采用无网格伽辽金法求解电容层析成像正问题

由于有限元法求解电容层析成像正问题的计算准备及后处理非常费时，对正问题的三维求解造成了瓶颈，为此，提出采用无网格伽辽金法求解电容层析成像正问题，获得正问题的弱变分形式，并用拉格朗日乘子法施加边界条件，从而得到数值解．在同样的仿真条件下，2种方法的计算时间分别为14．046S和5．078S．对5种典型流型进行仿真，结果表明，2种方法计算结果的最大相对误差为2．25％．因此，无网格伽辽金法与有限元法具有相当的精度，且计算速度有较大提高．

Solution of Forward Problem for Electrical Capacitance Tomography Based on Element-Free Galerkin Method

Electrical capacitance tomography(ECT) is often used to identify two-(multi-) phase flow regime and investigate the distribution of solids.Usually,forward problem is solved using finite element method(FEM).But the preparation of data and postprocessing for this method are time-consuming.This leads to the three-dimensional computation bottleneck for ECT.For this reason,the element-free Galerkin method(EFGM) is proposed.In this method,in order to obtain the numerical solution,the shape function is constructed by moving least square(MLS),the weak form of the variational equation of the studied problem is used to deduce the discrete equation and Lagrange multipliers are used to satisfy essential boundary conditions.Compared with FEM that needs elements, only nodal data are necessary in EFGM.The computation time for these two methods are 14.046 s and 5.078 s respectively on the same simulation conditions.Finally,simulation research is done for five typical flow regimes using FEM and EFGM,respectively.Simulation results show that EFGM has the(tiny) difference in accuracy compared with FEM,the maximum relative error for the computation results of these two methods is 2.25~%,while computation speed improves greatly.