• Interaction and multiscale mechanics
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• 제3권2호
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• pp.111-121
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• 2010

Dynamic analysis of nano/micro bio-sensors based on a multiscale atomistic/continuum theory is introduced. We use a generalized atomistic finite element method (GAFEM) to analyze a bio-sensor which has $3{\times}N_a{\times}N_p$ degrees of freedom, where $N_p$ is the number of representative unit cells and $N_a$ is the number of atoms per unit cell. The stiffness matrix is derived from interatomic potential between pairs of atoms. This work contains two studies: (1) the resonance analysis of nano bio-sensors with different amount of target analyte and (2) the dependence of resonance frequency on finite element mesh. We also examine the Courant-Friedrichs-Lewy (CFL) condition based on the highest resonance frequency. The CFL condition is the criterion for the time step used in the dynamic analysis by GAFEM. Our studies can be utilized to predict the performance of micro/nano bio-sensors from atomistic perspective.

• Environmental Engineering Research
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• 제21권2호
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• pp.171-179
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• 2016

This study analyzes guidelines to select optimum number of grids to represent behavior of a given water system appropriately. The EFDC model was chosen as a 3-D hydrodynamic and water quality model and salt was chosen as a surrogate variable of pollutant. The model is applied to an artificial canal that receives salt water from coastal area and fresh water from a river from respective gate according to previously developed gate operation rule. Grids are subdivided in vertical and horizontal (longitudinal) directions, respectively until no significant changes are found in salinity concentrations. The optimum grid size was determined by comparing errors in average salt concentrations between a test grid systems against the most complicated grid system. MSE (mean squared error) and MAE (mean absolute error) are used to compare errors. The CFL (Courant-Friedrichs-Lewy) number was used to determine the optimum number of grid systems for the study site though it can be used when explicit numerical method is applied only. This study suggests errors seem acceptable when both MSE and MAE are less than unity approximately.

• 대기
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• 제33권4호
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• pp.331-341
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• 2023

A numerical forecasting models usually predict future states by performing time integration considering fixed static time-steps. A time-step that is too long can cause model instability and failure of forecast simulation, and a time-step that is too short can cause unnecessary time integration calculations. Thus, in numerical models, the time-step size can be determined by the CFL (Courant-Friedrichs-Lewy)-condition, and this condition acts as a necessary condition for finding a numerical solution. A static time-step is defined as using the same fixed time-step for time integration. On the other hand, applying a different time-step for each integration while guaranteeing the stability of the solution in time advancement is called an adaptive time-step. The adaptive time-step algorithm is a method of presenting the maximum usable time-step suitable for each integration based on the CFL-condition for the adaptive time-step. In this paper, the adaptive time-step algorithm is applied for the Korean Integrated Model (KIM) to determine suitable parameters used for the adaptive time-step algorithm through the monthly verifications of 10-day simulations (during January and July 2017) at about 12 km resolution. By comparing the numerical results obtained by applying the 25 second static time-step to KIM in Supercomputer 5 (Nurion), it shows similar results in terms of forecast quality, presents the maximum available time-step for each integration, and improves the calculation efficiency by reducing the number of total time integrations by 19%.

• 대한기계학회논문집B
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• 제34권10호
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• pp.925-931
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• 2010

본 논문은 공동 주위 난류유동특성을 LES 기법으로 수치해석을 수행하여 알아보았다. 본 연구에 적용된 레이놀즈수는 공동 깊이만큼의 높이 h 에서의 유속을 기준으로 $1.0{\times}10^5$ 이며 3 차원 공동에서의 유동특성을 알아보았다. 적절한 비압축성 Filtered Navier-Stokes 방정식을 적용하기 위해, 계산격자를 공동 표면 근처에는 조밀하게 멀어질수록 성기게 생성하였으며, 이는 계산시간을 단축시키며 빠른 수렴을 도와준다. 또한, Boussinesq 가설을 subgrid-scale 난류모델에 적용하였고, Subgrid-scale 난류점성을 얻기 위해 smagorinsky-Lilly SGS 모델을 적용하였으며, 그 때의 CFL 수는 1.0 이다. 또한, 본 논문은 서로 다른 4 가지 형상의 공동의 및 입구조건의 변화에 따른 유동 특성도 함께 연구되었다.

• 한국해양공학회지
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• 제7권1호
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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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• 한국전산유체공학회 1998년도 추계 학술대회논문집
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• pp.7-12
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• 1998

Optimized high-order compact(OHOC) schemes were proposed, which have high spatial order of truncation and resolution to simulate the aeroacoustic problems due to unsteady compressible flows. Generally, numerical schemes are categorized explicit or implicit by time-marching method. In this research, OHOC differences which were developed with explicit time-marching method is used to have implicit formulation and the implicit OHOC differences result in block hepta-diagonal matrix. This paper presents the comparisons between the explicit and implicit OHOC schemes with a second order accuracy of time in the 1-d linear wave convection problem, and between the explicit OHOC scheme of 4th-order accuracy in time and the implicit OHOC scheme of 1st-order accuracy in tine for the 1-d nonlinear wave convection problem. With these comparisons, the characteristics of implicit OHOC scheme are shown in the point of CFL number.

• 한국전산유체공학회지
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• 제12권2호
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• pp.14-20
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• 2007

We present an improved immersed boundary method for computing incompressible viscous flow around an arbitrarily moving body on a fixed computational grid. The main idea is to incorporate feedback forcing scheme of virtual boundary method with Peskin's regularized delta function approach in order to use large CFL number and transfer quantities between Eulerian and Lagrangian domain effectively. From the analysis of stability limits and effects of feedback forcing gains, optimum regions of the feedback forcing are suggested.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2002년도 학술대회지
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• pp.225-228
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• 2002

Supersonic jet impingement on a flat plate has been investigated to show the flow physics for different jet heights and to demonstrate the adequacy of the characteristics-based flux-difference Wavier-Stokes code Current study also compares the steady-state solutions obtained with variable CFL number for different grid spacing with the time-accurate unsteady solutions using the inner iterations, displaying a good agreement between the two sets of numerical solutions. The unsteady nature of wall fluctuations due to bouncing of the plate shock is also uncovered for high pressure ratios. The methodology is then applied to a complex vertical launcher system where the jet plume hits the bottom wail, deflects into the plenum and eventually exits through the vertical uptake. Flow structures within vertical launcher system are captured and solutions are partially verified against the flight test data. Present jet impingement study thus shows the usefulness of CFD in designing a complex structure and predicting flow behavior within such a system.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2007년도 춘계 학술대회논문집
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• pp.23-29
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• 2007

We present an improved immersed boundary method for computing incompressible viscous flow around an arbitrarily moving body on a fixed computational grid The main idea is to incorporate feedback forcing scheme of virtual boundary method with Peskin's regularized delta function approach in order to use large CFL number and transfer quantities between Eulerian and Lagrangian domain effectively. From the analysis of stability limits and effects of feedback forcing gains, optimum regions of the feedback forcing are suggested.

• 대한기계학회논문집B
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• 제27권8호
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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.