Finite Difference Scheme for the Numerical Solution of Fluid Flow and Heat Transfer Problems on Nonstaggered Grids

Thiart, G. D.

doi:10.1080/10407799008961732

Cited by 60 publications

(45 citation statements)

References 18 publications

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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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“…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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“…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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“…The development of the complete flux scheme is inspired by papers by Thiart [10,11]. The basic idea of the complete flux scheme is to compute the numerical flux at a cell interface from a local (one-dimensional) boundary value problem for the entire equation, including the source term.…”

Section: Introductionmentioning

confidence: 99%

“…The surface integral of the flux over the boundary Γ j,l = ∂Ω j,l contains four terms and is given by 10) where for example r = r j+1/2 denotes the interface {r j+1/2 }× 0, 2π × z l−1/2 , z l+1/2 , and likewise for all other interfaces. For the approximation of the volume integrals in (2.5) we use once more the midpoint rule, giving the approximation…”

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confidence: 99%

The Complete Flux Scheme for Conservation Laws in Curvilinear Coordinates

Boonkkamp¹,

Anthonissen²

2012

Finite Volume Method - Powerful Means of Engineering Design

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Finite Difference Scheme for the Numerical Solution of Fluid Flow and Heat Transfer Problems on Nonstaggered Grids

Cited by 60 publications

References 18 publications

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

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

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

The Complete Flux Scheme for Conservation Laws in Curvilinear Coordinates

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