• Title/Summary/Keyword: Implicit Time Discretization

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PRECONDITIONED NAVIER-STOKES COMPUTATION FOR WEAKLY COMPRESSIBLE FLOW ANALYSIS ON UNSTRUCTURED MESH (비정렬격자와 예조건화 기법을 이용한 저압축성 점성유동해석)

  • Son, S.J.;Ahn, H.T.
    • Journal of computational fluids engineering
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    • v.18 no.3
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    • pp.79-86
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    • 2013
  • Preconditioned compressible Navier-Stokes equations are solved for almost incompressible flows. Unstructured meshes are utilized for spatial discretization of complex flow domain. Effectiveness of the current preconditioning algorithm, with respect to various Reynolds numbers and Mach numbers, is demonstrated by the solution of canonical problems for incompressible flows, e.g. driven cavity flows.

Numerical result of complex quick time behavior of viscoelastic fluids in flow domains with traction boundaries

  • Kwon, Young-Don
    • Korea-Australia Rheology Journal
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    • v.19 no.4
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    • pp.211-219
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    • 2007
  • Here we demonstrate complex transient behavior of viscoelastic liquid described numerically with the Leonov model in straight and contraction channel flow domains. Finite element and implicit Euler time integration methods are employed for spatial discretization and time marching. In order to stabilize the computational procedure, the tensor-logarithmic formulation of the constitutive equation with SUPG and DEVSS algorithms is implemented. For completeness of numerical formulation, the so called traction boundaries are assigned for flow inlet and outlet boundaries. At the inlet, finite traction force in the flow direction with stress free condition is allocated whereas the traction free boundary is assigned at the outlet. The numerical result has illustrated severe forward-backward fluctuations of overall flow rate in inertial straight channel flow ultimately followed by steady state of forward flow. When the flow reversal occurs, the flow patterns exhibit quite complicated time variation of streamlines. In the inertialess flow, it takes much more time to reach the steady state in the contraction flow than in the straight pipe flow. Even in the inertialess case during startup contraction flow, quite distinctly altering flow patterns with the lapse of time have been observed such as appearing and vanishing of lip vortices, coexistence of multiple vortices at the contraction comer and their merging into one.

Transient Simulation of Graphene Sheets using a Deterministic Boltzmann Equation Solver

  • Hong, Sung-Min
    • JSTS:Journal of Semiconductor Technology and Science
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    • v.17 no.2
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    • pp.288-293
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    • 2017
  • Transient simulation capability with an implicit time derivation method is a missing feature in deterministic Boltzmann equation solvers. The H-transformation, which is critical for the stable simulation of nanoscale devices, introduces difficulties for the transient simulation. In this work, the transient simulation of graphene sheets is reported. It is shown that simulation of homogeneous systems can be done without abandoning the H-transformation, as much as a specially designed discretization method is employed. The AC mobility and step response of the graphene sheet on the $SiO_2$ substrate are simulated.

Numerical Analysis of Flow- and Heat Transfer of a Spinning Blunt Body at Mach 5 (마하수 5에서 회전하는 blunt body의 유동 및 열전달에 관한 수치해석)

  • Lee Myung Sup;Lee Chang Ho;Park Seung O
    • 한국전산유체공학회:학술대회논문집
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    • 2000.05a
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    • pp.172-177
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    • 2000
  • In this numerical work, three dimensional supersonic laminar flow and heat transfer of a blunt body(sphere-cone) at Mach 5 is simulated. The effects of angle of attack and the spin rate on the now and heat transfer are analysed. To solve the three dimensional compressible Wavier-Stokes equation, a finite volume method with the modified LDFSS scheme is employed for spatial discretization, and a point SGS implicit method is used for time integration. It is found that the heat transfer rate increases at the windward side and decreases at the leeward side with the angle of attack. The heat transfer rate at all surfaces slightly increases with the spin rate.

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Aerodynamic Performance Analysis of a Shrouded Rotor Using an Unstructured Mesh Flow Solver

  • Lee H. D.;Kwon O. J.;Joo J.
    • 한국전산유체공학회:학술대회논문집
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    • 2003.10a
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    • pp.263-265
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    • 2003
  • The aerodynamic performance of a shrouded tail rotor in hover has been studied by using a compressible inviscid flow solver on unstructured meshes. The numerical method is based on a cell­centered finite-volume discretization and an implicit Gauss-Seidel time integration. The results show that the performance of an isolated rotor without shroud compares well with experiment. In the case of a shrouded rotor, correction of the collective pitch angle is made such that the overall performance matches with experiment to account for the uncertainties of the experimental model configuration. Details of the flow field compare well with the experiment confirming the validity of the present method.

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ERROR ESTIMATES FOR A GALERKIN METHOD FOR A COUPLED NONLINEAR SCHRÖDINGER EQUATIONS

  • Omrani, Khaled;Rahmeni, Mohamed
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.1
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    • pp.219-244
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    • 2020
  • In this paper, we approximate the solution of the coupled nonlinear Schrödinger equations by using a fully discrete finite element scheme based on the standard Galerkin method in space and implicit midpoint discretization in time. The proposed scheme guarantees the conservation of the total mass and the energy. First, a priori error estimates for the fully discrete Galerkin method is derived. Second, the existence of the approximated solution is proved by virtue of the Brouwer fixed point theorem. Moreover, the uniqueness of the solution is shown. Finally, convergence orders of the fully discrete Crank-Nicolson scheme are discussed. The end of the paper is devoted to some numerical experiments.

Effects of Earth-Tube Characteristics on the Soil-Air Heat Exchanger Performances (지중매설관의 특성이 토양 - 공기 열교환기 성능에 미치는 영향)

  • 김영복
    • Journal of Biosystems Engineering
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    • v.22 no.4
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    • pp.459-468
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    • 1997
  • To optimize the design and operation of a soil- air heat exchanger system, the effects of variables characterizing system design and operation on the performance of the system were analyzed by a theoretical model which included the three-dimensional transient heat conduction equation. The solution of the theoretical model was acquired by a computer program that uses Finite Difference Methods and Gauss-Seidel iteration computation, in which the time discretization scheme was an implicit difference appoximation. The computer program was validated first by comparison of the results for different grid sizes. Air outlet temperature, energy gain, and heat exchange efficiency of the system were analyzed based upon the tube diameter, tube length, tube thickness, and tube thermal diffusivity.

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Numerical Analysis of Solid Propellant Ignition ~Numerical Formulation Assessment~

  • Shimada, Toru;Novozhilov, Boris V.
    • Proceedings of the Korean Society of Propulsion Engineers Conference
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    • 2004.03a
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    • pp.528-531
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    • 2004
  • For a simple one-dimensional ignition problem a mathematical model is described to investigate the difficulties in numerical simulations. Some computation results are obtained and comparison is made with analytical solution. Discussions are made on topics such as 1) coordinate transformation, 2) gas-phase and solid-phase analysis; (divergence form of the governing system, a finite-volume discretization, implicit time integration, upwind split flux, spatial accuracy improvement are described. Mass, reagent mass, and energy conservations are solved.), and 3) method to determine quantities on the burning surface (matching). Results obtained for small values of the non-dimensional pressure show a steady-combustion and good agreement with the analytical solution. Numerical instability appeared for larger values of the pressure, discussion on the cause of the problem is made. This effort is a part of a study of flame spread phenomena on solid propellant surface.

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CONSEQUENCE OF BACKWARD EULER AND CRANK-NICOLSOM TECHNIQUES IN THE FINITE ELEMENT MODEL FOR THE NUMERICAL SOLUTION OF VARIABLY SATURATED FLOW PROBLEMS

  • ISLAM, M.S.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.19 no.2
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    • pp.197-215
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    • 2015
  • Modeling water flow in variably saturated, porous media is important in many branches of science and engineering. Highly nonlinear relationships between water content and hydraulic conductivity and soil-water pressure result in very steep wetting fronts causing numerical problems. These include poor efficiency when modeling water infiltration into very dry porous media, and numerical oscillation near a steep wetting front. A one-dimensional finite element formulation is developed for the numerical simulation of variably saturated flow systems. First order backward Euler implicit and second order Crank-Nicolson time discretization schemes are adopted as a solution strategy in this formulation based on Picard and Newton iterative techniques. Five examples are used to investigate the numerical performance of two approaches and the different factors are highlighted that can affect their convergence and efficiency. The first test case deals with sharp moisture front that infiltrates into the soil column. It shows the capability of providing a mass-conservative behavior. Saturated conditions are not developed in the second test case. Involving of dry initial condition and steep wetting front are the main numerical complexity of the third test example. Fourth test case is a rapid infiltration of water from the surface, followed by a period of redistribution of the water due to the dynamic boundary condition. The last one-dimensional test case involves flow into a layered soil with variable initial conditions. The numerical results indicate that the Crank-Nicolson scheme is inefficient compared to fully implicit backward Euler scheme for the layered soil problem but offers same accuracy for the other homogeneous soil cases.

Prediction of Aeroelastic Displacement Under Close BVI Using Unstructured Dynamic Meshes (비정렬 동적격자를 이용한 블레이드-와류 간섭에 따른 공탄성 변위예측)

  • Jo, Kyu-Won;Oh, Woo-Sup;Kwon, Oh-Joon;Lee, In
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.30 no.8
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    • pp.37-45
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    • 2002
  • A two-dimensional unsteady, inviscid flow solver has been developed for the simulation of airfoil-vortex interactions on unstructured dynamically adapted meshes. The Euler solver is based on a second-order accurate implicit time integration using a point Gauss-Seidel relaxation scheme and a dual time-step subiteration. A vertex-centered, finite-volume discretization is used in conjunction with the Roe's flux-difference splitting. An unsteady solution-adaptive dynamic mesh scheme is used by adding and deleting mesh points to take account of both spatial and temporal variations of the flow field. The effect of vortex interaction on the aeroelastic displacement of an airfoil attached to the idealized two degree-of-freedom spring system is investigated.