Two Energy-Preserving Compact Finite Difference Schemes for the Nonlinear Fourth-Order Wave Equation

Liu, Xiaoyi; Wang, Tingchun; Jin, Shilong; Xu, Qiaoqiao

doi:10.1007/s42967-022-00193-2

Cited by 3 publications

(1 citation statement)

References 27 publications

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“…(12) Calculate the partial derivative of the objective function to the iterative variable and construct the Jacobian matrix. The Schubert method was used to calculate the modified value of the inside iteration variable [22,23]. Damping factors can be used if necessary.…”

Section: Outer Loop Iterationmentioning

confidence: 99%

Inside–Out Method for Simulating a Reactive Distillation Process

Wang

Sun

et al. 2020

Processes

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Reactive distillation is a technical procedure that promotes material strengthening and its simulation plays an important role in the design, research, and optimization of reactive distillation. The solution to the equilibrium mathematical model of the reactive distillation process involves the calculation of a set of nonlinear equations. In view of the mutual influence between reaction and distillation, the nonlinear enhancement of the mathematical model and the iterative calculation process are prone to fluctuations. In this study, an improved Inside–Out method was proposed to solve the reaction distillation process. The improved Inside–Out methods mainly involved—(1) the derivation of a new calculation method for the K value of the approximate thermodynamic model from the molar fraction summation equation and simplifying the calculation process of the K value, as a result; and (2) proposal for an initial value estimation method suitable for the reactive distillation process. The algorithm was divided into two loop iterations—the outer loop updated the relevant parameters and the inside loop solved the equations, by taking the isopropyl acetate reactive distillation column as an example for verifying the improved algorithm. The simulation results presented a great agreement with the reference, and only the relative deviation of the reboiler heat duty reached 2.57%. The results showed that the calculation results were accurate and reliable, and the convergence process was more stable.

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Section: Outer Loop Iterationmentioning

confidence: 99%