• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.6
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• pp.788-802
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• 1998

A numerical method using dual time stepping and preconditioning procedure for efficient computations of unsteady low speed compressible flow problems is developed. The time-derivative preconditioning method which is valid at low speed flow conditions cannot maintain temporal accuracy because of the modification of the time-derivative term in Navier-Stokes equations. The dual time stepping procedure is incorporated to enable the time accurate computations and this procedure introduces a pseudo-time derivative in addition to the physical time derivative. At a given physical time, an inner iteration can be carried out until a steady state in pseudo-time is achieved. This will effectively yield a time accurate solution. Computational capabilities of the above algorithm are demonstrated through computation of a variety of practical fluid flows and it is shown that the algorithms is efficient in the essentially incompressible flows and low Mach number compressible flows with heat source.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.7
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• pp.1840-1850
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• 1994

Enhancement of numerical algorithms for low speed compressible flow will be considered. Contemporary time-marching algorithm has been widely accepted and applied as the method of choice for transonic, supersonic and hypersonic flows. In the low Mach number regime, time-marching algorithms do not fare as well. When the velocity is small, eigenvalues of the system of compressible equations differ widely so that the system becomes very stiff and the convergence becomes very slow. This characteristic can lead to difficulties in computations of many practical engineering problems. In the present approach, the time-derivative preconditioning method will be used to control the eigenvalue stiffness and to extend computational capabilities over a wide range of flow conditions (from very low Mach number to supersonic flow). Computational capabilities of the above algorithm will be demonstrated through computation of a variety of practical engineering problems.

• 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.

• 한국연소학회:학술대회논문집
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• 2005.10a
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• pp.269-272
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• 2005

Due to the high density and heating value, liquid fuel is attractive for ramjet propulsion system. Liquid fuel requires time to evaporation and mix with incoming air before ignition; insufficient evaporation and mixing result in low combustion efficiency and instability. So the numerical studies are conducted to investigate the spray and combustion characteristics of a liquid-fueled dump type Integrated Rocket Ramjet combustor. The governing equations are solved by means of a finite-volume using time derivative preconditioning method for chemical reacting flow. The liquid phase is treated by solving Lagrangian equations of motion and transport for the life histories of a statistically significant sample of individual droplets.

• 한국연소학회:학술대회논문집
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• 2006.04a
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• pp.218-222
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• 2006

Due to the high density and heating value, liquid fuel is attractive for ramjet propulsion system. Liquid fuel requires time to evaporation and mix with incoming air before ignition; insufficient evaporation and mixing result in low combustion efficiency and instability. So the numerical studies are conducted to investigate the spray and combustion characteristics of a liquid-fueled dump type Ramjet combustor. The governing equations are solved by means of a finite-volume using time derivative preconditioning method for chemical reacting flow. The liquid phase is treated by solving Lagrangian equations of motion and transport for the life histories of a statistically significant sample of individual droplets.

• 한국전산유체공학회:학술대회논문집
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• 1998.05a
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• pp.35-42
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• 1998

Time marching algorithms applied to compressible Navier-Stokes equation have a convergence problem at low Mach number. It is mainly due to the eigenvalue stiffness and pressure singularity as Mach number approaches to zero. Among the several methods to overcome the shortcomings of time marching scheme, time derivative preconditioning method have been used successfully. In this numerical analysis, we adopted a preconditioner of K.H. Chen and developed a two-dimensional, axisymmetric Navier-Stokes program. The steady state driven cavity flow and backward facing step flow problems were computed to confirm the accuracy and the robustness of preconditioned algorithm for low Mach number flows. And the transonic and supersonic flows insice the JPL axisymmetric nozzle internal flow is exampled to investigate the effects of preconditioning at high Mach number flow regime. Test results showed excellent agreement with the experimental data.