• Journal of Ocean Engineering and Technology
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• v.7 no.1
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• pp.33-55
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• 1993

선수충격파의 문제를 푸는데 있어서 Boundary Integral Method(BIM)의 여러가지 수치 해석방법이 검토되었으며, 특히 여러가지 Time stepping scheme, Green function, far-field 조건등에 따른 수치해석안정성과 정확성의 상관관계가 연구되었다. von Neumann 안정성해석과 matrix 안정성해석 등을 이용한 선형 안정성해석을 기초로하여, 수치해석방법의 안정성 여부를 체계적으로 조사할 수 있는 parameter(Free Surface Stability number)를 설정하고, 이 parameter의 변화에 따른 비선형 운동해석을 연구하였다. 그 결과 비선형성이 심하지 않은 기진파의 경우에서는 비선형 운동해석의 수치해석 안정성의 선형 수치해석 안정성과 큰 차이가 없음을 알 수 있게 된다.

• 한국전산유체공학회:학술대회논문집
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• 2003.08a
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• pp.49-55
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• 2003

A comprehensive study has been made for the investigation of the convergence characteristics of the LU scheme for the Euler equations using von Neumann stability analysis. The stability results indicate that the convergence rate is governed by a specific parameter combination. Based on this insight it is shown that the LU scheme will not suffer convergence deterioration at any grid aspect ration if the local time step is defined using appropriate parameter combination. The numerical results demonstrate that this time step definition gives uniform convergence for grid aspect ratios from one to $1\times10^4$.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.32 no.9
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• pp.1-11
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• 2004

A comprehensive study has been made for the investigation of the convergence and stability characteristics of the LU scheme for solving the Euler equations on unstructured meshes. The von Neumann stability analysis technique was initially applied to a scalar model equation, and then the analysis was extended to the Euler equations. The results indicated that the convergence rate is governed by a specific combination of flow parameters. Based on this insight, it was shown that the LU scheme does not suffer any convergence deterioration at all grid aspect ratios, as long as the local time step is defined using an appropriate parameter combination.

• Journal of Korea Soil Environment Society
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• v.5 no.1
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• pp.3-12
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• 2000

The multi-region model, to describe preferential flow, is an equation representing solute transport in soils by dividing soil into numerous pore groups and using the hydraulic properties of the soil. As the model partial differential equation (PDE) is solved numerically with finite difference methods. a modified equivalent partial differential equation(MEPDE) of the partial differential equation of the multi-region model is derived to analyze the accuracy and consistency of the solution of the model PDE and the Von Neumann method is used to analyze the stability of the finite difference scheme. The evaluation obtained from the MEPDE indicated that the finite difference scheme was found to be consistent with the model PDE and had the second order accuracy The stability analysis is performed to analyze the model PDE with the amplification ratio and the phase lag using the Von Neumann method. The amplification ratio of the finite difference scheme gave non-dissipative results with various Peclet numbers and yielded the most high values as the Peclet number was one. The phase lag showed that the frequency component of the finite difference scheme lagged the true solution. From the result of the stability analysis for the model PDE, it is analyzed that the model domain should be discretized in the range of Pe < 1.0 and Cr < 2.0 to obtain the more accurate solution.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.215-222
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• 2000

A multigrid algorithm is developed for solving the one- dimensional initial boundary value problem. The numerical solutions of linear and nonlinear Burgers; equation for various initial conditions are studied. The stability conditions are derived by Von -Neumann analysis . Numerical results are presented.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.35 no.3
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• pp.183-195
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• 2007

Comprehensive mathematical comparison of numerical dissipation vector was made for a compressible and the preconditioned version Roe's Riemann solvers. Choi and Merkle type preconditioning method was selected from the investigation of the convergence characteristics of the various preconditioning methods for the flows over a two-dimensional bump. The investigation suggests a way of migration from a compressible code to a preconditioning code with a minor changes in Eigenvalues while maintaining the same code structure. Von Neumann stability condition and viscous Jacobian were considered additionally to improve the stability and accuracy for the viscous flow analysis. The developed code was validated through the applications to the standard validation problems.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.7 no.4
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• pp.320-327
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• 1996

This paper presents that the lossy or amplification property of the Finite Difference-Time Domain(FD-TD) method based on the leap-frog scheme is theoretically verified by using a plane wave analysis. The basic algorithm of the FD-TD method is introduced in order to help understanding the analysis procedure. Since our analysis is formulated by the Von Neumann's approach, the stability inequality is also produced as an another outcome.

• Nuclear Engineering and Technology
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• v.35 no.1
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• pp.45-54
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• 2003

A hyperbolic two-phase, two-fluid equation system developed in the previous work has been implemented in an existing nuclear safety analysis code, MARS. Although the implicit treatment of interfacial pressure force term introduced in momentum equation of the hyperbolic equation system is required to enhance the numerical stability, it is very difficult to implement in the code because it is not possible to maintain the existing numerical solution structure. As an alternative, two-step approach with stabilizer momentum equations has been selected. The results of a linear stability analysis by Von-Neumann method show the equivalent stability improvement with fully-implicit solution method. To illustrate the applicability, the new solution scheme has been implemented into the best-estimate thermal-hydraulic analysis code, MARS. This paper also includes the comparisons of the simulation results for the perturbation propagation and water faucet problems using both two-step method and the original solution scheme.

• 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.