• Title/Summary/Keyword: Step-diagonal method

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MULTI SPLITTING PRECONDITIONERS FOR A SYMMETRIC POSITIVE DEFINITE MATRIX

  • Yun Jae-Heon;Kim Eun-Heui;Oh Se-Young
    • Journal of applied mathematics & informatics
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    • v.22 no.1_2
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    • pp.169-180
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    • 2006
  • We study convergence of multisplitting method associated with a block diagonal conformable multisplitting for solving a linear system whose coefficient matrix is a symmetric positive definite matrix which is not an H-matrix. Next, we study the validity of m-step multisplitting polynomial preconditioners which will be used in the preconditioned conjugate gradient method.

UNSTEADY AERODYNAMIC ANALYSIS OF HELICOPTER ROTOR BLADES USING DIAGONAL IMPLICIT HARMONIC BALANCE METHOD (중첩 격자 기법이 적용된 대각 내재적 조화균형법을 이용한 헬리콥터 로터 블레이드의 비정상 공력 해석)

  • Im, D.K.;Choi, S.I.;Kim, E.;Kwon, J.H.;Park, S.H.
    • Journal of computational fluids engineering
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    • v.17 no.1
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    • pp.70-77
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    • 2012
  • In this paper, diagonal implicit harmonic balance method with overset grid technique is applied to analyze helicopter rotor blade flow in hover and forward flight condition. The chimera grid need interpolation time with sub-grid and background grid in moving problem such as forward flight on every time step. Present method is available enough to reduce the grid module interpolation time. In order to demonstrate present method, Caradonna & Tung's and AH-1G rotor blades are used and the results are compared to other researchers' result and experimental data.

Transverse and Diagonal Mode Structures of Three-dimensional Detonation Wave (3차원 데토네이션 파의 수평 및 대각선 모드 파면 구조)

  • Cho Deok-Rae;Choi Jeong-Yeol
    • Proceedings of the Korean Society of Propulsion Engineers Conference
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    • v.y2005m4
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    • pp.343-346
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    • 2005
  • Three dimensional structures of detonation wave propagating through a square-shaped duct were investigated using computational method and parallel processing. Inviscid fluid dynamics equations coupled with $variable-{\gamma}$ formulation and simplified one-step Arrhenius chemical reaction model were analysed by MUSCL-type TVD scheme and four stage Runge-Kutta time integration. The unsteady computational results in three dimension show the detailed mechanism of transverse mode and diagonal mode of detonation wave instabilities resulting same cell length but different cell width in smoked-foil record.

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A three-dimensional numerical model for shallow water flows using a free surface correction method (자유수면 보정기법을 이용한 3차원 천수유동 수치모형)

  • Jang, Won-Jae;Lee, Seung-Oh;Cho, Yong-Sik
    • 한국방재학회:학술대회논문집
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    • 2007.02a
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    • pp.181-185
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    • 2007
  • A free-surface correction(FSC) method is presented to solve the 3-D shallow water equations. Using the mode splitting process, FSC method can simulate shallow water flows under the hydrostatic assumption. For the hydrostatic pressure calculation, the momentum equations are firstly discretized using a semi-implicit scheme over the vertical direction leading to the tri-diagonal matrix systems. A semi-implicit scheme has been adopted to reduce the numerical instability caused by relatively small vertical length scale compare to horizontal one. and, as the free surface correction step the final horizontal velocity fields are corrected after the final surface elevations are obtained. Finally, the vertical final velocity fields can be calculated from the continuity equation. The numerical model is applied to the calculation of the simulation of flow fields in a rectangular open channel with the tidal influence. The comparisons with the analytical solutions show overall good agreements between the numerical results and analytical solutions.

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Operator-splitting methods respecting eigenvalue problems for shallow shelf equations with basal drag

  • Geiser, Jurgen;Calov, Reinhard
    • Coupled systems mechanics
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    • v.1 no.4
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    • pp.325-343
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    • 2012
  • We present different numerical methods for solving the shallow shelf equations with basal drag (SSAB). An alternative approach of splitting the SSAB equation into a Laplacian and diagonal shift operator is discussed with respect to the underlying eigenvalue problem. First, we solve the equations using standard methods. Then, the coupled equations are decomposed into operators for membranes stresses, basal shear stress and driving stress. Applying reasonable parameter values, we demonstrate that the operator of the membrane stresses is much stiffer than the operator of the basal shear stress. Here, we could apply a new splitting method, which alternates between the iteration on the membrane-stress operator and the basal-shear operator, with a more frequent iteration on the operator of the membrane stresses. We show that this splitting accelerates and stabilize the computational performance of the numerical method, although an appropriate choice of the standard method used to solve for all operators in one step speeds up the scheme as well.

STUDY OF THREE-DIMENSIONAL DETONATION WAVE STRUCTURES USING PARALLEL PROCESSING (병렬 처리를 이용한 3차원 데토네이션 파 구조 해석)

  • Cho D.R.;Choi J.Y.
    • 한국전산유체공학회:학술대회논문집
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    • 2005.10a
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    • pp.151-155
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    • 2005
  • Three-dimensional structures of unsteady detonation wave propagating through a square-shaped tube is studied using computational method and parallel processing. Inviscid fluid dynamics equations coupled with variable-${\gamma}$ formulation and simplified one-step Arrhenius chemical reaction model were analysed by a MUSCL-type TVD scheme and four stage Runge-Kutta time integration. Results in three dimension show the two unsteady detonation wave propagating mode, the Rectangular and diagonal mode of detonation wave instabilities. Two different modes of instability showed the same cell length but different cell width and the geometric similarities in smoked-foil record.

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NUMERICAL STUDY OF THREE-DIMENSIONAL DETONATION WAVES USING PARALLEL PROCESSING (병렬 처리를 이용한 3차원 테토네이션 파 수치해석)

  • Cho, D.R.;Choi, J.Y.
    • 한국연소학회:학술대회논문집
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    • 2005.10a
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    • pp.15-19
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    • 2005
  • Three-dimensional structures of unsteady detonation wave propagating through a square-shaped tube is studied using computational method and parallel processing. Inviscid fluid dynamics equations coupled with variable-${\gamma}$ formulation and simplified one-step Arrhenius chemical reaction model were analysed by a MUSCL-type TVD scheme and four stage Runge-Kutta time integration. Results in three dimension show the two unsteady detonation wave propagating mode, the Rectangular and diagonal mode of detonation wave instabilities. Two different modes of instability showed the same cell length but different cell width and the geometric similarities in smoked-foil record.

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