A single cell high order scheme for the convection‐diffusion equation with variable coefficients

Gupta, Murli M.; Manohar, Ram; Stephenson, J. W.

doi:10.1002/fld.1650040704

Cited by 226 publications

(181 citation statements)

References 4 publications

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“…Dennis and Hudson [1], MacKinnon and Johnson [2], Gupta et al [3], Spotz and Carey [4] and Li et al [5] have demonstrated the efficiency of the high order compact schemes on the streamfunction and vorticity formulation of 2-D steady incompressible Navier-Stokes equations.…”

Section: Introductionmentioning

confidence: 99%

Fourth-order compact formulation of Navier-Stokes equations and driven cavity flow at high Reynolds numbers

Ertürk

Gökçöl

2005

Int. J. Numer. Meth. Fluids

109

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SUMMARYA new fourth order compact formulation for the steady 2-D incompressible Navier-Stokes equations is presented. The formulation is in the same form of the Navier-Stokes equations such that any numerical method that solve the Navier-Stokes equations can easily be applied to this fourth order compact formulation. In particular in this work the formulation is solved with an efficient numerical method that requires the solution of tridiagonal systems using a fine grid mesh of 601×601. Using this formulation, the steady 2-D incompressible flow in a driven cavity is solved up to Reynolds number of 20,000 with fourth order spatial accuracy. Detailed solutions are presented.

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Section: Introductionmentioning

confidence: 99%

Fourth-order compact formulation of Navier-Stokes equations and driven cavity flow at high Reynolds numbers

Ertürk

Gökçöl

2005

Int. J. Numer. Meth. Fluids

109

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“…The derivation of fourth-order finite difference approximations on the rotated grid is based on Taylor series expansions which is similar to the one investigated by Gupta, Manohar and Stephenson [7,12]. To formulate the rotated fourth-order nine-point finite difference scheme, we consider the following grid stencil: By considering all alternate points on the solution domain for the case 9 n as illustrated in FIGURE 2, a point iterative scheme based on the rotated finite difference formula can be formulated.…”

Section: The Npf Finite Difference Schemesmentioning

confidence: 99%

“…A set of such boundary approximations are listed in [14]. On the contrary, the compact scheme does not need any special boundary approximation [7].…”

Section: The Npf Finite Difference Schemesmentioning

confidence: 99%

“…The fourth-order nine-point compact finite difference scheme for solving the convection-diffusion equation with constant and variable coefficients on uniform grid was introduced by Gupta, Manohar and Stephenson in the early 80's [6,7]. Similar fourth-order compact schemes have been developed by Dennis and Hudson [8], MacKinnon and Johnson [9], Li, Tang and Fornberg [10], Spotz and Carey [11].…”

Section: Introductionmentioning

confidence: 99%

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New high order iterative scheme in the solution of convection-diffusion equation

Ling¹,

Ali²

2014

AIP Conference Proceedings

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Abstract. In this paper, a new fourth-order nine-point finite difference scheme based on the rotated grid combined with the traditional Successive Over Relaxation (SOR)-type iterative method is discussed in solving the two-dimensional convection-diffusion partial differential equation (pde) with variable coefficients. Numerical experiments are carried out to verify the high accuracy solution of the scheme. Comparisons with the exact solutions also show that the rotated scheme converges faster than the existing compact scheme of the same order.

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“…See [45,33] for a review on fundamental formulations of incompressible Navier-Stokes equations. The appearance and growing popularity of "compact schemes" brought a renewed interest in the aforementioned methods ( [26,17,18,43,42,19,50,35,1,13]). The purestreamfunction formulation for the time-dependent Navier-Stokes system in planar domains has been used in [31,32,30] some twenty years ago.…”

Section: Introductionmentioning

confidence: 99%

A High Order Compact Scheme for the Pure-Streamfunction Formulation of the Navier-Stokes Equations

Ben‐Artzi

Croisille²,

Fishelov

2009

J Sci Comput

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Abstract. In this paper we continue the study, which was initiated in [10,28,9,7], of the numerical resolution of the pure streamfunction formulation of the timedependent two-dimensional Navier-Stokes equation. Here we focus on enhancing our second-order scheme, introduced in [28,9,7], to fourth order accuracy. We construct fourth order approximations for the Laplacian, the biharmonic and the nonlinear convective operators. The scheme is compact (nine-point stencil) for the Laplacian and the biharmonic operators, which are both treated implicitly in the time-stepping scheme. The approximation of the convective term is compact in the no-leak boundary conditions case and is nearly compact (thirteen points stencil) in the case of general boundary conditions. However, we stress that in any case no unphysical boundary condition was applied to our scheme. Numerical results demonstrate that the fourth order accuracy is actually obtained for several testcases.

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A single cell high order scheme for the convection‐diffusion equation with variable coefficients

Cited by 226 publications

References 4 publications

Fourth-order compact formulation of Navier-Stokes equations and driven cavity flow at high Reynolds numbers

Fourth-order compact formulation of Navier-Stokes equations and driven cavity flow at high Reynolds numbers

New high order iterative scheme in the solution of convection-diffusion equation

A High Order Compact Scheme for the Pure-Streamfunction Formulation of the Navier-Stokes Equations

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