A numerical method for the solution of the wave model and convection dominated diffusion type models for catalytic packed bed reactors

Iordanidis, AA; Annaland, van M Martin Sint; Kronberg, Alexandre E.; Kuipers, J.A.M.

doi:10.1016/j.compchemeng.2004.04.011

Cited by 4 publications

(1 citation statement)

References 17 publications

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“…In this paper, a new computationally cost‐effective numerical method that combines hybrid Padé (HPD) schemes with ADI method (HPD‐ADI) is proposed to solve the CDD equation. From a physical point of view, the CDD equation is quite fundamental in describing a broad class of problems in physical, chemical, biological, and engineering sciences . For instance, the typical ﬂow Peclet number in chaotic advection micromixing is about 1000 for a ﬂow rate of 1 mm/s, channel width of 100 μ m and characteristic diffusivity in the order of 10 −10 m 2 s −1 for most biochemical molecules such as deoxyribonucleic acid, ribonucleic acid, and proteins in aqueous solutions .…”

Section: Introductionmentioning

confidence: 99%

A high‐order alternating direction implicit method for the unsteady convection‐dominated diffusion problem

Sun

Haake

et al. 2011

Numerical Methods in Fluids

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SUMMARY A high‐order alternating direction implicit (ADI) method for solving the unsteady convection‐dominated diffusion equation is developed. The fourth‐order Padé scheme is used for the discretization of the convection terms, while the second‐order Padé scheme is used for the diffusion terms. The Crank–Nicolson scheme and ADI factorization are applied for time integration. After ADI factorization, the two‐dimensional problem becomes a sequence of one‐dimensional problems. The solution procedure consists of multiple use of a one‐dimensional tridiagonal matrix algorithm that produces a computationally cost‐effective solver. Von Neumann stability analysis is performed to show that the method is unconditionally stable. An unsteady two‐dimensional problem concerning convection‐dominated propagation of a Gaussian pulse is studied to test its numerical accuracy and compare it to other high‐order ADI methods. The results show that the overall numerical accuracy can reach third or fourth order for the convection‐dominated diffusion equation depending on the magnitude of diffusivity, while the computational cost is much lower than other high‐order numerical methods. Copyright © 2011 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 99%