• 한국전산유체공학회:학술대회논문집
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• 2009.04a
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• pp.269-276
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• 2009

The local preconditioning method has both robust convergence and accurate solutions by using local flow properties for parameters in the preconditioning matrix. Preconditioning methods have been very effective to low speed inviscid flows. In the viscous and turbulent flows, deterioration of convergence should be overcame on the high aspect ratio grids to get better convergence and accuracy. In the present study, the local time stepping and min-CFL/max-VNN definitions are applied to compare the results and we propose the method that switches between two methods. The min-CFL definition is applied for inviscid flow problems and the min-CFL/max-VNN definition is implemented to viscous and turbulent flow problems.

• 한국전산유체공학회:학술대회논문집
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• 2002.10a
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• pp.95-102
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• 2002

Studies of the numerical characteristics of implicit upwind schemes, such as upwind ADI, Line Gauss-Seidel(LGS) and Point Gauss-Seidel(LU) algorithms, for preconditioned Navier-Stokes equations ate performed. All the algorithms are expressed in approximate factorization form and Von Neumann stability analysis and convergence studies are made. Preconditioning is applied for efficient convergence at low Mach numbers and low Reynolds numbers. For high aspect ratio computations, the ADI and LGS algorithms show efficient and uniform convergence up to moderate aspect ratio if we adopt viscous preconditioning based on min- CFL/max- VNN time-step definition. The LU algorithm, on the other hand, shows serious deterioration in convergence rate as the grid aspect ratio increases. Computations for practical applications also verify these results.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.8
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• pp.1122-1133
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• 2003

Numerical characteristics of implicit upwind schemes, such as upwind ADI, line Gauss-Seidel (LGS) and point Gauss-Seidel (LU) algorithms, for Navier-Stokes equations have been investigated. Time-derivative preconditioning method was applied for efficient convergence at low Mach/Reynolds number regime as well as at large grid aspect ratios. All the algorithms were expressed in approximate factorization form and von Neumann stability analysis was performed to identify stability characteristics of the above algorithms in the presence of high grid aspect ratios. Stability analysis showed that for high aspect ratio computations, the ADI and LGS algorithms showed efficient damping effect up to moderate aspect ratio if we adopt viscous preconditioning based on min-CFL/max-VNN time-step definition. The LU algorithm, on the other hand, showed serious deterioration in stability characteristics as the grid aspect ratio increases. Computations for several practical applications also verified these results.