Improved Finite-Difference Scheme for the Solution of Convection-Diffusion Problems With the Simplen Algorithm

Thiart, G. D.

doi:10.1080/10407799008944943

Cited by 42 publications

(30 citation statements)

References 10 publications

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“…This algorithm was designed for stationary incompressible 37 flow problems. Many variations and improvements have been proposed, such as SIMPLER [53], SIMPLEC [11], SIMPLEN [71]. The method can be also extended to compressible flow computations [16].…”

Section: Pressure Correction Algorithms For the 1d Casementioning

confidence: 99%

Numerical Simulation of Pulse-Tube Refrigerators

Lyulina

Mattheij²,

Tijsseling³

et al. 2004

International Journal of Nonlinear Sciences and Numerical Simulation

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Section: Pressure Correction Algorithms For the 1d Casementioning

confidence: 99%

Numerical Simulation of Pulse-Tube Refrigerators

Lyulina

Mattheij²,

Tijsseling³

et al. 2004

International Journal of Nonlinear Sciences and Numerical Simulation

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“…This compactness is a clear advantage over high resolution schemes based on flux/slope limiters [4,11] or (W)ENO reconstruction [8]. Our scheme is inspired by two papers by Thiart [9,10].…”

Section: Introductionmentioning

confidence: 99%

A Compact High Order Finite Volume Scheme for Advection-Diffusion-Reaction Equations

Anthonissen

Boonkkamp

2009

AIP Conference Proceedings

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Abstract. We present a new integral representation for the flux of the advection-diffusion-reaction equation, which is based on the solution of a local boundary value problem for the entire equation, including the source term. The flux therefore consists of two parts, corresponding to the homogeneous and particular solution of the boundary value problem. Applying Gauss-Legendre quadrature rules to the integral representation gives the high order finite volume complete flux scheme, which is fourth order accurate for both diffusion dominated and advection dominated flow.

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“…Our scheme is inspired by two papers by Thiart [30,31]. In these papers a finite volume method is combined with an exponential scheme for the flux.…”

Section: Introductionmentioning

confidence: 99%

The Finite Volume-Complete Flux Scheme for Advection-Diffusion-Reaction Equations

Boonkkamp

Anthonissen

2010

J Sci Comput

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We present a new finite volume scheme for the advection-diffusion-reaction equation. The scheme is second order accurate in the grid size, both for dominant diffusion and dominant advection, and has only a three-point coupling in each spatial direction. Our scheme is based on a new integral representation for the flux of the one-dimensional advection-diffusion-reaction equation, which is derived from the solution of a local boundary value problem for the entire equation, including the source term. The flux therefore consists of two parts, corresponding to the homogeneous and particular solution of the boundary value problem. Applying suitable quadrature rules to the integral representation gives the complete flux scheme. Extensions of the complete flux scheme to two-dimensional and time-dependent problems are derived, containing the cross flux term or the time derivative in the inhomogeneous flux, respectively. The resulting finite volume-complete flux scheme is validated for several test problems.

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Improved Finite-Difference Scheme for the Solution of Convection-Diffusion Problems With the Simplen Algorithm

Cited by 42 publications

References 10 publications

Numerical Simulation of Pulse-Tube Refrigerators

Numerical Simulation of Pulse-Tube Refrigerators

A Compact High Order Finite Volume Scheme for Advection-Diffusion-Reaction Equations

The Finite Volume-Complete Flux Scheme for Advection-Diffusion-Reaction Equations

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