In this paper,a cell average technique(CAT)based parameter estimation method is proposed for cooling crystallization involved with particle growth,aggregation and breakage,by establishing a more efficient and accurate...In this paper,a cell average technique(CAT)based parameter estimation method is proposed for cooling crystallization involved with particle growth,aggregation and breakage,by establishing a more efficient and accurate solution in terms of the automatic differentiation(AD)algorithm.To overcome the deficiency of CAT that demands high computation cost for implementation,a set of ordinary differential equations(ODEs)entailed from CAT based discretized population balance equation(PBE)are solved by using the AD based high-order Taylor expansion.Moreover,an AD based trust-region reflective(TRR)algorithm and another interior-point(IP)algorithm are established for estimating the kinetic parameters associated with particle growth,aggregation and breakage.As a result,the estimation accuracy can be further improved while the computation cost can be significantly reduced,compared to the existing algorithms.Benchmark examples from the literature are used to illustrate the accuracy and efficiency of the AD-based CAT,TRR and IP algorithms in comparison with the existing algorithms.Moreover,seeded batch cooling crystallization experiments ofβform L-glutamic acid are performed to validate the proposed method.展开更多
This paper is the second part of the article and is devoted to the construction and analysis of new non-linear optimal weights for WENO interpolation capable of rising the order of accuracy close to discontinuities fo...This paper is the second part of the article and is devoted to the construction and analysis of new non-linear optimal weights for WENO interpolation capable of rising the order of accuracy close to discontinuities for data discretized in the cell averages.Thus,now we are interested in analyze the capabilities of the new algorithm when working with functions belonging to the subspace L1\L2 and that,consequently,are piecewise smooth and can present jump discontinuities.The new non-linear optimal weights are redesigned in a way that leads to optimal theoretical accuracy close to the discontinuities and at smooth zones.We will present the new algorithm for the approximation case and we will analyze its accuracy.Then we will explain how to use the new algorithm in multiresolution applications for univariate and bivariate functions.The numerical results confirm the theoretical proofs presented.展开更多
基金supported in part by the National Natural Science Foundation of China(61633006)the Fundamental Research Funds for the Central Universities of China(DUT2018TB06)National Key Research and Development Program of China(2017YFA0700300)。
文摘In this paper,a cell average technique(CAT)based parameter estimation method is proposed for cooling crystallization involved with particle growth,aggregation and breakage,by establishing a more efficient and accurate solution in terms of the automatic differentiation(AD)algorithm.To overcome the deficiency of CAT that demands high computation cost for implementation,a set of ordinary differential equations(ODEs)entailed from CAT based discretized population balance equation(PBE)are solved by using the AD based high-order Taylor expansion.Moreover,an AD based trust-region reflective(TRR)algorithm and another interior-point(IP)algorithm are established for estimating the kinetic parameters associated with particle growth,aggregation and breakage.As a result,the estimation accuracy can be further improved while the computation cost can be significantly reduced,compared to the existing algorithms.Benchmark examples from the literature are used to illustrate the accuracy and efficiency of the AD-based CAT,TRR and IP algorithms in comparison with the existing algorithms.Moreover,seeded batch cooling crystallization experiments ofβform L-glutamic acid are performed to validate the proposed method.
基金The first and second authors have been supported through project 20928/PI/18(Proyecto financiado por la Comunidad Autonoma de la Region de Murcia a traves de la convocatoria de Ayudas a proyectos para el desarrollo de investigacion cientffica y tecnica por grupos competitivos,incluida en el Programa Regional de Fomento de la Investigacion Cientffica y Tecnica(Plan de Actuacion 2018)de la Fundacion Seneca-Agencia de Ciencia y Tecnologia de la Region de Murcia)by the national research project MTM2015-64382-P(MINECO/FEDER)The third author has been supported through the National Science Foundation grant DMS-1719410.
文摘This paper is the second part of the article and is devoted to the construction and analysis of new non-linear optimal weights for WENO interpolation capable of rising the order of accuracy close to discontinuities for data discretized in the cell averages.Thus,now we are interested in analyze the capabilities of the new algorithm when working with functions belonging to the subspace L1\L2 and that,consequently,are piecewise smooth and can present jump discontinuities.The new non-linear optimal weights are redesigned in a way that leads to optimal theoretical accuracy close to the discontinuities and at smooth zones.We will present the new algorithm for the approximation case and we will analyze its accuracy.Then we will explain how to use the new algorithm in multiresolution applications for univariate and bivariate functions.The numerical results confirm the theoretical proofs presented.
