基于改进有限容积法的数群平衡方程数值方法研究

Numerical solution of population balance equation based on improved finite volume method

采用改进有限容积法对数群平衡方程进行数值计算,数群平衡方程涉及生长、团聚过程。对数群平衡方程进行数学变换,即把数量守恒方程变换为质量守恒方程,用非均匀几何网格对计算区域进行离散,运用有限容积法对变换后的方程进行离散求解,把数值计算结果与分析解和直接用有限容积法计算数群平衡方程的数值结果进行对比。研究结果表明:只考虑生长事件,改进有限容积法计算结果与分析解基本一致,有限容积法计算结果出现了显著的失真;只考虑团聚事件,2种方法计算结果都与分析解基本一致;同时考虑生长和团聚事件,改进有限容积法计算结果与分析解基本一致,有限容积法计算结果与分析解对比出现了失真。

The improved finite volume method was used to calculate the population balance equation, and growth and aggregation processes were involved in the population balance equation. Population balance equation was transformed in the mathematical way, namely converted the quantity conservation equation into mass conservation equation. And then the non-uniform geometric grid was used to discrete computational domain and the finite volume method was used to calculate the transformed equation. The numerical results with analytical solutions and the results from finite volume method to calculate the population balance equation were compared. The results show that in the event of pure growth process, the calculation results of the improved finite volume method are consistent with analytical solutions, and a significant numerical distortion turns up as a result of the finite volume method. In the event of pure reunion process, the results of both methods are consistent with the analytical solutions. In the event of the growth and reunion process both affected, the results of the improved finite volume method are consistent with the analytical solutions and numerical distortion occurs as a result of the finite volume method compared with the analytical solution.