Extension to three-dimensional problems of the upwind finite element scheme based on the choice of up- and downwind points

Fujima, Shoichi; Tabata, Masaaki; Yasuji, Fukasawa

doi:10.1016/0045-7825(94)90021-3

Cited by 23 publications

(1 citation statement)

References 13 publications

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“…The solver is tested by a 3D lid-driven cavity problem. The current results of Re = 400 (Figure 4 [28], which convince us the success of the current scheme. The efficiency of the incomplete balancing domain decomposition preconditioner is also tested by comparing it with other preconditioners and results are shown in Figure 5.…”

Section: Validation and Efficiencysupporting

confidence: 72%

Investigation of the Contamination Control in a Cleaning Room with a Moving AGV by 3D Large-Scale Simulation

Yao

Zhu

2013

Journal of Applied Mathematics

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The motions of the airflow induced by the movement of an automatic guided vehicle (AGV) in a cleanroom are numerically studied by large-scale simulation. For this purpose, numerical experiments scheme based on domain decomposition method is designed. Compared with the related past research, the high Reynolds number is treated by large-scale computation in this work. A domain decomposition Lagrange-Galerkin method is employed to approximate the Navier-Stokes equations and the convection diffusion equation; the stiffness matrix is symmetric and an incomplete balancing preconditioned conjugate gradient (PCG) method is employed to solve the linear algebra system iteratively. The end wall effects are readily viewed, and the necessity of the extension to 3 dimensions is confirmed. The effect of the high efficiency particular air (HEPA) filter on contamination control is studied and the proper setting of the speed of the clean air flow is also investigated. More details of the recirculation zones are revealed by the 3D large-scale simulation.

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Section: Validation and Efficiencysupporting

confidence: 72%

Investigation of the Contamination Control in a Cleaning Room with a Moving AGV by 3D Large-Scale Simulation

Yao

Zhu

2013

Journal of Applied Mathematics

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Numerical Simulation of Three-Dimensional Incompressible Flow by a New Formulation

Lin

1996

Int. J. Numer. Meth. Fluids

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A new mathematical formulation, called the pseudovorticity–velocity formulation, of the three‐dimensional incompressible Navier–Stokes equations is presented as an alternative to the vorticity–velocity approach. For the model lid‐driven cavity flow problem in two and three dimensions, combined with an explicit mixed spectral /finite different numerical scheme the proposed formulation is found to be efficient and very accurate as compared with the results available in the literature. In particular, the simulation results demonstrate an attractive feature of the present formulation compared with the vorticity–velocity approach, namely that the divergence‐free condition of the velocity field can always be achieved on a non‐staggered mesh.

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Transient solutions for three‐dimensional lid‐driven cavity flows by a least‐squares finite element method

Tang

Cheng

Tsang

1995

Numerical Methods in Fluids

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SUMMARYA time-accurate least-squares finite element method is used to simulate three-dimensional flows in a cubic cavity with a uniform moving top. The time-accurate solutions are obtained by the Crank-Nicolson method for time integration and Newton linearization for the convective terms with extensive linearization steps. A matrix-free algorithm of the Jacobi conjugate gradient method is used to solve the symmetric, positive definite linear system of equations. To show that the least-squares finite element method with the Jacobi conjugate gradient technique has promising potential to provide implicit, fully coupled and time-accurate solutions to large-scale three-dimensional fluid flows, we present results for three-dimensional lid-driven flows in a cubic cavity for Reynolds numbers up to 3200.

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Extension to three-dimensional problems of the upwind finite element scheme based on the choice of up- and downwind points

Cited by 23 publications

References 13 publications

Investigation of the Contamination Control in a Cleaning Room with a Moving AGV by 3D Large-Scale Simulation

Investigation of the Contamination Control in a Cleaning Room with a Moving AGV by 3D Large-Scale Simulation

Numerical Simulation of Three-Dimensional Incompressible Flow by a New Formulation

Transient solutions for three‐dimensional lid‐driven cavity flows by a least‐squares finite element method

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