A high-order Padé ADI method for unsteady convection–diffusion equations

You, Donghyun

doi:10.1016/j.jcp.2005.10.001

Cited by 63 publications

(64 citation statements)

References 24 publications

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“…[11] and references therein), including methods for solution of a variety of linear and nonlinear PDEs [12][13][14][15][16][17][18][19][20][21], as well as methods of high-order of spatial and temporal accuracy [22][23][24][25][26]. As suggested above, previous unconditionally stable alternating-direction methods can only achieve high-order accuracy in presence of a formulation of the given PDE on domains given by the union of a finite number of rectangular regions.…”

Section: Introductionmentioning

confidence: 99%

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High-order unconditionally stable FC-AD solvers for general smooth domains I. Basic elements

Bruno

Lyon

2010

Journal of Computational Physics

112

199

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Section: Introductionmentioning

confidence: 99%

“…Development of alternating direction schemes using high-order finite-difference discretizations for rectangular domains, in turn, is currently an active area of research; see e.g. [25,26,33,34]. A great deal of activity currently focuses in the area of embedded-boundary (EB) methods [35][36][37][38][39][40][41][42][43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

High-order unconditionally stable FC-AD solvers for general smooth domains I. Basic elements

Bruno

Lyon

2010

Journal of Computational Physics

112

199

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“…A discussion regarding the diffusive effects of the HOC scheme (6) can be found in [23]. The numerical errors of (6) in terms of phase and amplitude are discussed in [17], where it was shown that the HOC scheme produces significantly enhanced dissipation at high cell Reynolds numbers.…”

Section: High-order Adi Schemesmentioning

confidence: 99%

“…The scheme is second-order accurate in time and fourth-order accurate in space and performs better than the HOC-ADI scheme especially for problems with boundary layers. Recently, You [17] proposed a fourth-order Padé scheme-based ADI method that showed high accuracy and better phase and amplitude errors than the PR-and HOC-ADI schemes. However, to retain the tridiagonal matrix algorithm further factorizations were introduced, making the implementation of the scheme complex and resulting in a relatively high computational cost.…”

Section: Introductionmentioning

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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“…Difference schemes of a high order of approximation arouse interest among authors [17,21,26,27]. In the article of Mohanty [18], two-level implicit difference methods of O(τ 2 + h 4 ) using 19-spatial grid points for the solving the three space dimensional heat conduction equation is proposed.…”

Section: Introductionmentioning

confidence: 99%

Exact Difference Schemes for Multidimensional Heat Conduction Equations

Lapinska-Chrzczonowicz

2007

Comput. Methods Appl. Math.

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-The initial boundary-value problem for the two-dimensional heat conduction equationis considered. A new difference scheme approximating the above equation is constructed. The error of approximation of the considered scheme is O((σ − 0.5)(, where σ is a weight. The main difference between the method proposed in the present paper and the other difference schemes is that for the traveling wave solutions u(x, t) = U 1 2athe considered scheme is exact if the grid steps satisfy definite conditions γ 1 = aτ /h 1 = 1/2, γ 2 = bτ /h 2 = 1/2. The iteration method is used to solve a nonlinear difference equation.

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A high-order Padé ADI method for unsteady convection–diffusion equations

Cited by 63 publications

References 24 publications

High-order unconditionally stable FC-AD solvers for general smooth domains I. Basic elements

High-order unconditionally stable FC-AD solvers for general smooth domains I. Basic elements

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

Exact Difference Schemes for Multidimensional Heat Conduction Equations

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