不可压缩粘性流SU/PG有限元之N-R迭代格式

N-R Iteration of SU/PG FEM for Incompressible Viscous Flow

对不可压缩粘性层流建立了SU/PG有限元的Newton-Raphson同步迭代算法,完成了相应矩阵公式的推导;重新确定了SU/PG中的人工扩散因子;借助面向对象方法开发了相应的计算程序。通过充分发展管流的数值解与理论解的对比,表明本文算法的可行性;并完成了沿后台阶流动现象的数值模拟,得到了不同雷诺数下出口断面的速度分布。

For incompressible visous flow, the Newton-Raphson synchronous iteration method of SU/PG FEM was established, and the matrix formulations were derived in detail. A new algorithm was employed to determine the artificial diffusion factor in SU/PG. The object-oriented approach was introduced in program development. Via comparing the numeric results with theoretical results of the sufficiently developed tube flow, the proposed method was demonstrated. Finally, the numeric simulation of fluid flowing past backward-facing step was carried out and the horizontal velocity distribution at outlet under different Reynolds number was obtained.