• 제목/요약/키워드: Gauss-Seidel iteration

검색결과 21건 처리시간 0.024초

Diffusion synthetic acceleration with the fine mesh rebalance of the subcell balance method with tetrahedral meshes for SN transport calculations

  • Muhammad, Habib;Hong, Ser Gi
    • Nuclear Engineering and Technology
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    • 제52권3호
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    • pp.485-498
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    • 2020
  • A diffusion synthetic acceleration (DSA) technique for the SN transport equation discretized with the linear discontinuous expansion method with subcell balance (LDEM-SCB) on unstructured tetrahedral meshes is presented. The LDEM-SCB scheme solves the transport equation with the discrete ordinates method by using the subcell balances and linear discontinuous expansion of the flux. Discretized DSA equations are derived by consistently discretizing the continuous diffusion equation with the LDEM-SCB method, however, the discretized diffusion equations are not fully consistent with the discretized transport equations. In addition, a fine mesh rebalance (FMR) method is devised to accelerate the discretized diffusion equation coupled with the preconditioned conjugate gradient (CG) method. The DSA method is applied to various test problems to show its effectiveness in speeding up the iterative convergence of the transport equation. The results show that the DSA method gives small spectral radii for the tetrahedral meshes having various minimum aspect ratios even in highly scattering dominant mediums for the homogeneous test problems. The numerical tests for the homogeneous and heterogeneous problems show that DSA with FMR (with preconditioned CG) gives significantly higher speedups and robustness than the one with the Gauss-Seidel-like iteration.

Jacobian 행렬의 비 대각 요소를 보존시킬 수 있는 조류계산에 관한 연구 (A Study on the load Flow Calculation for preserving off Diagonal Element in Jacobian Matrix)

  • 이종기;최병곤;박정도;류헌수;문영현
    • 대한전기학회논문지:전력기술부문A
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    • 제48권9호
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    • pp.1081-1087
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    • 1999
  • Load Flow calulation methods can usually be divided into Gauss-Seidel method, Newton-Raphson method and decoupled method. Load flow calculation is a basic on-line or off-line process for power system planning. operation, control and state analysis. These days Newton-Raphson method is mainly used since it shows remarkable convergence characteristics. It, however, needs considerable calculation time in construction and calculation of inverse Jacobian matrix. In addition to that, Newton-Raphson method tends to fail to converge when system loading is heavy and system has a large R/X ratio. In this paper, matrix equation is used to make algebraic expression and then to slove load flow equation and to modify above defects. And it preserve P-Q bus part of Jacobian matrix to shorten computing time. Application of mentioned algorithm to 14 bus, 39 bus, 118 bus systems led to identical results and the same numbers of iteration obtained by Newton-Raphson method. The effect of computing time reduction showed about 28% , 30% , at each case of 39 bus, 118 bus system.

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비정렬 격자계에서 균질혼합 모델을 이용한 2차원 수중익형 주위의 캐비테이션 유동 해석 (CAVITATION FLOW SIMULATION FOR A 2-D HYDROFOIL USING A HOMOGENEOUS MIXTURE MODEL ON UNSTRUCTURED MESHES)

  • 안상준;권오준
    • 한국전산유체공학회지
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    • 제17권1호
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    • pp.94-100
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    • 2012
  • In this paper, the cavitating flows around a hydrofoil have been numerically investigated by using a 2-d multi-phase RANS flow solver based on pseudo-compressibility and a homogeneous mixture model on unstructured meshes. For this purpose, a vertex-centered finite-volume method was utilized in conjunction with 2nd-order Roe's FDS to discretize the inviscid fluxes. The viscous fluxes were computed based on central differencing. The Spalart-Allmaras one equation model was employed for the closure of turbulence. A dual-time stepping method and the Gauss-Seidel iteration were used for unsteady time integration. The phase change rate between the liquid and vapor phases was determined by Merkle's cavitation model based on the difference between local and vapor pressure. Steady state calculations were made for the modified NACA66 hydrofoil at several flow conditions. Good agreements were obtained between the present results and the experiment for the pressure coefficient on a hydrofoil surface. Additional calculation was made for cloud cavitation around the hydrofoil. The observation of the vapor structure, such as cavity size and shape, was made, and the flow characteristics around the cavity were analyzed. Good agreements were obtained between the present results and the experiment for the frequency and the Strouhal number of cavity oscillation.

이중시간전진법과 k-$\omega$ 난류모델을 이용한 익렬 내부 비정상 유동해석 (Unsteady cascade flow calculations of using dual time stepping and the k-$\omega$ turbulence model)

  • 최창호;유정열
    • 대한기계학회논문집B
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    • 제21권12호
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    • pp.1624-1634
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    • 1997
  • A numerical study on two-dimensional unsteady transonic cascade flow has been performed by adopting dual time stepping and the k-.omega. turbulence model. An explicit 4 stage Runge-Kutta scheme for the compressible Navier-Stokes equations and an implicit Gauss-Seidel iteration scheme for the k-.omega. turbulence model are proposed for fictitious time stepping. This mixed time stepping scheme ensures the stability of numerical computation and exhibits a good convergence property with less computation time. Typical steady-state convergence accelerating schemes such as local time stepping, residual smoothing and multigrid combined with dual time stepping shows good convergence properties. Numerical results are presented for unsteady laminar flow past a cylinder and turbulent shock buffeting problem for bicircular arc cascade flow is discussed.

핵 융합로 제1벽의 냉각성능에 관한 수치해석적 연구 (Numerical analysis of the cooling effects for the first wall of fusion reactor)

  • 정인수;황영규
    • 설비공학논문집
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    • 제11권1호
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    • pp.18-30
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    • 1999
  • A heat transfer analysis for the two-dimensional (2-D) steady state using finite difference method (FDM) is performed to predict the thermal behavior of the primary first-wall (FW) system of fusion reactor under various geometric and thermo-hydraulic conditions, such as the beryllium (Be) armor thickness, pitch of cooling tube, and coolant velocity. The FW consists of authentic steel (type 316 stainless steel solution annealed) for cooling tubes, Cu for cooling tubes embedding material, and Be for a protective armor, based on the International Thermonuclear Experiment Reactor (ITER) report. The present 2-D analysis, the control volume discretized with hybrid grid (rectangular grid and polar grid) and Gauss-Seidel iteration method are adapted to solve the governing equations. In the present study, geometric and thermo-hydraulic parameters are optimized with consideration of several limitations. Consequently, it is suggested that the adequate pitch of cooling tube is 22-32mm, the beryllium armor thickness is 10-12mm, and that the coolant velocity is 4.5m/s-6m/s for $100^{\circ}C$ of inlet coolant temperature. The cooling tube should locate near beryllium armor. But, it would be better for locating the center of Cu wall, considering problems of material and manufacturing. Also, 2-D analysis neglecting the axial temperature distribution of cooling tube is appropriate, regarding the discretization error in axial direction.

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Jacobian 행렬의 비 대각 요소를 보존시킬 수 있는 조류계산에 관한 연구 (A Study on a Load Flow calculation for Preserved Jacobian Matrix's elements except diagonal terms)

  • 문영현;이종기;최병곤;박정도;류헌수
    • 대한전기학회:학술대회논문집
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    • 대한전기학회 1998년도 추계학술대회 논문집 학회본부A
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    • pp.311-315
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    • 1998
  • Load Flow calculation methods can usually be divided into Gauss-Seidel method, Newton-Raphson method and decoupled method. Load flow calculation is a basic on-line or off-line process for power system planning, operation, control and state analysis. These days Newton-Raphson method is mainly used since it shows remarkable convergence characteristics. It, however, needs considerable calculation time in construction and calculation of inverse Jacobian matrix. In addition to that, Newton-Raphson method tends to fail to converge when system loading is heavy and system has a large R/X ratio. In this paper, matrix equation is used to make algebraic expression and then to solve load flow equation and to modify above defects. And it preserve certain part of Jacobian matrix to shorten the time of calculation. Application of mentioned algorithm to 14 bus, 39 bus, 118 bus systems led to identical result and the number of iteration got by Newton-Raphson method. The effect of time reduction showed about 28%, 30%, at each case of 39 bus, 118 bus system.

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통계적 패킷 음성 / 데이터 다중화기의 성능 해석 (Performance Analysis of a Statistical Packet Voice/Data Multiplexer)

  • 신병철;은종관
    • 한국통신학회논문지
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    • 제11권3호
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    • pp.179-196
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    • 1986
  • 본 논문에서는 통계적 패킷 음성/데이터 다중화기의 성능을 연구하였다. 성능해석은 음성과 데이터가 서로 분리된 한정된 queue를 사용하고, 전송에 있어서 음성이 데이터보다 우선권을 갖는 것을 가정하고, 다중화기의 출력 link를 시간 slot단위로 나누고 음성은 (M+1)-state의 Markov Process로, 데이터는 Poisson process로 modeling 하여 수행하였다. 전송시 음성신호가 데이터 신호보다 우선권을 가지므로 음성의 queueing behavior는 data에 거의 영향을 받지 않는다. 다라서 본 연구에서는 음성의 queueing behavior를 먼저 해석한 다음 data의 queueing behavior를 해석하였다. 패킷 음성 다중화기의 성능 해석은 입력상태와 buffer의 점유를 2차원의 Markov chain을 가지고 formulation하였고, 집적된 음성/data의 다중화기는 data를 추가한 3차원 Markov chain으로 하였다. 이러한 model을 사용하여 Gauss-Seidel방법으로 결과를 얻고 simulation으로 입증하였다. 이들 결과로 부터 음성 가입자의 수, 출력 link용량, 음성의 queue크기, 음성의 overflow확률에서는 서로 trade-off가 있고 data에서도 비슷한 tradeoff가 있음을 알았다. 또한 입력 traffic량과 link의 용량에 따라서 음성과 데이타간의 성능에서 서로 tradeoff가 있고, TASI의 이득이 2이상이고 음성가입자의 수가 적을 경우 데이타의 평균 지연시간은 buffer의 최대길이 보다 길음을 알아내었다.

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단형질 개체모형을 이용한 한우 육종가 추정프로그램 개발 (Development of Algorithm in Analysis of Single Trait Animal Model for Genetic Evaluation of Hanwoo)

  • 구양모;김정일;송치은;이기환;신재영;장현기;최태정;김시동;박병호;조광현;이승수;최연호;김병우;이정규;송훈
    • Journal of Animal Science and Technology
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    • 제55권5호
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    • pp.359-365
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    • 2013
  • 단형질 개체모형을 이용한 육종가 추정프로그램의 해를 구하는 컴퓨터 프로그램을 포트란 언어를 이용하여 자체개발하였고, 프로그램은 자료기반으로 반복적으로 계산을 해 나가는 간접법을 이용한 것으로 일반적인 알고리즘으로 프로그램을 개발하고 이의 효율을 개선한 개선알고리즘으로 프로그램을 개발하여, 두 프로그램 간 효율을 비교하였다. 기존의 전통적인 알고리즘은 순차적인 반복문을 이용하여 자료를 읽고 기록하는 방법이며, 새로운 알고리즘은 효과별로 LHS를 직접 작성하여 추정하는 방법을 사용하였다. 개발된 두 가지 프로그램으로 육종가를 추정하고, 그 추정 값이 정확하게 평가되었는지 알아보기 위하여 기존에 개발되어 사용되고 있는 BLUPF90 (Misztal, 2007)과 MTDFREML (Boldman 등, 1999)과 비교하여 보았다. 서로 다른 프로그램으로 추정된 육종가간의 상관은 전체 항목에서 99% 이상 고도의 상관이 나타났으며, 프로그램 추정치 간의 높은 상관으로 볼 때 Model I, Model II는 정확하게 개발되었고 평가된 것을 확인할 수 있었다. Solution이 수렴 될 때까지의 반복횟수는 Model I은 2,568 round, Model II는 1,038 round로 수렴되어 Model II가 Model I보다 작은 반복횟수에서 수렴이 된 것을 확인할 수 있었으며, 수렴속도는 Model I은 256.008초, Model II는 235.729초로 Model II가 Model I 보다 약 10% 정도 개선된 것을 확인할 수 있었다. 개발된 프로그램을 기존 D/B와 연계한다면 농가 및 지자체 등에 지속적인 개량 정보를 제공할 수 있으며, 농가 단위 암소 유전능력평가로 암소개량을 도모할 수 있을 것이라 사료된다.

우주발사체의 플룸에 따른 유동박리 현상에 대한 수치적 연구 (NUMERICAL INVESTIGATION OF PLUME-INDUCED FLOW SEPARATION FOR A SPACE LAUNCH VEHICLE)

  • 안상준;허남건;권오준
    • 한국전산유체공학회지
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    • 제18권2호
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    • pp.66-71
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    • 2013
  • In this paper, the supersonic flows around space launch vehicles have been numerically simulated by using a 3-D RANS flow solver. The focus of the study was made for investigating plume-induced flow separation(PIFS). For this purpose, a vertex-centered finite-volume method was utilized in conjunction with 2nd-order Roe's FDS to discretize the inviscid fluxes. The viscous fluxes were computed based on central differencing. The Spalart-Allmaras model was employed for the closure of turbulence. The Gauss-Seidel iteration was used for time integration. To validate the flow solver, calculation was made for the 0.04 scale model of the Saturn-5 launch vehicle at the supersonic flow condition without exhaust plume, and the predicted results were compared with the experimental data. Good agreements were obtained between the present results and the experiment for the surface pressure coefficient and the Mach number distribution inside the boundary layer. Additional calculations were made for the real scale of the Saturn-5 configuration with exhaust plume. The flow characteristics were analyzed, and the PIFS distances were validated by comparing with the flight data. The KSLV-1 is also simulated at the several altitude conditions. In case of the KSLV-1, PIFS was not observed at all conditions, and it is expected that PIFS is affected by the nozzle position.

강성 결합 기법을 통한 2계 자유도 플러터 해석 (Strongly Coupled Method for 2DOF Flutter Analysis)

  • 주완돈;이관중;이동호;이기학
    • 한국항공우주학회지
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    • 제34권1호
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    • pp.24-31
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    • 2006
  • 본 연구에서는 완전 내재적 기법을 이용한 2계 자유도 모델에 대한 플러터 해석을 수행하였다. 유동해석을 위하여 2차원 Navier-Stokes 지배방정식을 ε-SST 난류모델과 DP-SGS 병렬화 기법을 이용해 구성하였다. 구조해석을 위하여 피치 와 플런지의 2계 자유도를 갖는 모델을 구성하였으며 시간영역에서의 해석을 위하여 유동해석과 마찬가지로 이중 시간 전진 기법을 이용하였다. 가상 시간 전진에서 유체-구조 결합을 통해서 강성결합을 구현하였으며 이를 천음속 플러터 예측에 적용하였다. 플러터 해석의 전형적인 응답인 감쇠응답, 중립응답, 발산응답 및 limit cycle oscillation (LCO) 등을 계산하였으며, 더불어 플러터 속도 경계곡선을 작성하였다. 천음속 플러터 해석은 난류모델 뿐만 아니라 유체-구조 결합 방법에 따라 다른 특성을 보임을 확인하였다.