A local pseudo arc-length method（LPALM）for solving hyperbolic conservation laws is presented in this paper.The key idea of this method comes from the original arc-length method,through which the critical points are bypassed by transforming the computational space.The method is based on local changes of physical variables to choose the discontinuous stencil and introduce the pseudo arc-length parameter,and then transform the governing equations from physical space to arc-length space.In order to solve these equations in arc-length coordinate,it is necessary to combine the velocity of mesh points in the moving mesh method,and then convert the physical variable in arclength space back to physical space.Numerical examples have proved the effectiveness and generality of the new approach for linear equation,nonlinear equation and system of equations with discontinuous initial values.Non-oscillation solution can be obtained by adjusting the parameter and the mesh refinement number for problems containing both shock and rarefaction waves.
A particle mapping transportation algorithm was proposed on the basis of the particle-in-cell method.The particles with rectangular influence domains were employed in the transportation algorithm to reduce the numerical fluctuations.Based on the error analysis in the process of particle motion computation,a prediction-correction algorithm was introduced to improve the computational accuracy.Furthermore,the performance of the particle mapping transportation method was evaluated by using the rotation,the slotted disk and the shear advection tests,and the results were compared with other interface reconstruction methods.Finally,the hemispherical projectile penetration into a steel target was numerically simulated.The results showed that the proposed method produced less numerical fluctuations and exhibited clear material interfaces,which indicated that it is accurate and effective.
针对爆炸与冲击问题并行仿真计算软件PMMIC-3D(Parallel Multi-Material in Cell 3D)的计算网格为正交六面体网格的特点,开发与PMMIC-3D接口统一的可对任意复杂三维实体模型进行大规模有限差分网格生成的三维前处理软件MESH-3D.MESH-3D采用CSG和STL模型两种建模方式进行复杂实体建模,并采用基于边的整体切片算法,借鉴计算机图形学中的扫描线填充算法完成三维有限差分网格划分.在绘制网格时,删除网格单元的公共面,大大缩短计算时间和减少存储空间,实现对网格的快速消隐显示.MESH-3D可实现百亿量级网格单元的生成和显示.三维前处理软件MESH-3D的开发有力地支持爆炸与冲击问题的仿真计算.
A Cartesian grid generation method is developed in this study.Two kinds of solid modeling methods,CSG and STL models,are used for complicated solid modeling.The staircase boundary approximation is implemented to handle irregular geometries and the computational domain is discretized using a regular Cartesian grid.Using the edge-based integral slice algorithm,the models are sliced with a set of parallel planes to generate 2D slices information.The scan line filling technique is used to achieve grid generation after slicing.Two grid generation examples with a CSG model and a STL model are given to test the capability of the grid generation method.For grid displaying,a method is proposed to remove the hidden surfaces fasten based on the topology of orthogonal hexahedral grids.The parallelization of grid displaying is achieved by employing multi-threaded parallel technique.Parallel test results show that the parallel algorithm has the absolute advantage on speed compared to the serial algorithm.
