Analytical solutions of governing equations of various phenomena have their irre-placeable theoretical meanings. In addition, they can also be the benchmark solu-tions to verify the outcomes and codes of numerical sol...Analytical solutions of governing equations of various phenomena have their irre-placeable theoretical meanings. In addition, they can also be the benchmark solu-tions to verify the outcomes and codes of numerical solutions, and even to develop various numerical methods such as their differencing schemes and grid generation skills as well. A hybrid method of separating variables for simultaneous partial differential equation sets is presented. It is proposed that different methods of separating variables for different independent variables in the simultaneous equa-tion set may be used to improve the solution derivation procedure, for example, using the ordinary separating method for some variables and using extraordinary methods of separating variables, such as the separating variables with addition promoted by the first author, for some other variables. In order to prove the ability of the above-mentioned hybrid method, a lot of analytical exact solutions of two-buoyancy convection in porous media are successfully derived with such a method. The physical features of these solutions are given.展开更多
针对数值法或解析法研究永磁直线同步电机(permanent magnet linear synchronous motor,PMLSM)性能时存在的不足,采用数值解析混合法研究PMLSM磁场,把电机的磁场划分区域,针对各区域特点分别采用纯解析法和数值法,气隙区包括永磁体无网...针对数值法或解析法研究永磁直线同步电机(permanent magnet linear synchronous motor,PMLSM)性能时存在的不足,采用数值解析混合法研究PMLSM磁场,把电机的磁场划分区域,针对各区域特点分别采用纯解析法和数值法,气隙区包括永磁体无网格剖分,采用解析法获得此区的磁场解析表达式;初级齿槽区采用有限元法研究电枢不同励磁形式、齿槽及端部半填槽对磁场的影响。解析和有限元法通过两者的边界条件相耦合,建立并求解电机的磁场,获得空载电势与磁链参数,分析工作在SPWM-VI下PMLSM的动态性能,提出PMLSM空载电势实验的一种新方法,仿真和实验结果进行比较分析,验证了数值解析混合法分析PMLSM性能的正确性及快速性。展开更多
基金the National Natural Science Foundation of China (Grant No. 50576097)the National Basic Research Development Program of China (Grant No. 2007CB206902)
文摘Analytical solutions of governing equations of various phenomena have their irre-placeable theoretical meanings. In addition, they can also be the benchmark solu-tions to verify the outcomes and codes of numerical solutions, and even to develop various numerical methods such as their differencing schemes and grid generation skills as well. A hybrid method of separating variables for simultaneous partial differential equation sets is presented. It is proposed that different methods of separating variables for different independent variables in the simultaneous equa-tion set may be used to improve the solution derivation procedure, for example, using the ordinary separating method for some variables and using extraordinary methods of separating variables, such as the separating variables with addition promoted by the first author, for some other variables. In order to prove the ability of the above-mentioned hybrid method, a lot of analytical exact solutions of two-buoyancy convection in porous media are successfully derived with such a method. The physical features of these solutions are given.
文摘针对数值法或解析法研究永磁直线同步电机(permanent magnet linear synchronous motor,PMLSM)性能时存在的不足,采用数值解析混合法研究PMLSM磁场,把电机的磁场划分区域,针对各区域特点分别采用纯解析法和数值法,气隙区包括永磁体无网格剖分,采用解析法获得此区的磁场解析表达式;初级齿槽区采用有限元法研究电枢不同励磁形式、齿槽及端部半填槽对磁场的影响。解析和有限元法通过两者的边界条件相耦合,建立并求解电机的磁场,获得空载电势与磁链参数,分析工作在SPWM-VI下PMLSM的动态性能,提出PMLSM空载电势实验的一种新方法,仿真和实验结果进行比较分析,验证了数值解析混合法分析PMLSM性能的正确性及快速性。
