High-Order Compact ADI Methods for Parabolic Equations

Li, Jichun; Chen, Yitung; Liu, Guoqing

doi:10.1016/j.camwa.2006.11.010

Cited by 59 publications

(43 citation statements)

References 27 publications

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“…In contrast to the case Re = 200, the HPD-ADI scheme produces a distorted solution and shows small phase errors as one can see from Figure 3(b). We notice that all the previous calculations were carried out using the factored scheme (19) based on the Crank-Nicolson time integration, that is with a second-order accuracy in time, and without a correction term ( (E) n = 0). We next examine the effectiveness of the modified scheme (21).…”

Section: Numerical Experimentsmentioning

confidence: 99%

A hybrid Padé ADI scheme of higher‐order for convection–diffusion problems

Karaa

2009

Numerical Methods in Fluids

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SUMMARYA high-order Padé alternating direction implicit (ADI) scheme is proposed for solving unsteady convection-diffusion problems. The scheme employs standard high-order Padé approximations for spatial first and second derivatives in the convection-diffusion equation. Linear multistep (LM) methods combined with the approximate factorization introduced by Beam and Warming (J. Comput. Phys. 1976; 22: 87-110) are applied for the time integration. The approximate factorization imposes a second-order temporal accuracy limitation on the ADI scheme independent of the accuracy of the LM method chosen for the time integration. To achieve a higher-order temporal accuracy, we introduce a correction term that reduces the splitting error. The resulting scheme is carried out by repeatedly solving a series of pentadiagonal linear systems producing a computationally cost effective solver. The effects of the approximate factorization and the correction term on the stability of the scheme are examined. A modified wave number analysis is performed to examine the dispersive and dissipative properties of the scheme. In contrast to the HOC-based schemes in which the phase and amplitude characteristics of a solution are altered by the variation of cell Reynolds number, the present scheme retains the characteristics of the modified wave numbers for spatial derivatives regardless of the magnitude of cell Reynolds number. The superiority of the proposed scheme compared with other high-order ADI schemes for solving unsteady convection-diffusion problems is discussed. A comparison of different time discretizations based on LM methods is given.

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Section: Numerical Experimentsmentioning

confidence: 99%

A hybrid Padé ADI scheme of higher‐order for convection–diffusion problems

Karaa

2009

Numerical Methods in Fluids

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“…In this section we investigate a high-order compact ADI method as in the paper by Chen and Liu [25] for the two-dimensional equation analysed in the previous chapter. The highorder ADI as opposed to the Peaceman-Rachford ADI method provides a higher accuracy.…”

Section: High-order Compact Adi Methodsmentioning

confidence: 99%

“…We take the sixth-order compact formulas, developed by Chen and Liu [25] and also found in more detail in the paper by Gaitonde and Visbal [27], to approximate the derivatives in (5.5) and (5.6). The resulting formula is,…”

Section: Derivation Of the High-order Compact Adi Methods For The Two-mentioning

confidence: 99%

See 2 more Smart Citations

Numerical investigation of the parabolic mixed derivative diffusion equation via Alternating Direction Implicit methods

Sathinarain

Harley

Momoniat

2013

Computers & Mathematics with Applications

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Evolutionary design of optimum distillation column sequence

Boozarjomehry¹,

Laleh²,

Svrcek³

2011

Can J Chem Eng

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Synthesis of the optimum distillation column sequence (DCS), which incorporates a huge search space composed of both conventional and complex arrangements, is a highly complicated combinatorial problem in the field of chemical process design and optimisation. In this study, a novel procedure for the synthesis of optimum DCS proposed by Boozarjomehry et al. [Boozarjomehry et al., Can. J. Chem. Eng. 87, 477–492 (2009)] is expanded to include the complex distillation arrangements. The method is based on evolutionary algorithms, and the total annual cost (TAC) is the main criterion used to screen alternatives. Efficient procedure has been proposed for encoding mechanism to include and classify various complex arrangements together with conventional distillation columns. All columns existing in each DCS alternative are designed using the most recommended short‐cut methods to estimate the TAC of the DCS. Four standard benchmark case studies are carried out to clearly demonstrate the excellent performance of the proposed method. The produced results for these problems indicate that the proposed method outperforms the other existing approaches in terms of flexibility, accuracy and comprehensiveness. © 2011 Canadian Society for Chemical Engineering

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High-Order Compact ADI Methods for Parabolic Equations

Cited by 59 publications

References 27 publications

A hybrid Padé ADI scheme of higher‐order for convection–diffusion problems

A hybrid Padé ADI scheme of higher‐order for convection–diffusion problems

Numerical investigation of the parabolic mixed derivative diffusion equation via Alternating Direction Implicit methods

Evolutionary design of optimum distillation column sequence

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