation for a given time step involves two phases. The first phase is a Lagrangian phase in which the grid is allowed to distort with the material. In the second advection phase, transportation of mass, internal energy and momentum across grid boundaries is computed. The grid subdivision algorithm based on the Young’s interface reconstruction algorithm is proposed to treat the transportation of the mixed grids. In this algorithm, the mixed grids are subdivided based on a certain rule until the subgrids contain only one material. The advantage of this algorithm is that it only needs to calculate the transportation between pure grids, escaping the complexity encountered in the transportation of mixed grids. In order to improve the accuracy, the pure grids as the neighboring grid of the mixed grids are all subdivided. The method is as follows: $$ DL_p = \left\{ \begin{gathered} DL_m - C (DL_m - C \geqslant 1) \hfill \\ 1 (DL_m - C < 1) \hfill \\ \end{gathered} \right. $$ where DLm, DLp are the subdivision hierarchy numbers for the mixed grid and pure grid respectively; C is the space between the above two grids’ serial numbers. A series of computer simulations for objects with different shapes moving in translational flow field, rotating flow field and shear flow field in two dimensional Descartes coordinates are performed as test problems to verify the above algorithm. The simulation results verify that the grid subdivision algorithm is simple and efficient.