Covariant Velocity-Based Calculation Procedure With Nonstaggered Grids for Computation of Pulsatile Flows

Lee, Denz; Chiu, Jeng Jiann

doi:10.1080/10407799208944905

Cited by 18 publications

(11 citation statements)

References 20 publications

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“…If the diagonal dominance for coefficient matrix of the pressurecorrection equation can be enhanced, it will be easier to get an accurate pressure correction, and the convergence of the algorithm is therefore improved. The method of choosing cell face velocities, as indicated by Lee and Chiu (1992) and Choi et al (1993aChoi et al ( , 1993b, is concerned with using physical covariant velocities instead of the widely used contravariant components at cell faces to derive``another'' pressure-correction equation. However, this method cannot enhance the diagonal dominance for the coefficient matrix of the equation, as the two pressure-correction equations are equivalent.…”

Section: Discretisation Equationsmentioning

confidence: 99%

“…Furthermore, if we choose the components of physical covariant velocities, V i to calculate the convection at cell faces,``another'' pressure correction equation can be derived; this has been indicated by Karki and Patankar (1988a), Lee and Chiu (1992), and Choi et al (1993aChoi et al ( , 1993b. That is, according to equation (8) and Table I (11) and (12), we have:…”

Section: Discretisation Equationsmentioning

confidence: 99%

“…To improve such performance, many studies have attempted to employ different velocity components as dependent variables. For example, Patankar (1988a, 1988b) and Lee and Chiu (1992) chose the covariant physical components, while Xi et al (1991) and Sharatchandra and Rhode (1994) used the contravariant components as dependent variables. Meanwhile, other investigators tried to obtain a pressure-correction equation in which the coefficient matrix may be stronger in diagonal dominance by using different velocity components at cell faces of control volume.…”

Section: Introductionmentioning

confidence: 99%

“…Meanwhile, other investigators tried to obtain a pressure-correction equation in which the coefficient matrix may be stronger in diagonal dominance by using different velocity components at cell faces of control volume. For instance, Karki and Patankar (1988a, 1988b, 1989, Lee and Chiu (1992), and Choi et al (1993aChoi et al ( , 1993b applied physical covariant velocities at cell faces instead of the widely used contravariant components. Indeed, all of these studies have contributed a lot to improving the SIMPLE algorithm and made it more efficient and suitable for solving transport problems of fluid flow and heat transfer.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The effect of choosing dependent variables and cell‐face velocities on convergence of the SIMPLE algorithm using non‐orthogonal grids

Lai

Yan

2001

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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In this paper the effects of choosing dependent variables and cell face velocities on convergence of the SIMPLE algorithm are discussed. Using different velocity components as either dependent variables or cell-face velocities, both convergent rate and calculation accuracy of the algorithm are compared and studied. A novel method, named``cross-correction'', is developed to improve the convergence of the algorithm of using non-orthogonal grids. Cases with benchmark and analytical solutions are used for numerical experiments and validation. The results show that, although different velocity components are employed as either dependent variables or cell face velocities, there is no obvious difference in both the convergent rates and numerical solutions. Moreover, the``cross-correction'' method is validated by computations with several first-order and high-order convection schemes; and the generality of convergence improvement achieved by the method is shown in the paper.The current issue and full text archive of this journal is available at

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Section: Discretisation Equationsmentioning

confidence: 99%

Section: Discretisation Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The effect of choosing dependent variables and cell‐face velocities on convergence of the SIMPLE algorithm using non‐orthogonal grids

Lai

Yan

2001

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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“…They estimated the degree of the dependence of numerical solutions on the velocity underrelaxation factor and obtained a formulation of the momentum interpolation which is independent of the velocity underrelaxation factor for a converged solution in Cartesian co-ordinates. The momentum interpolation method has achieved great success and is now being widely used in a variety of fluid flow calculations [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Study of the effect of the non-orthogonality for non-staggered grids—the theory

Zhang

1998

Int. J. Numer. Meth. Fluids

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A Segregated Solution Algorithm for Incompressible Flows in General Co-Ordinates

Sheu

Lee

1996

Int. J. Numer. Meth. Fluids

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To analyse an incompressible Navier4tokes flow problem in a boundary-fitted curvilinear co-odinatc system is definitely not a trivial task. In the primitive variable formulation, choices between wrhg variables and their storage points have to be made judiciously. The present work engages Contravariant velocity components and scalar pressure which stagger each other in the mesh to prevent even-odd pressure oscillations from emerging. Now that smoothness of the pnssure field is attainable, the remaining task is to ensure a disuete divergence-fire velocity field for an incompmsible flow simulation. Aside h m the flux discretiZations, the indqensable metric tensors, Jacobian and Chistoffel symbols in the transformed equations should be approximated with care. The guidmg idea is to get the property of geometric identity Pertaining to these grid-sensitive discretizatons. In addition, how to maintain the revertible one-toone equivalence at the discrete level between primitive and contravariant velocities is another theme in the present staggered formulation. A semi-implicit segregated solution algorithm felicitous for a large-scale flow simulation was utilized to solve the entire set of basic equations iteratively. Also of note is that the present segregated solution algorithm has the Virtue of reqUiring no userspecified relaxation pammeters for speedmg up the satisfaction of incompmsibility in an optimal sense. "hu benchmark problems, including an analytic problem, were investigated to j u s t i e the capability of the present formulation in handing problems with complex geometry. The test cases considered and the results obtained herein make a useful contribution in solving problems subsuming cells with arbitrary shapcs in a boundary-fitted grid system.

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Covariant Velocity-Based Calculation Procedure With Nonstaggered Grids for Computation of Pulsatile Flows

Cited by 18 publications

References 20 publications

The effect of choosing dependent variables and cell‐face velocities on convergence of the SIMPLE algorithm using non‐orthogonal grids

The effect of choosing dependent variables and cell‐face velocities on convergence of the SIMPLE algorithm using non‐orthogonal grids

Study of the effect of the non-orthogonality for non-staggered grids—the theory

A Segregated Solution Algorithm for Incompressible Flows in General Co-Ordinates

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