• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.6
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• pp.753-765
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• 2003

A finite element code for the numerical solution of the Navier-Stokes equation is parallelized by vertex-oriented domain decomposition. To accelerate the convergence of iterative solvers like conjugate gradient method, parallel block ILU, iterative block ILU, and distributed ILU methods are tested as parallel preconditioners. The effectiveness of the algorithms has been investigated when P1P1 finite element discretization is used for the parallel solution of the Navier-Stokes equation. Two-dimensional and three-dimensional Laplace equations are calculated to estimate the speedup of the preconditioners. Calculation domain is partitioned by one- and multi-dimensional partitioning methods in structured grid and by METIS library in unstructured grid. For the domain-decomposed parallel computation of the Navier-Stokes equation, we have solved three-dimensional lid-driven cavity and natural convection problems in a cube as benchmark problems using a parallelized fractional 4-step finite element method. The speedup for each parallel preconditioning method is to be compared using upto 64 processors.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.39 no.5
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• pp.415-423
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• 2015

In this study, we present a grid refinement model in the lattice Boltzmann method (LBM) for two-dimensional incompressible fluid flow. That is, the model combines the desirable features of the lattice Boltzmann method and stream function-vorticity formulations. In order to obtain an accurate result, very fine grid (or lattice) is required near the solid boundary. Therefore, the grid refinement model is used in the lattice Boltzmann method for stream function-vorticity formulation. This approach is more efficient in that it can obtain the same accurate solution as that in single-block approach even if few lattices are used for computation. In order to validate the grid refinement approach for the stream function-vorticity formulation, the numerical simulations of lid-driven cavity flows were performed and good results were obtained.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.7 no.4
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• pp.622-632
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• 1995

The present numerical study is aimed to investigate time-dependent characteristics of a two-dimensional lid-driven square cavity flow of three high Reynolds numbers, $7.5{\times}10^3$, $10^4$ and $3{\times}10^4$. A conservative convection term on irregular grids was adopted by renewing the MAC type difference schemes on regular grids. Relaxation of velocity and pressure is implemented by SOLA algorithm. In case of $Re=7.5{\times}10^3$, flow behavior converges to steady state after a transient period. But for $Re=10^4$, periodic unsteady sinusoidal fluctuation of local velocity and kinetic energy is found and continuous movements of small eddies in the secondary flow regions are also discovered. Random generation of eddies and their active migrating behavior are detected for $Re=3{\times}10^4$, resulting in complete unsteady and non-linear flow characteristics. And, an organized structure similar to a Moffat vortex is also observed from the time-mean flow patterns. Furthermore, a typoon-like vortex(TLV) appears intemittently and rotates along the separation regions and boundary layers.

• Journal of Magnetics
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• v.18 no.3
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• pp.321-325
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• 2013

The problem of mixed convection in a differentially heated lid-driven square cavity filled with Cu-water nanofluid under effect of a magnetic field is investigated numerically. The left and right walls of the cavity are kept at temperatures of $T_h$ and $T_c$ respectively while the horizontal walls are adiabatic. The top wall of the cavity moves in own plane from left to right. The effects of some pertinent parameters such as Richardson number (ranging from 0.1 to 10), the volume fraction of the nanoparticles (ranging 0 to 0.1) and the Hartmann number (ranging from 0 to 60) on the fluid flow and temperature fields and the rate of heat transfer in the cavity are investigated. It must be noted that in all calculations the Prandtl number of water as the pure fluid is kept at 6.8, while the Grashof number is considered fixed at 104. The obtained results show that the rate of heat transfer increases with an increase of the Reynolds number, while but it decreases with increase in the Hartmann number. Moreover it is found that based the Richardson and Hartmann numbers by increase in volume fraction of the nanoparticles the rate of heat transfer can be enhanced or deteriorated compared to the based fluid.

• Journal of computational fluids engineering
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• v.10 no.2
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• pp.38-47
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• 2005

Substructuring methods are often used in finite element structural analyses. In this study a multi-level substructuring(MLSS) algorithm is developed and proposed as a possible candidate for finite element fluid solvers. The present algorithm consists of four stages such as a gathering, a condensing, a solving and a scattering stage. At each level, a predetermined number of elements are gathered and condensed to form an element of higher level. At the highest level, each sub-domain consists of only one super-element. Thus, the inversion process of a stiffness matrix associated with internal degrees of freedom of each sub-domain has been replaced by a sequential static condensation of gathered element matrices. The global algebraic system arising from the assembly of each sub-domain matrices is solved using a well-known iterative solver such as the conjugare gradient(CG) or the conjugate gradient squared(CGS) method. A time comparison with CG has been performed on a 2-D Poisson problem. With one domain the computing time by MLSS is comparable with that by CG up to about 260,000 d.o.f. For 263,169 d.o.f using 8 x 8 sub-domains, the time by MLSS is reduced to a value less than $30\%$ of that by CG. The lid-driven cavity problem has been solved for Re = 3200 using the element interpolation degree(Deg.) up to cubic. in this case, preconditioning techniques usually accompanied by iterative solvers are not needed. Finite element formulation for the incompressible flow has been stabilized by a modified residual procedure proposed by Ilinca et al.[9].

• Journal of Biomedical Engineering Research
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• v.20 no.1
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• pp.29-36
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• 1999

The objective of this study is to analyse the flow field in the branching duct by visualizing the flow phenomena using the PIV system. A bifurcation model is fabricated with transparent acrylic resin to visualize the whole flow field with the PIV system. Water was used as the working fluid and the conifer powder as the tracer particles. The single-frame and two-frame methods of the PIV system and 2-frame of the grey level correlation method are applied to obtain the velocity vectors from the images captured in the flow filed. The velocity distributions in a lid-driven cavity flow are compared with the so-called standard experimental data, which was obtained from by 4-frame method in order to validate experimental results of the PIV measurements. The flow patterns of a Newtonian fluid in a branching duct were successfully visualized by using the PIV system and the sub-pixel and the area interpolation method were used to obtain the final velocity vectors. The velocity vectors obtained from the PIV system are in good agreement with the numerical results of the 3-dimensional branch flow. The results of numerical analyses and the PIV experiments for the three-dimensional flows in the branch ing duct show the recirculation zone distal to the branching point and the sizes of the recirculation length and height of the tow different methods are in good agreement.

• Journal of Korea Water Resources Association
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• v.47 no.6
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• pp.537-546
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• 2014

Surface image velocimetry was introduced as an efficient and sage alternative to conventional river flow measurement methods during floods. The conventional surface image velocimetry uses a pair of images to estimate velocity fields using cross-correlation analysis. This method is appropriate to analyzing images taken with a short time interval. It, however, has some drawbacks; it takes a while to analyze images for the verage velocity of long time intervals and is prone to include errors or uncertainties due to flow characteristics and/or image taking conditions. Methods using spatio-temporal images, called STIV, were developed to overcome the drawbacks of conventional surface image velocimetry. The grayscale-gradient tensor method, one of various STIVs, has shown to be effectively reducing the analysis time and is fairly insusceptible to any measurement noise. It, unfortunately, can only be applied to the main flow direction. This means that it can not measure any two-dimensional flow field, e.g. flow in the vicinity of river structures and flow around river bends. The present study aimed to develop a new method of analyzing spatio-temporal images in two-dimension using cross-correlation analysis. Unlike the conventional STIV, the developed method can be used to measure two-dimensional flow substantially. The method also has very high spatial resolution and reduces the analysis time. A verification test using artificial images with lid-driven cavity flow showed that the maximum error of the method is less than 10 % and the average error is less than 5 %. This means that the developed scheme seems to be fairly accurate, even for two-dimensional flow.