دانلود رایگان مقاله حل عددی معادله تعادل جمعیت با استفاده از روش متوسط سلول اصلاح شده به طور موثر

Abstract

In order to increase the accuracy of the modified cell average technique (mCAT) alongside the zeroth and first moments and increase the speed of the technique, a new supplemental solver has been developed in the region of high amount time, a region where the ratio of the zeroth moment to the initial zeroth moment (μ0(t)/μ0(0)) is too small or too large depending on the process and the amount of error is high there. The solver is conceptually easy to understand and straightforward for programming. A number of analytically solved problems were simulated by incorporating this solver into the mCAT and the results were compared with the previous solver. Significant improvements for different phenomenon especially the aggregation related systems were observed.

4. Conclusion

In this study, a new supplemental solver that takes the place of its predecessor at last paper (Mostafaei et al., 2015) is devised. The new solver enhanced the accuracy of the important elements of mCAT method; density function and both the zeroth and first moment at high amount time, something that was never done before for this kind of method. The supplemental solver was based on the mathematics of the mCAT method and the solver itself was dependent on the type of the process. After that even a replacement that acted as a shortcut was proposed based on the essence ofthe solver and nature of processes like breakage and aggregation. The results were surprising, because not only that in all cases the new supplemental solver was very accurate especially in systems involving aggregation that the error of both the old supplemental solver and CAT were very high but also the method was much faster. In other words in addition to increase the accuracy of mCAT method with this new supplemental solver, the computation time is lowered too.