Bivariate Extension of the Quadrature Method of Moments for Batch Crystallization Models
Bivariate Extension of the Quadrature Method of Moments for Batch Crystallization Models
复制标题
批量结晶模型矩量求积法的双变量推广
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
A. Seidel
中科院分区：
文献类型：
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作者：
Shamsul Qamar;Saima Noor;Q. U. Ain;A. Seidel
本文提出了求解二维间歇结晶模型的矩量求积法的二元推广，该模型包括晶体的成核、尺寸相关的生长、聚集和溶解在溶解单元中小于某一临界尺寸的小原子核。在该方法中，利用低阶矩的正交多项式来求取正交横坐标(点)和权值。本文考虑了几个具有不同工艺组合的基准问题。用解析解和高分辨率有限体积格式验证了该方法的精度和效率。在所有测试问题中都观察到了极好的一致性。结果表明，与高分辨率有限体积格式相比，该方法具有较高的计算效率和计算精度。
This Article presents a bivariate extension of the quadrature method of moments for solving two-dimensional batch crystallization models involving crystals nucleation, size-dependent growths, aggregation, and dissolution of small nuclei below certain critical size in a dissolution unit. In this technique, orthogonal polynomials of lower order moments are used to find the quadrature abscissas (points) and weights. Several benchmark problems with different combinations of processes are considered in this Article. The accuracy and efficiency of the proposed method are validated against the analytical solutions and the high-resolution finite volume scheme. Excellent agreements were observed in all test problems. It was found that the current method is very efficient and accurate as compared to the high-resolution finite volume scheme.