• Title/Summary/Keyword: Implicit Formulation

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Papers : Implicit Formulation of Rotor Aeromechanic Equations for Helicopter Flight Simulation (논문 : 헬리콥터 비행 시뮬레이션을 위한 로터운동방정식 유도)

  • Kim, Chang-Ju
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.30 no.3
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    • pp.8-16
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    • 2002
  • The implicit formulation of rotor dynamics for helicopter flight simulation has been derived and and presented. The generalized vector kinematics regarding the relative motion between coordinates were expressed as a unified matrix operation and applied to get the inertial velocities and accelerations at arbitaty rotor blade span position. Based on these results the rotor aeromechanic equations for flapping dynamics, lead-lag dynamics and torque dynamics were formulated as an implicit form. Spatial integration methods of rotor dynamic equations along blade span and the expanded applicability of the present implicit formulations for arbitrary hings geometry and hinge sequences have been investigated. Time integration methods for present DAE(Differential Algebraic Equation) to calculate dynamic response calculation are recommenaded as future works.

A RANDOM GENERALIZED NONLINEAR IMPLICIT VARIATIONAL-LIKE INCLUSION WITH RANDOM FUZZY MAPPINGS

  • Khan, F.A.;Aljohani, A.S.;Alshehri, M.G.;Ali, J.
    • Nonlinear Functional Analysis and Applications
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    • v.26 no.4
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    • pp.717-731
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    • 2021
  • In this paper, we introduce and study a new class of random generalized nonlinear implicit variational-like inclusion with random fuzzy mappings in a real separable Hilbert space and give its fixed point formulation. Using the fixed point formulation and the proximal mapping technique for strongly maximal monotone mapping, we suggest and analyze a random iterative scheme for finding the approximate solution of this class of inclusion. Further, we prove the existence of solution and discuss the convergence analysis of iterative scheme of this class of inclusion. Our results in this paper improve and generalize several known results in the literature.

Reduction of Computing Time through FDM using Implicit Method and Latent Heat Treatment in Solidification Analysis (FDM에 의한 응고해석시 계산시간 단축을 위한 음적해법의 적용과 잠열처리방법)

  • Kim, Tae-Gyu;Choi, Jung-Kil;Hong, Jun-Pyo;Lee, Zin-Hyoung
    • Journal of Korea Foundry Society
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    • v.13 no.4
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    • pp.323-332
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    • 1993
  • An implicit finite difference formulation with three methods of latent heat treatment, such as equivalent specific heat method, temperature recovery method and enthalpy method, was applied to solidification analysis. The Neumann problem was solved to compare the numerical results with the exact solution. The implicit solutions with the equivalent specific heat method and the temperature recovery method were comparatively consistent with the Neumann exact solution for smaller time steps, but its error increased with increasing time step, especially in predicting the solidification beginning time. Although the computing time to solve energy equation using temperature recovery method was shorter than using enthalpy method, the method of releasing latent heat is not realistic and causes error. The implicit formulation of phase change problem requires enthalpy method to treat the release of latent heat reasonably. We have modified the enthalpy formulation in such a way that the enthalpy gradient term is not needed, and as a result of this modification, the computation stability and the computing time were improved.

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Coupled Finite Element Analysis for Semi-implicit Linear and Fully-implicit Nonlinear Scheme in Partially Saturated Porous Medium

  • Kim, Jae-Hong;Regueiro, Richard A.
    • Land and Housing Review
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    • v.1 no.1
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    • pp.59-65
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    • 2010
  • The paper presents a comparison between a semi-implicit time integration linear finite element implementation and fully-implicit nonlinear Newton-Raphson finite element implementation of a triphasic small strain mixture formulation of an elastic partially saturated porous medium. The pore air phase pressure pa is assumed atmospheric, i.e., $p_a$ = 0, although the formulation and implementation are general to handle increase in pore air pressure as a result of loading, if needed. The solid skeleton phase is assumed linear isotropic elastic and partially saturated 'consolidation' in the presence of surface infiltration and traction is simulated. The verification of the implementation against an analytical solution for partially saturated pore water flow (no deformation) and comparison between the two implementations is presented and the important of the porosity-dependent nature of the partially saturated permeability is assessed on comparison with a commercial code for the partially saturated flow with deformation. As a result, the response of partially saturated permeability subjected to the porosity influences on the saturation of a soil, and the different behaviors of the partially saturated soil between staggered and monolithic coupled programs is worth of attention because the negative pore water pressure in the partially saturated soil depends on the difference.

DELTA-FORMULATION OF A SEGREGATED NAVIER-STOKES SOLVER WITH A DUAL-TIME INTEGRATION (이중시간적분법을 이용한 순차적 유동해석 기법)

  • Kim, J.;Tack, N.I.;Kim, S.B.;Kim, M.H.;Lee, W.J.
    • 한국전산유체공학회:학술대회논문집
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    • 2006.10a
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    • pp.31-35
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    • 2006
  • The delta-formulation of the Navier-Stokes equations has been popularly used in the aerodynamics area. Implicit algorithm can be easily implemented in that by using Taylor series expansion. This formulation is extended for an unsteady analysis by using a dual-time integration. In the meanwhile, the incompressible flows with heat transfers which occur in the area of thermo-hydraulics have been solved by a segregated algorithm such as the SIMPLE method, where each equation is discretised by using an under-relaxed deferred correction method and solved sequentially. In this study, the dual-time delta formulation is implemented in the segregated Navier-Stokes solver which is based on the collocated cell-centerd scheme with un unstructured mesh FVM. The pressure correction equation is derived by the SIMPLE method. From this study, it was found that the Euler dual-time method in the delta formulation can be combined with the SIMPLE method.

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Development of Optimized Compact Finite Difference Schemes (최적화된 집적 유한 차분법을 위한 내재적 시간전진 기법의 개발)

  • Park N. S.;Kim J. W.;Lee D. J.
    • 한국전산유체공학회:학술대회논문집
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    • 1998.11a
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    • pp.7-12
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    • 1998
  • Optimized high-order compact(OHOC) schemes were proposed, which have high spatial order of truncation and resolution to simulate the aeroacoustic problems due to unsteady compressible flows. Generally, numerical schemes are categorized explicit or implicit by time-marching method. In this research, OHOC differences which were developed with explicit time-marching method is used to have implicit formulation and the implicit OHOC differences result in block hepta-diagonal matrix. This paper presents the comparisons between the explicit and implicit OHOC schemes with a second order accuracy of time in the 1-d linear wave convection problem, and between the explicit OHOC scheme of 4th-order accuracy in time and the implicit OHOC scheme of 1st-order accuracy in tine for the 1-d nonlinear wave convection problem. With these comparisons, the characteristics of implicit OHOC scheme are shown in the point of CFL number.

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Enhanced Second-order Implicit Constraint Enforcement for Dynamic Simulations

  • Hong, Min;Welch, Samuel W.J.;Jung, Sun-Hwa;Choi, Min-Hyung;Park, Doo-Soon
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.2 no.1
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    • pp.51-62
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    • 2008
  • This paper proposes a second-order implicit constraint enforcement method which yields enhanced controllability compared to a first-order implicit constraints enforcement method. Although the proposed method requires solving a linear system twice, it yields superior accuracy from the constraints error perspective and guarantees the precise and natural movement of objects, in contrast to the first-order method. Thus, the proposed method is the most suitable for exact prediction simulations. This paper describes the numerical formulation of second-order implicit constraints enforcement. To prove its superiority, the proposed method is compared with the firstorder method using a simple two-link simulation. In this paper, there is a reasonable discussion about the comparison of constraints error and the analysis of dynamic behavior using kinetic energy and potential energy.

Convergence of Nonlocal Integral Operator in Peridynamics (비국부 적분 연산기로 표현되는 페리다이나믹 방정식의 수렴성)

  • Jo, Gwanghyun;Ha, Youn Doh
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.34 no.3
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    • pp.151-157
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    • 2021
  • This paper is devoted to a convergence study of the nonlocal integral operator in peridynamics. The implicit formulation can be an efficient approach to obtain the static/quasi-static solution of crack propagation problems. Implicit methods require constly large-matrix operations. Therefore, convergence is important for improving computational efficiency. When the radial influence function is utilized in the nonlocal integral equation, the fractional Laplacian integral equation is obtained. It has been mathematically proved that the condition number of the system matrix is affected by the order of the radial influence function and nonlocal horizon size. We formulate the static crack problem with peridynamics and utilize Newton-Raphson methods with a preconditioned conjugate gradient scheme to solve this nonlinear stationary system. The convergence behavior and the computational time for solving the implicit algebraic system have been studied with respect to the order of the radial influence function and nonlocal horizon size.

Parallelization of an Unstructured Implicit Euler Solver (내재적 방법을 이용한 비정렬 유동해석 기법의 병렬화)

  • Kim J. S.;Kang H. J.;Park Y. M.;Kwon O. J.
    • Journal of computational fluids engineering
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    • v.5 no.2
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    • pp.20-27
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    • 2000
  • An unstructured implicit Euler solver is parallelized on a Cray T3E. Spatial discretization is accomplished by a cell-centered finite volume formulation using an upwind flux differencing. Time is advanced by the Gauss-Seidel implicit scheme. Domain decomposition is accomplished by using the k-way n-partitioning method developed by Karypis. In order to analyze the parallel performance of the solver, flows over a 2-D NACA 0012 airfoil and 3-D F-5 wing were investigated.

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Parallelization of an Unstructured Implicit Euler Solver (내재적 방법을 이용한 비정렬 유동해석 기법의 병렬화)

  • Kim J. S.;Kang H. J.;Park Y. M.;Kwon O. J.
    • 한국전산유체공학회:학술대회논문집
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    • 1999.11a
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    • pp.193-200
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    • 1999
  • An unstructured implicit Euler solver is parallelized on a Cray T3E. Spatial discretization is accomplished by a cell-centered finite volume formulation using an unpwind flux differencing. Time is advanced by the Gauss-Seidel implicit scheme. Domain decomposition is accomplished by using the k-way N-partitioning method developed by Karypis. In order to analyze the parallel performance of the solver, flows over a 2-D NACA 0012 airfoil and a 3-D F-5 wing were investigated.

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