• 유체기계공업학회:학술대회논문집
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• 유체기계공업학회 1999년도 유체기계 연구개발 발표회 논문집
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• pp.163-169
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• 1999

The numerical procedure has been developed for simulating incompressible viscous flow around a turbine stage with rotor-stator interaction. This study solves 2-D unsteady incompressible Navier-Stokes equations on a non-orthogonal curvilinear coordinate system. The Marker-and-Cell concept is applied to efficiently solve continuity equation. To impose an accurate boundary condition, O-H multiblocked grid system is generated. O-type grid and H-type grid is generated near and outer rotor-stator The cubic-spline interpolation is applied to handle a relative motion of a rotor to the stator. Turbulent flows have been modeled by the Baldwin- Lomax turbulent model. To validate present procedure, the time averaged pressure coefficients around the rotor and stator are compared with experiment and a good agreement obtained.

• 대한수학회지
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• 제59권3호
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• pp.519-548
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• 2022

In this paper, a stabilized-penalized collocated finite volume (SPCFV) scheme is developed and studied for the stationary generalized Navier-Stokes equations with mixed Dirichlet-traction boundary conditions modelling an incompressible biological fluid flow. This method is based on the lowest order approximation (piecewise constants) for both velocity and pressure unknowns. The stabilization-penalization is performed by adding discrete pressure terms to the approximate formulation. These simultaneously involve discrete jump pressures through the interior volume-boundaries and discrete pressures of volumes on the domain boundary. Stability, existence and uniqueness of discrete solutions are established. Moreover, a convergence analysis of the nonlinear solver is also provided. Numerical results from model tests are performed to demonstrate the stability, optimal convergence in the usual L² and discrete H¹ norms as well as robustness of the proposed scheme with respect to the choice of the given traction vector.

• 대한수학회지
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• 제50권5호
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• pp.1129-1163
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• 2013

Based on finite element discretization, two linearization approaches to the defect-correction method for the steady incompressible Navier-Stokes equations are discussed and investigated. By applying $m$ times of Newton and Picard iterations to solve an artificial viscosity stabilized nonlinear Navier-Stokes problem, respectively, and then correcting the solution by solving a linear problem, two linearized defect-correction algorithms are proposed and analyzed. Error estimates with respect to the mesh size $h$, the kinematic viscosity ${\nu}$, the stability factor ${\alpha}$ and the number of nonlinear iterations $m$ for the discrete solution are derived for the linearized one-step defect-correction algorithms. Efficient stopping criteria for the nonlinear iterations are derived. The influence of the linearizations on the accuracy of the approximate solutions are also investigated. Finally, numerical experiments on a problem with known analytical solution, the lid-driven cavity flow, and the flow over a backward-facing step are performed to verify the theoretical results and demonstrate the effectiveness of the proposed defect-correction algorithms.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2009년 추계학술대회논문집
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• pp.49-55
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• 2009

This paper evaluates performances of a recently developed divergence-free finite element method based on Hermite interpolated stream functions. Velocity bases are derived from Hermite interpolated stream functions to form divergence-free basis functions. These velocity basis functions constitute a solenoidal function space, and the simple gradient of the Hermite functions constitute an irrotational function space. The incompressible Navier-Stokes equation is orthogonally decomposed into a solenoidal and an irrotational parts, and the decoupled Navier-Stokes equations are projected onto their corresponding spaces to form proper variational formulations. To access accuracy and convergence of the present algorithm, three test problems are selected. They are lid-driven cavity flow, flow over a backward-facing step and buoyancy-driven flow within a square enclosure. Hermite interpolation functions from cubic to quintic are chosen to run the test problems. Numerical results are shown. In all cases it has shown that the present method has performed well in accuracies and convergences. Moreover, the present method does not require an upwinding or a stabilized term.

• 대한수학회지
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• 제45권3호
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• pp.645-681
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• 2008

The Navier-Stokes system for heat-conducting incompressible fluids is studied in a domain ${\Omega}{\subset}R^3$. The viscosity, heat conduction coefficients and specific heat at constant volume are allowed to depend smoothly on density and temperature. We prove local existence of the unique strong solution, provided the initial data satisfy a natural compatibility condition. For the strong regularity, we do not assume the positivity of initial density; it may vanish in an open subset (vacuum) of ${\Omega}$ or decay at infinity when ${\Omega}$ is unbounded.

• 한국해양공학회지
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• 제25권5호
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• pp.9-14
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• 2011

The divergence-free finite elements introduced in this paper are derived from Hermite functions, which interpolate stream functions. Velocity bases are derived from the curl of the Hermite functions. These velocity basis functions constitute a solenoidal function space, and the gradient of the Hermite functions constitute an irrotational function space. The incompressible Navier-Stokes equation is orthogonally decomposed into its solenoidal and irrotational parts, and the decoupled Navier-Stokes equations are then projected onto their corresponding spaces to form appropriate variational formulations. The degrees of the Hermite functions we introduce in this paper are bi-cubis, quartic, and quintic. To verify the accuracy and convergence of the present method, three well-known benchmark problems are chosen. These are lid-driven cavity flow, flow over a backward facing step, and buoyancy-driven flow within a square enclosure. The numerical results show good agreement with the previously published results in all cases.

• 한국전산유체공학회지
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• 제1권1호
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• pp.35-46
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• 1996

원심형 임펠러 내부 유로등 큰 곡률을 수반하는 터보기계 요소의 유동해석을 위한 계산코드를 개발하였다. 이 코드에서는 곡선좌표계에 유도된 3차원 비압축성 Navier-Stokes의 운동 방정식을 SMAC 음해법으로 푼다. 이 코드를 이용하여 유로의 단면이 정사각형이고 90도로 굽은 덕트내부의 층류 입구유동을 해석하고, 굽은 관 특유의 유동현상을 수치모사하였다 또한 곡관부 입구에서 충분히 발달한 유동, 또는 발달중인 유동이 유입될 경우에 이것이 곡관부 내부의 유동에 미치는 영향을 상·하류의 계산영역이 서로 다를 몇몇 유동장에 대하여 조사하고, 본 계산에서 얻어진 결과와 실형결과와의 비교로 본 3차원 유동해석 코드의 유효성을 검토 하였다.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2000년도 추계학술대회논문집B
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• pp.597-602
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• 2000

In a MEMS(micro-electro mechanical system), the fluid may slip near the surface of a solid and have a discontinuous temperature profile. A numerical prediction in this slip flow region can provide a reasonable guide for the design and fabrication of micro devices. The compressible Navier-Stokes equation with Maxwell/smoluchowski boundary condition is solved for two simple systems; couette flow and pressure driven flow in a long channel. We found that the couette flow could be regarded as an incompressible system in low speed regions. For the pressure driven flow system, we observed nonlinear distribution of pressure in the long channel and numerical results showed a good agreement with the experimental results.

• 대한수학회보
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• 제44권3호
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• pp.547-567
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• 2007

We obtain spatial-temporal decay rates of weak solutions of incompressible flows in exterior domains. When a domain has a boundary, the pressure term yields difficulties since we do not have enough information on the pressure term near the boundary. For our calculations we provide an idea which does not require any pressure information. We also estimated the spatial and temporal asymptotic behavior for strong solutions.

• 대한기계학회논문집B
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• 제24권10호
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• pp.1335-1342
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• 2000

Three-dimensional flow analysis and numerical optimization methods are presented for the design of an axial-flow fan. Steady, incompressible, three-dimensional Reynolds-averaged Navier-Stokes equations are used as governing equations, and standard k- ${\varepsilon}$ turbulence model is chosen as a turbulence model. Governing equations are discretized using finite volume method. Steepest descent method, conjugate gradient method and BFGS method are compared to determine the searching directions. Golden section method and quadratic fit-sectioning method are tested for one dimensional search. Objective function is defined as a ratio of generation rate of the turbulent kinetic energy to pressure head. Two variables concerning sweep angle distribution are selected as the design variables. Performance of the final fan designed by the optimization was tested experimentally.