为准确计算渤海海冰的动力过程,本文将质点网格方法(Particle in cell,简称PIC),引入到渤海海冰数值模拟中。该方法首先在欧拉坐标系下对海冰动力方程和连续方程进行差分求解,并插值出各网格内海冰质点的速度和密集度,然后在拉格朗日... 为准确计算渤海海冰的动力过程,本文将质点网格方法(Particle in cell,简称PIC),引入到渤海海冰数值模拟中。该方法首先在欧拉坐标系下对海冰动力方程和连续方程进行差分求解,并插值出各网格内海冰质点的速度和密集度,然后在拉格朗日坐标系下对海冰质点的位移和各网格的平均冰厚进行确定。PIC方法将欧拉法与拉格朗日法相结合,避免了欧拉坐标下有限差分法的数值扩散和拉格朗日坐标下光滑质点流体动力学计算量大的缺点。在对渤海海冰动力过程的数值模拟中采用了Hibler的粘塑性本构模型,并考虑了海冰热力作用过程。利用PIC方法对辽东湾海冰进行了48h数值模拟,结果表明:该方法可成功地处理海冰流变过程,精确计算出冰缘线位置和海冰分布状况,对海冰厚度和密集度的计算精度均优于有限差分法。PIC方法在精确模拟海冰的重叠和堆积过程,以及为冰区油气作业提供详实的海冰信息方面都有良好的应用前景。展开更多
This paper presents the dimension split element-free Galerkin （DSEFG） method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-d...This paper presents the dimension split element-free Galerkin （DSEFG） method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares （IMLS） approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method.展开更多
文摘 为准确计算渤海海冰的动力过程,本文将质点网格方法(Particle in cell,简称PIC),引入到渤海海冰数值模拟中。该方法首先在欧拉坐标系下对海冰动力方程和连续方程进行差分求解,并插值出各网格内海冰质点的速度和密集度,然后在拉格朗日坐标系下对海冰质点的位移和各网格的平均冰厚进行确定。PIC方法将欧拉法与拉格朗日法相结合,避免了欧拉坐标下有限差分法的数值扩散和拉格朗日坐标下光滑质点流体动力学计算量大的缺点。在对渤海海冰动力过程的数值模拟中采用了Hibler的粘塑性本构模型,并考虑了海冰热力作用过程。利用PIC方法对辽东湾海冰进行了48h数值模拟,结果表明:该方法可成功地处理海冰流变过程,精确计算出冰缘线位置和海冰分布状况,对海冰厚度和密集度的计算精度均优于有限差分法。PIC方法在精确模拟海冰的重叠和堆积过程,以及为冰区油气作业提供详实的海冰信息方面都有良好的应用前景。
基金supported by the National Natural Science Foundation of China (Grants 11571223, 51404160)Shanxi Province Science Foundation for Youths (Grant 2014021025-1)
文摘This paper presents the dimension split element-free Galerkin （DSEFG） method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares （IMLS） approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method.
