• 대한수학회논문집
• /
• 제14권4호
• /
• pp.833-842
• /
• 1999

In this paper, we construct a fully discrete solution of the incompressible Navier Stokes equations using implicit Runge kutta method. We prove the existence of the fully discrete solution.

• 대한수학회지
• /
• 제49권1호
• /
• pp.113-138
• /
• 2012

We construct a mild solutions of the Navier-Stokes equations in half spaces for nondecaying initial velocities. We also obtain the uniform bound of the velocity field and its derivatives.

• 한국전산유체공학회:학술대회논문집
• /
• 한국전산유체공학회 2000년도 추계 학술대회논문집
• /
• pp.129-134
• /
• 2000

An efficient numerical method to solve the unsteady incompressible Navier-Stokes equations is developed. A fully implicit time advancement is employed to avoid the CFL(Courant-Friedrichs-Lewy) restriction, where the Crank-Nicholson discretization is used for both the diffusion and convection terms. Based on a block LU decomposition, velocity-pressure decoupling is achieved in conjunction with the approximate factorization. Main emphasis is placed on the additional decoupling of the intermediate velocity components with only n th time step velocity The temporal second-order accuracy is Preserved with the approximate factorization without any modification of boundary conditions. Since the decoupled momentum equations are solved without iteration, the computational time is reduced significantly. The present decoupling method is validated by solving the turbulent minimal channel flow unit.

• 동력기계공학회지
• /
• 제2권3호
• /
• pp.15-20
• /
• 1998

An integrated computing system has been developed for a Navier-Stokes design procedure of an axial-flow compressor blades. The process is done on the four separate steps, i.e., determination of the basic profiles, generation of computational grids, cascade flow simulation and analysis of the computed results in design sense. Applications are made to the blade design of the LP compressor. Computational results are analyzed with respect to the flow-field characteristics and are compared with the expected design requirements. The present system are coupled with the design procedure of the turbomachinery blades using the Navier-Stokes technique.

• 한국전산유체공학회지
• /
• 제16권4호
• /
• pp.72-83
• /
• 2011

A high-order discontinuous Galerkin method for the two-dimensional compressible Navier-Stokes equations was developed on unstructured triangular meshes. For this purpose, the BR2 methd(the second Bassi and Rebay discretization) was adopted for space discretization and an implicit Euler backward method was used for time integration. Numerical tests were conducted to estimate the convergence order of the numerical solutions of the Poiseuille flow for which analytic solutions are available for comparison. Also, the flows around a flat plate, a 2-D circular cylinder, and an NACA0012 airfoil were numerically simulated. The numerical results showed that the present implicit discontinuous Galerkin method is an efficient method to obtain very accurate numerical solutions of the compressible Navier-Stokes equations on unstructured meshes.

• 유체기계공업학회:학술대회논문집
• /
• 유체기계공업학회 2000년도 유체기계 연구개발 발표회 논문집
• /
• pp.169-175
• /
• 2000

A design method for transonic turbine blades is developed based on Navier-Stokes equations. The present computing process is done on the four separate steps, 1.e., determination of the blade profile, generation of the computational grids, cascade flow simulation and analysis of the computed results in the sense of the aerodynamic performance. The blade shapes are designed using the cubic polynomials under the control of the design parameters. Numerical methods for the flow equations are based on Van-Leer's FVS with an upwind TVD scheme on the finite volume. Applications are made to the VKI transonic rotor blades. Computed results are analyzed with respect to the aerodynamic performance and are compared with the experimental data.

• 한국전산유체공학회:학술대회논문집
• /
• 한국전산유체공학회 2010년 춘계학술대회논문집
• /
• pp.397-403
• /
• 2010

The Immersed boundary method(IBM) is one of CFD techniques which can simulate flow field around complex objectives using simple Cartesian grid system. In the previous studies the IBM has mostly been implemented to fractional step method based Navier-Stokes solvers. In these cases, pressure buildup near IB was found to occur when linear interpolation and stadard mass conservation is used and the interpolation scheme became complicated when higher order of interpolation is adopted. In this study, we implement the IBM to an incompressible Navier-Stokes solver which uses SIMPLE algorithm. Bi-linear and quadratic interpolation equations were formulated by using only geometric information of boundary to reconstruct velocities near IB. Flow around 2D circular cylinder at Re=40 and 100 was solved by using these formulations. It was found that the pressure buildup was not observed even when the bi-linear interpolation was adopted. The use of quadratic interpolation made the predicted aerodynamic forces in good agreement with those of previous studies.

• 충청수학회지
• /
• 제19권3호
• /
• pp.283-289
• /
• 2006

Roh[1] derived 2D g-Navier-Stokes equations from 3D Navier-Stokes equations. In this paper, we will see the space $L^2({\Omega},\;g)$, which is the weighted space of $L^2({\Omega})$, as natural generalized space of $L^2({\Omega})$ which is mathematical setting for Navier-Stokes equations. Our future purpose is to use the space $L^2({\Omega},\;g)$ as mathematical setting for the g-Navier-Stokes equations. In addition, we will see Helmoltz-Leray projection on $L^2_{per}({\Omega},\;g)$) and compare with the one on $L^2_{per}({\Omega})$.

• 대한기계학회논문집
• /
• 제16권2호
• /
• pp.313-324
• /
• 1992

Two-dimensional Navier-Stokes code has been developed for analysis of turbomachinery blade rows and other internal flows. The Navier-Stokes equations are written in a Cartesian coordinate system, then mapped into a generalized body-fitted coordinate system. All direction of viscous terms are incorporated and turbulent effects are modeled using the Baldwin-Lomax algebraic model. Equation are discretized using finite difference method on the C-type grids and solved using implicit LU-ADI decomposition scheme. Calculations are made at a VKI turbine cascade flow in a transonic wind-tunnel and compared to experimental data. Present numerical scheme is shown to be in good agreement with the previous experimental results and simulates the two-dimensional viscous flow phenomena.

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