A new hybrid numerical scheme of combining an E-CUSP(Energy-Convective Upwind and Split Pressure) method for the fluid part and the Constrained Transport(CT) for the magnetic induction part is proposed.In order to avo...A new hybrid numerical scheme of combining an E-CUSP(Energy-Convective Upwind and Split Pressure) method for the fluid part and the Constrained Transport(CT) for the magnetic induction part is proposed.In order to avoid the occurrence of negative pressure in the reconstructed profiles and its updated value,a positivity preserving method is provided.Furthermore,the MHD equations are solved at each physical time step by advancing in pseudo time.The use of dual time stepping is beneficial in the computation since the use of dual time stepping allows the physical time step not to be limited by the corresponding values in the smallest cell and to be selected based on the numerical accuracy criterion.This newly established hybrid scheme combined with positivity preserving method and dual time technique has demonstrated the accurateness and robustness through numerical experiments of benchmark problems such as the 2D Orszag-Tang vortex problem and the3 D shock-cloud interaction problem.展开更多
Because exact analytic solution is not available, we use double expansion and boundary collocation to construct an approximate solution for a class of two-dimensional dual integral equations in mathematical physics. T...Because exact analytic solution is not available, we use double expansion and boundary collocation to construct an approximate solution for a class of two-dimensional dual integral equations in mathematical physics. The integral equations by this procedure are reduced to infinite algebraic equations. The accuracy of the solution lies in the boundary collocation technique. The application of which for some complicated initialboundary value problems in solid mechanics indicates the method is powerful.展开更多
The characteristics of a collisional dual frequency （DF） sheath near an electrode with a cylindrical hole are studied by utilizing a two-dimensional model which includes time-dependent fluid equations coupled with t...The characteristics of a collisional dual frequency （DF） sheath near an electrode with a cylindrical hole are studied by utilizing a two-dimensional model which includes time-dependent fluid equations coupled with the Poisson equation and an equivalent-circuit model, The effects of the gas pressure on the two-dimensional profiles of the potential, electric field, ion fluid velocity in a DF sheath are investigated. The simulation results show that the cylindrical hole on the electrode has a significant influence on the DF sheath structure, i.e., the sheath profile tends to wrap around the contour of the hole feature. Moreover, it is shown that the structure of the DF sheath is different from that of a single frequency （SF） sheath because the profile of the DF sheath is modulated by the combination of the high and low frequency sources. In addition the characteristics of the DF sheath are obviously affected by the collisional effects in the DF sheath.展开更多
基金Supported by the National Basic Research Program of China(2012CB825601)the National Natural Science Foundationof China(41031066,41231068,41274192,41074121,41204127)+1 种基金the Knowledge Innovation Program of the ChineseAcademy of Sciences(KZZD-EW-01-4)the Specialized Research Fund for State Key Laboratories
文摘A new hybrid numerical scheme of combining an E-CUSP(Energy-Convective Upwind and Split Pressure) method for the fluid part and the Constrained Transport(CT) for the magnetic induction part is proposed.In order to avoid the occurrence of negative pressure in the reconstructed profiles and its updated value,a positivity preserving method is provided.Furthermore,the MHD equations are solved at each physical time step by advancing in pseudo time.The use of dual time stepping is beneficial in the computation since the use of dual time stepping allows the physical time step not to be limited by the corresponding values in the smallest cell and to be selected based on the numerical accuracy criterion.This newly established hybrid scheme combined with positivity preserving method and dual time technique has demonstrated the accurateness and robustness through numerical experiments of benchmark problems such as the 2D Orszag-Tang vortex problem and the3 D shock-cloud interaction problem.
基金Project supported by the National Natural Science Foundation of China(No.K19672007)
文摘Because exact analytic solution is not available, we use double expansion and boundary collocation to construct an approximate solution for a class of two-dimensional dual integral equations in mathematical physics. The integral equations by this procedure are reduced to infinite algebraic equations. The accuracy of the solution lies in the boundary collocation technique. The application of which for some complicated initialboundary value problems in solid mechanics indicates the method is powerful.
基金supported by National Natural Science Foundation of China (Nos.10635010,10572035)
文摘The characteristics of a collisional dual frequency （DF） sheath near an electrode with a cylindrical hole are studied by utilizing a two-dimensional model which includes time-dependent fluid equations coupled with the Poisson equation and an equivalent-circuit model, The effects of the gas pressure on the two-dimensional profiles of the potential, electric field, ion fluid velocity in a DF sheath are investigated. The simulation results show that the cylindrical hole on the electrode has a significant influence on the DF sheath structure, i.e., the sheath profile tends to wrap around the contour of the hole feature. Moreover, it is shown that the structure of the DF sheath is different from that of a single frequency （SF） sheath because the profile of the DF sheath is modulated by the combination of the high and low frequency sources. In addition the characteristics of the DF sheath are obviously affected by the collisional effects in the DF sheath.
