• Kyungpook Mathematical Journal
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• 제52권4호
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• pp.359-373
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• 2012

The block LU factorization is used to solve the coupled Stokes equations arisen from an optimal control problem subject to Stokes equations. The convergence of the spectral element solution is proved. Some numerical evidences are provided for the model coupled Stokes equations. Moreover, as an application, this algorithm is performed for an optimal control problem.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2005년도 추계 학술대회논문집
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• pp.111-116
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• 2005

Two coupling methods for the Navier-Stokes equations and a two-equation turbulence model equations are compared. They are the strongly coupled method and the loosely coupled method. The strongly coupled method solves the Navier-Stokes equations and the two-equation turbulence model equations simultaneously, while the loosely coupled method solves the Navier-Stokes equation with the turbulence viscosity fixed and subsequently solves the turbulence model equations with all the flow quantities fixed. In this paper, performances of two coupling methods are compared for two and three-dimensional problems.

• 대한수학회지
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• 제53권1호
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• pp.127-146
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• 2016

We consider a coupled system of Keller-Segel type equations and the incompressible Navier-Stokes equations in spatial dimension two. We show temporal decay estimates of solutions with small initial data and obtain their asymptotic profiles as time tends to infinity.

• 대한기계학회논문집
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• 제11권5호
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• pp.755-761
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• 1987

본 연구에서는 익형 위에 발생하는 박리기포 주위를 사용한 박리기포 주위 유 동해석에 목적을 두고, 원시변수(primitive variable)를 사용한 부분 포물형 Navier -Stokes 방정식을 사용하여 층류유동에 관한 간단한 기본계산을 통해 비교적 박리기포 가 큰 외부유동(external flow)에도 부분 포물형 방정식이 적용될 수 있음을 보이고자 한다.수치해법은 Galpin 등 이 이차원 관유동(channel flow)에 완전 Navier-Stokes 방정식의 해법으로 사용한 CELS(coupled equation line solver) 방법을 부분 포물형 방정식에 적합하게 수정하여 사용하였다.

• 대한수학회보
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• 제51권3호
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• pp.847-862
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• 2014

Finite element approximation solutions of the optimal control problems for stochastic Stokes equations with the forcing term perturbed by white noise are considered. Error estimates are established for the fully coupled optimality system using Brezzi-Rappaz-Raviart theory. Numerical examples are also presented to examine our theoretical results.

• 한국전산유체공학회지
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• 제21권1호
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• pp.10-18
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• 2016

Numerical boundary conditions are as important as the governing equations when analyzing the fluid flows numerically. An explicit boundary condition method updates the solutions at the boundaries with extrapolation from the interior of the computational domain, while the implicit boundary condition method in conjunction with an implicit time integration method solves the solutions of the entire computational domain including the boundaries simultaneously. The implicit boundary condition method, therefore, is more robust than the explicit boundary condition method. In this paper, steady compressible 2-Dimensional Navier-Stokes solver is developed. We present the implicit boundary condition method coupled with LU-SGS(Lower Upper Symmetric Gauss Seidel) method. Also, the explicit boundary condition method is implemented for comparison. The preconditioning Navier-Stokes equations are solved on unstructured meshes. The numerical computations for a number of flows show that the implicit boundary condition method can give accurate solutions.

• 대한수학회보
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• 제58권3호
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• pp.729-744
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• 2021

In this paper we prove global existence and uniqueness of axisymmetric strong solutions for the three dimensional electro-hydrodynamic model based on the coupled Navier-Stokes-Poisson-Nernst-Planck system in the exterior of a cylinder. The key ingredient is that we use the axisymmetry of functions to derive the L^p interpolation inequalities, which allows us to establish all kinds of a priori estimates for the velocity field and charged particles via several cancellation laws.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2000년도 춘계 학술대회논문집
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• pp.66-72
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• 2000

Aerodynamic sensitivity analysis is performed for the Navier-Stokes equations coupled with two-equation turbulence models using a discrete adjoint method and a direct differentiation method respectively. Like the mean flow equations, the turbulence model equations are also hand-differentiated to accurately calculate the sensitivity derivatives of flow quantities with respect to design variables in turbulent viscous flows. Both the direct differentiation code and the adjoint variable code adopt the same time integration scheme with the flow solver to efficiently solve the differentiated equations. The sensitivity codes are then compared with the flow solver in terms of solution accuracy, computing time and computer memory requirements. The sensitivity derivatives obtained from the sensitivity codes with different turbulence models are compared with each other. Using two-equation turbulence models, it is observed that a usual assumption of constant turbulent eddy viscosity in adjoint methods may lead to seriously inaccurate results in highly turbulent flows.

• 한국전산유체공학회지
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• 제7권4호
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• pp.19-27
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• 2002

An efficient implicit multigrid method is presented for the Navier-Stokes and k-ω turbulence equations. Freezing and limiting strategies are applied to improve the robustness and convergence of the multigrid method. The eddy viscosity and strongly nonlinear production terms of turbulence are frozen in the coarser grids by passing down the values without update of them. The turbulence equations together with the Navier-Stokes equations, however, are consecutively solved on the coarser grids in a loosely coupled fashion. A simple limit for k is also introduced to circumvent slow-down of convergence. Numerical results for the unseparated and separated transonic airfoil flows show that all computations converge well without any robustness problem and the computing time is reduced to a factor of about 3 by the present multigrid method.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2002년도 학술대회지
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• pp.31-34
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• 2002

An efficient implicit multigrid method is presented for the Navier-Stokes and $k-{\omega}$ turbulence equations. Freezing and limiting strategies are applied to improve the robustness and convergence of the multigrid method. The eddy viscosity and strongly nonlinear production terms of turbulence are frozen in the coarser grids by passing down the values without update of them. The turbulence equations together with the Navier-Stokes equations, however, are consecutively solved on the coarser grids in a loosely coupled fashion. A simple limit for k is also introduced to circumvent slow-down of convergence. Numerical results for the unseparated and separated transonic airfoil flows show that all computations converge well without any robustness problem and the computing time is reduced to a factor of about 3 by the present multigrid method.