CAJ | 학술논문

提出采用无网格法求解带速度项的电磁场控制方程,并结合有限元中的流线迎风稳定化方法对由速度项引起的无网格法解中的数值振荡进行抑制.避免了采用迎风有限元法求解带速度项的电磁场控制方程时所带来的网格畸变以及人工稳定项中二阶导数项被忽略的问题.针对1D及由A-ψ-A矢量模型所描述的带速度项的电磁场控制方程,讨论其无网格法流线迎风方案,并建立稳定化的离散数值模型.数值结果表明:尽管无网格方法中流线迎风的稳定因子不再是优化的,但其对由速度项引起的电磁场控制方程无网格解中数值振荡的抑制效果是显著的,流线迎风无网格法能有效地求解带速度项的电磁场控制方程.
제출채용무망격법구해대속도항적전자장공제방정,병결합유한원중적류선영풍은정화방법대유속도항인기적무망격법해중적수치진탕진행억제.피면료채용영풍유한원법구해대속도항적전자장공제방정시소대래적망격기변이급인공은정항중이계도수항피홀략적문제.침대1D급유A-ψ-A시량모형소묘술적대속도항적전자장공제방정,토론기무망격법류선영풍방안,병건립은정화적리산수치모형.수치결과표명:진관무망격방법중류선영풍적은정인자불재시우화적,단기대유속도항인기적전자장공제방정무망격해중수치진탕적억제효과시현저적,류선영풍무망격법능유효지구해대속도항적전자장공제방정.
In order to avoid the grid distortion when the FEM is used to compute electromagnetic field e-quations with velocity term and the loss of accuracy which is induced by the omission of the second-order derivative in artificial diffusion term, the meshfree method coupling streamline upwinding approach is pro-posed for these equations. Based on the investigation of stabilization factor in the meshfree method, a vector form of streamline upwinding was implemented for these equations. The numerical model of stream-line upwinding meshfree method for electromagnetic field equations with velocity term which were formula-ted by the magnetic vector potential and the scalar potential was deduced. Different equations were used to verify the effect of streamline upwinding meshfree method. The non-physical oscillation contained in the meshfree method solution of electromagnetic field equations with velocity term can be suppressed ef-fectively by streamline upwinding.