• Journal of Korean Society of Coastal and Ocean Engineers
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• v.30 no.4
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• pp.143-152
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• 2018

Numerical convergence and stability of TVD schemes have been applied in the FUNWAVE-TVD model were compared. The fourth order accurate MUSCL-TVD scheme using minmod limiter suggested by Yamamoto and Daiguji (1993), the fourth order accurate MUSCL-TVD scheme using van-Leer limiter suggested by Erduran et al. (2005) and the second order accurate MUSCL-TVD scheme using van-Leer limiter in Zhou et al. (2001) were compared. Comparisons of the numerical scheme were conducted with experimental data of Vincent and Briggs irregular wave experiments. In comparison with the fourth order accurate scheme using van-Leer limiter, the fourth order accurate scheme using minmod limiter is less dissipative but required lower CFL condition for stable numerical solution. On the other hand, the scheme using van-Leer limiter required smaller resolution spatial grid due to numerical dissipation, but relatively higher CFL condition can be used compared to the scheme using minmod limiter. In the breaking wave experiments which were conducted using high resolution spatial grid to reduce numerical dissipation, the characteristic of the schemes can be clearly observed. Numerical instabilities and blow-up of the numerical solutions were found in the irregular wave breaking simulation with the scheme using minmod limiter. However, the simulation can be completed with the scheme using van-Leer limiter, but required low CFL condition. Good agreements with the observed data were also observed in the results using van-Leer limiter.

• Journal of computational fluids engineering
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• v.10 no.1
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• pp.99-106
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• 2005

Performance of first, second and third order accurate methods for calculation of in viscid fluxes in fluid flow governing equations are investigated here. For the purpose, an upwind method based on Roe's scheme is used to solve 2-dimensional Euler equations. To increase the accuracy of the method two different schemes are applied. The first one is a second and third order upwind-based algorithm with the MUSCL extrapolation Van Leer (1979), based on primitive variables. The other one is an upwind-based algorithm with the Chakravarthy extrapolation to the fluxes of mass, momentum and energy. The results show that the thickness of shock layer in the third order accuracy is less than its value in second order. Moreover, applying limiter eliminates the oscillations near the shock while increases the thickness of shock layer especially in MUSCL method using Van Albada limiter.

• Journal of computational fluids engineering
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• v.12 no.1
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• pp.43-52
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• 2007

A comparative study on flux functions for the 2-dimensional Euler equations has been conducted. Explicit 4-stage Runge-Kutta method is used to integrate the equations. Flux functions used in the study are Steger-Warming's, van Leer's, Godunov's, Osher's(physical order and natural order), Roe's, HLLE, AUSM, AUSM+, AUSMPW+ and M-AUSMPW+. The performance of MUSCL limiters and MLP limiters in conjunction with flux functions are compared extensively for steady and unsteady problems.

• Proceedings of the Korea Water Resources Association Conference
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• 2019.05a
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• pp.109-109
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• 2019

본 연구에서는 강우-유출 과정 모의를 위한 GPU 기반 확산파 모형을 개발하였다. 확산파 방정식을 풀기위한 수치기법으로는 유한체적법을 이용하였으며, van Leer TVD limiter를 적용한 MUSCL 기법을 이용하여 각 셀의 인터페이스의 물리적 성질을 재구성하여 구하였다. 또한, 침투를 고려하기 위하여 Horton 침투 모형을 이용하였다. 개발된 모형을 이용하여 1D single overland plane과 2D V-shaped overland에서 강우-유출 과정을 모의실험을 하였으며, 각각 해석해와 dynamic wave model을 이용하여 계산된 수치 결과와 비교하여 본 모형의 정확성을 검증하였다. 또한, 1D와 2D의 기복이 심한 지형에 적용하여 강우-유출과정이 본 모형을 통하여 물리적으로 타당한 해석이 가능함을 검증하였다. 마지막으로 복잡한 실제 지형에 적용하였으며, 측정값과의 비교를 통하여 실제 유역에서의 확산파 모형의 적정성을 검증하였다. 또한, 본 연구에서는 NVIDIA사의 GPU인 Geforce GTX 1050과 GPU의 병렬 연산 처리 능력을 활용할 수 있는 NVIDIA사의 CUDA-Fortran을 이용하여 GPU 기반 확산파 모형을 개발하였다. PC windows에서 CPU(Intel i7, 4.70 GHz) 기반 모형 대비 GPU 기반 모형의 계산속도 성능을 비교한 결과, 격자 간격이 증가할수록 CPU 기반 모형 대비 GPU 기반 모형의 연산 효율이 증가하였으며, 격자 간격이 $3200{\times}3200$일 때, CPU 기반 모형 대비 GPU 기반 모형의 연산 효율이 최대 약 150배 증가하였다.

• International Journal of Aeronautical and Space Sciences
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• v.13 no.3
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• pp.307-316
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• 2012

Numerical simulations of 3D aircraft configurations are performed in order to understand the effects of turbulence models on the prediction of aircraft's aerodynamic characteristics. An in-house CFD code that solves 3D RANS equations and two-equation turbulence model equations are used. The code applies Roe's approximated Riemann solver and an AF-ADI scheme. Van Leer's MUSCL extrapolation with van Albada's limiter is also adopted. Various versions of Menter's $k-{\omega}$ SST turbulence models as well as Coakley's $q-{\omega}$ model are incorporated into the CFD code. Menter's $k-{\omega}$ SST models include the standard model, the 2003 model, the model incorporating the vorticity source term, and the model containing controlled decay. Turbulent flows over a wing are simulated in order to validate the turbulence models contained in the CFD code. The results from these simulations are then compared with computational results from the $3^{rd}$ AIAA CFD Drag Prediction Workshop. Numerical simulations of the DLR-F6 wing-body and wing-body-nacelle-pylon configurations are conducted and compared with computational results of the $2^{nd}$ AIAA CFD Drag Prediction Workshop. Aerodynamic characteristics as well as flow features are scrutinized with respect to the turbulence models. The results obtained from each simulation incorporating Menter's $k-{\omega}$ SST turbulence model variations are compared with one another.

• 한국전산유체공학회:학술대회논문집
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• 2006.05a
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• pp.311-314
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• 2006

The supersonic flow around tandem cavities was investigated by three- dimensional numerical simulations using the Reynolds-Averaged Navier-Stokes(RANS) equation with the $\kappa-\omega$ thrbulence model. The flow around a cavity is characterized as unsteady flow because of the formation and dissipation of vortices due to the interaction between the freestream shear layer and cavity internal flow, the generation of shock and expansion waves, and the acoustic effect transmitted from wake flow to upstream. The upwind TVD scheme based on the flux vector split using van Leer's limiter was used as the numerical method. Numerical calculations were performed by the parallel processing with time discretizations carried out by the 4th-order Runge-Kutta method. The aspect ratio of cavities are 3 for the first cavity and 1 for the second cavity. The ratio of cavity interval to depth is 1. The ratio of cavity width to depth is 1 in the case of three dimensional flow. The Mach number and the Reynolds number were 1.5 and $4.5{\times}10^5$, respectively. The characteristics of the dominant frequency between two-dimensional and three-dimensional flows were compared, and the characteristics of the second cavity flow due to the fire cavity flow cavity flow was analyzed. Both two dimensional and three dimensional flow oscillations were in the 'shear layer mode', which is based on the feedback mechanism of Rossiter's formula. However, three dimensional flow was much less turbulent than two dimensional flow, depending on whether it could inflow and outflow laterally. The dominant frequencies of the two dimensional flow and three dimensional flows coincided with Rossiter's 2nd mode frequency. The another dominant frequency of the three dimensional flow corresponded to Rossiter's 1st mode frequency.

• Journal of Mechanical Science and Technology
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• v.20 no.8
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• pp.1256-1265
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• 2006

The supersonic flows around tandem cavities were investigated by two-dimensional and three-dimensional numerical simulations using the Reynolds-Averaged Navier-Stokes (RANS) equation with the k- ω turbulence model. The flow around a cavity is characterized as unsteady flow because of the formation and dissipation of vortices due to the interaction between the freestream shear layer and cavity internal flow, the generation of shock and expansion waves, and the acoustic effect transmitted from wake flow to upstream. The upwind TVD scheme based on the flux vector split with van Leer's limiter was used as the numerical method. Numerical calculations were performed by the parallel processing with time discretizations carried out by the 4th-order Runge- Kutta method. The aspect ratios of cavities are 3 for the first cavity and 1 for the second cavity. The ratio of cavity interval to depth is 1. The ratio of cavity width to depth is 1 in the case of three dimensional flow. The Mach number and the Reynolds number were 1.5 and $4.5{\times}10^5$, respectively. The characteristics of the dominant frequency between two- dimensional and three-dimensional flows were compared, and the characteristics of the second cavity flow due to the first cavity flow was analyzed. Both two dimensional and three dimensional flow oscillations were in the 'shear layer mode', which is based on the feedback mechanism of Rossiter's formula. However, three dimensional flow was much less turbulent than two dimensional flow, depending on whether it could inflow and outflow laterally. The dominant frequencies of the two dimensional flow and three dimensional flows coincided with Rossiter's 2nd mode frequency. The another dominant frequency of the three dimensional flow corresponded to Rossiter's 1st mode frequency.