• Title/Summary/Keyword: Taylor-Galerkin method

Search Result 15, Processing Time 0.024 seconds

Parallel finite element simulation of free surface flows using Taylor-Galerkin/level-set method (Taylor-Galerkin/level-set 방법을 이용한 자유 표면의 병렬 유한 요소 해석)

  • Ahn, Young-Kyoo;Choi, Hyoung-Gwon;Cho, Myung-Hwan;Yoo, Jung-Yul
    • Proceedings of the KSME Conference
    • /
    • 2008.11b
    • /
    • pp.2558-2561
    • /
    • 2008
  • In the present study, a parallel Taylor-Galerkin/level set based two-phase flow code was developed using finite element discretization and domain decomposition method based on MPI (Message Passing Interface). The proposed method can be utilized for the analysis of a large scale free surface problem in a complex geometry due to the feature of FEM and domain decomposition method. Four-step fractional step method was used for the solution of the incompressible Navier-Stokes equations and Taylor-Galerkin method was adopted for the discretization of hyperbolic type redistancing and advection equations. A Parallel ILU(0) type preconditioner was chosen to accelerate the convergence of a conjugate gradient type iterative solvers. From the present parallel numerical experiments, it has been shown that the proposed method is applicable to the simulation of large scale free surface flows.

  • PDF

A Study on an Effective Higher-Order Taylor-Galerkin Method for the Analysis of Structural Dynamics (동적 해석을 위한 효과적 고차 Taylor Galerkin법에 관한 연구)

  • 윤성기;박상훈
    • Journal of KSNVE
    • /
    • v.3 no.4
    • /
    • pp.353-359
    • /
    • 1993
  • In this study, the Taylor-Galerkin method is modified to take into consideration the third order term in the Taylor series of the fundamental variable. In the Taylor-Galerkin method, after expressing the governing equation of motion in conservation form, the temporal discretization is done first and then spatial discretization follows in contrast to the conventional approaches. A predictor-corrector type algorithm has been developed previously by the same author. A new computationally efficient direct algorithm is proposed in this study. A study on convergency and accuracy of the solution is carried out. Numerical examples show that this new algorithm exhibits the same order of accuracy with less computational effort.

  • PDF

FINITE ELEMENT ANALYSIS OF LEVEL SET FORMULATION (유한요소법을 이용한 level set 공식화의 해석)

  • Choi, H.G.
    • 한국전산유체공학회:학술대회논문집
    • /
    • 2009.11a
    • /
    • pp.223-227
    • /
    • 2009
  • In the present study, a least square weighted residual method and Taylor-Galerkin method were formulated and tested for the discretization of the two hyperbolic type equations of level set method; advection and reinitialization equations. The two approaches were compared by solving a time reversed vortex flow and three-dimensional broken dam flow by employing a four-step splitting finite element method for the solution of the incompressible Navier-Stokes equations. From the numerical experiments, it was shown that the least square method is more accurate and conservative than Taylor-Galerkin method and both methods are approximately first order accurate when both advection and reinitialization phase are involved in the evolution of free surface.

  • PDF

Application of Channel Routing Model by Taylor-Galerkin Finite Element Method -Modeling of Flow in Flood- (테일러-갤러킨 유한요소법에 의한 하도추적 모형의 적용 -홍수시 하천 유량 모의-)

  • Lee, Hae-Gyun
    • The Journal of the Korea Contents Association
    • /
    • v.11 no.1
    • /
    • pp.404-410
    • /
    • 2011
  • For the simulation of one-dimensional unsteady flow, the Taylor-Galerkin finite element method was adopted to the discretization of the Saint Venant equation. The model was applied to the backwater problem in a single channel and the flood routing in dendritic channel networks. The numerical solutions were compared with previously published results of finite difference and finite element methods and good agreement was observed. The model solves the continuity and the momentum equations in a sequential manner and this leads to easy implementation. Since the final system of matrix is tri-diagonal with a few additional entry due to channel junctions, the tri-diagonal matrix solution algorithm can be used with minor modification. So it is fast and economical in terms of memory for storing matrices.

Numerical Simulation of Mixing and Combustion in a Normal Injection of the Scramjet (초음속 연소기에서의 혼합과 연소현상에 관한 수치해석)

  • Moon, Su-Yeon;Lee, Choong-Won;Sohn, Chang-Hyun
    • Proceedings of the KSME Conference
    • /
    • 2001.11b
    • /
    • pp.475-480
    • /
    • 2001
  • The flowfield of transverse jet in a supersonic air stream subjected to shock wave turbulent boundary layer interactions is simulated numerically by Generalized Taylor Galerkin(GTG) finite element methods. Effects of turbulence are taken into account with a two-equation $(k-\varepsilon)$ model with a compressibility correction. Injection pressures and slot widths are varied in the present study. Pressure, separation extents, and penetration heights are compared with experimental data. Favorable comparisons with experimental measurements are demonstrated.

  • PDF

Numerical Simulation of Chemically Reacting Shock Wave-Turbulent Boundary Layer Interactions (화학반응이 있는 난류경계층과 충격파의 상호작용에 대한수치해석)

  • Mun, Su-Yeon;Lee, Chung-Won;Son, Chang-Hyeon
    • Transactions of the Korean Society of Mechanical Engineers B
    • /
    • v.26 no.3
    • /
    • pp.375-383
    • /
    • 2002
  • The flowfield of transverse jet in a supersonic air stream subjected to shock wave turbulent boundary layer interactions is simulated numerically by Generalized Taylor Galerkin(GTG) finite element methods. Effects of turbulence are taken into account with a two-equation (k-$\varepsilon$) model with a compressibility correction. Injection pressures and slot widths are varied in the present study. Pressure, separation extents, and penetration heights are compared with experimental data. Favorable comparisons with experimental measurements are demonstrated.

Adaptive Triangular Finite Element Method for Compressible Navier - Stokes Flows (삼각형 적응격자 유한요소법을 이용한 압축성 Navier-Stokes 유동의 해석)

  • Im Y. H.;Chang K. S.
    • Journal of computational fluids engineering
    • /
    • v.1 no.1
    • /
    • pp.88-97
    • /
    • 1996
  • This paper treats an adaptive finite-element method for the viscous compressible flow governed by Navier-Stokes equations in two dimensions. The numerical algorithm is the two-step Taylor-Galerkin mettled using unstructured triangular grids. To increase accuracy and stability, combined moving node method and grid refinement method have been used for grid adaption. Validation of the present algorithm has been made by comparing the present computational results with the existing experimental data and other numerical solutions. Four benchmark problems are solved for demonstration of the present numerical approach. They include a subsonic flow over a flat plate, the Carter flat plate problem, a laminar shock-boundary layer interaction. and finally a laminar flow around NACA0012 airfoil at zero angle of attack and free stream Mach number of 0.85. The results indicates that the present adaptive triangular grid method is accurate and useful for laminar viscous flow calculations.

  • PDF

Analysis of Stress Concentration Problems Using Moving Least Squares Finite Difference Method(I) : Formulation for Solid Mechanics Problem (이동최소제곱 유한차분법을 이용한 응력집중문제 해석(I) : 고체문제의 정식화)

  • Yoon, Young-Cheol;Kim, Hyo-Jin;Kim, Dong-Jo;Liu, Wing Kam;Belytschko, Ted;Lee, Sang-Ho
    • Journal of the Computational Structural Engineering Institute of Korea
    • /
    • v.20 no.4
    • /
    • pp.493-499
    • /
    • 2007
  • The Taylor expansion expresses a differentiable function and its coefficients provide good approximations for the given function and its derivatives. In this study, m-th order Taylor Polynomial is constructed and the coefficients are computed by the Moving Least Squares method. The coefficients are applied to the governing partial differential equation for solid problems including crack problems. The discrete system of difference equations are set up based on the concept of point collocation. The developed method effectively overcomes the shortcomings of the finite difference method which is dependent of the grid structure and has no approximation function, and the Galerkin-based meshfree method which involves time-consuming integration of weak form and differentiation of the shape function and cumbersome treatment of essential boundary.

Analysis of Dynamic Crack Propagation using MLS Difference Method (MLS 차분법을 이용한 동적균열전파 해석)

  • Yoon, Young-Cheol;Kim, Kyeong-Hwan;Lee, Sang-Ho
    • Journal of the Computational Structural Engineering Institute of Korea
    • /
    • v.27 no.1
    • /
    • pp.17-26
    • /
    • 2014
  • This paper presents a dynamic crack propagation algorithm based on the Moving Least Squares(MLS) difference method. The derivative approximation for the MLS difference method is derived by Taylor expansion and moving least squares procedure. The method can analyze dynamic crack problems using only node model, which is completely free from the constraint of grid or mesh structure. The dynamic equilibrium equation is integrated by the Newmark method. When a crack propagates, the MLS difference method does not need the reconstruction of mode model at every time step, instead, partial revision of nodal arrangement near the new crack tip is carried out. A crack is modeled by the visibility criterion and dynamic energy release rate is evaluated to decide the onset of crack growth together with the corresponding growth angle. Mode I and mixed mode crack propagation problems are numerically simulated and the accuracy and stability of the proposed algorithm are successfully verified through the comparison with the analytical solutions and the Element-Free Galerkin method results.

Study on the Solution of Reinitialization Equation for Level Set Method in the Simulation of Incompressible Two-Phase Flows (비압축성 2 상유동의 모사를 위한 Level Set 방법의 Reinitialization 방정식의 해법에 관한 연구)

  • Cho, Myung-Hwan;Choi, Hyoung-Gwon;Yoo, Jung-Yul
    • Transactions of the Korean Society of Mechanical Engineers B
    • /
    • v.32 no.10
    • /
    • pp.754-760
    • /
    • 2008
  • Computation of moving interface by the level set method typically requires the reinitialization of level set function. An inaccurate estimation of level set function $\phi$ results in incorrect free-surface capturing and thus errors such as mass gain/loss. Therefore, an accurate and robust reinitialization process is essential to the simulation of free-surface flows. In the present paper, we pursue further development of the reinitialization process, which evaluates level set function directly using a normal vector on the interface without solving there-distancing equation of hyperbolic type. The Taylor-Galerkin approximation and P1P1 splitting/SUPG (Streamline Upwind Petrov-Galerkin) FEM are adopted to discretize advection equation of the level set function and the incompressible Navier-Stokes equation, respectively. Advection equation and re-initialization process of free surface capturing are validated with benchmark problems, i.e., a broken dam flow and timereversed single vortex flow. The simulation results are in good agreement with the existing results.