• Journal of computational fluids engineering
• /
• v.2 no.2
• /
• pp.26-34
• /
• 1997

An implicit viscous turbulent flow solver is developed for two-dimensional geon unstructured triangular meshes. The flux terms are discretized based on a cell-centered formulation with the Roe's flux-difference splitting. The solution is advanced in time us backward-Euler time-stepping scheme. At each time step, the linear system of equation approximately solved wi th the Gauss-Seidel relaxation scheme. The effect of turbulence is with a standard k-ε two-equation model which is solved separately from the mean flow equation the same backward-Euler time integration scheme. The triangular meshes are generated advancing-front/layer technique. Validations are made for flows over the NACA 0012 airfoil. Douglas 3-element airfoil. Good agreements are obtained between the numerical result experiment.

• Journal of computational fluids engineering
• /
• v.3 no.2
• /
• pp.17-26
• /
• 1998

The three-dimensional incompressible Navier-Stokes equations have been solved by a node-centered finite volume method with unstructured hybrid grids. The pressure-velocity coupling is handled by the artificial compressibility algorithm and convective fluxes are obtained by Roe's flux difference splitting scheme with linear reconstruction of the solutions. Euler implicit method with Jacobi matrix solver is used for the time-integration. The viscous terms are discretised in a manner to handle any kind of grids such as tetragedra, prisms, pyramids, hexahedra, or mixed-element grid. Inviscid bump flow is solved to check the accuracy of high order convective flux discretisation. And viscous flows around a circular cylinder and a sphere are studied to show the efficiency and accuracy of the solver.

• 한국전산유체공학회:학술대회논문집
• /
• 1997.10a
• /
• pp.29-37
• /
• 1997

An implicit viscous turbulent flow solver is developed for two-dimensional geometries on unstructured triangular meshes. The flux terms are discretized based on a cell-centered finite-volume formulation with the Roe's flux-difference splitting. The solution is advanced in time using an implicit backward-Euler time-stepping scheme. At each time step, the linear system of equations is approximately solved with the Gauss-Seidel relaxation scheme. The effect of turbulence effects is approximated with a standard $k-{\varepsilon}$ two-equation model which is solved separately from the mean flow equations using the same backward-Euler time integration scheme. The triangular meshes are generated using an advancing-front/layer technique. Validations are made for flows over the NACA0012 airfoil and the Douglas 3-element airfoil. Good agreements are obtained between the numerical results and the experiment.

• 한국전산유체공학회:학술대회논문집
• /
• 1999.05a
• /
• pp.186-191
• /
• 1999

An Euler solver is developed to predict accurate aerodynamic data such as lift coefficient, drag coefficient, and moment coefficient. The conservation law form of the compressible Euler equations are used in the generalized curvilinear coordinates system. The Euler solver uses a finite volume method and the second order Roe's flux difference splitting scheme with min-mod flux limiter to calculate the fluxes accurately. An implicit scheme which includes the boundary conditions is implemented to accelerate the convergence rate. The multi-block grid is integrated into the flow solver for complex geometry. The flowfields are analyzed around NACA 0012 airfoil in the cases of $M_{\infty}=0.75,\;\alpha=2.0\;and\;M_{\infty}=0.80,\;\alpha=1.25$. The numerical results are compared with other numerical results from the literature. The final goal of this research is to prepare a robust and an efficient Navier-Stokes solver eventually.

• 한국전산유체공학회:학술대회논문집
• /
• 2010.05a
• /
• pp.389-396
• /
• 2010

In this paper, a new computational code was developed using Chorin's artificial compressibility method to solve the two-dimensional incompressible Navier-Stokes equations. In spatial derivatives, Roe's flux difference splitting was used for the inviscid flux, while central differencing was used for the viscous flux. Furthermore, AF-ADI with dual time stepping method was implemented for accurate unsteady computations. Two-equation turbulence models, Menter's $k-{\omega}$ SST model and Coakley's $q-{\omega}$ model, hae been adopted to solve high-Reynolds number flows. A number of numerical simulations were carried out for steady laminar and turbulent flow problems as well as unsteady flow problem. The code was verified and validated by comparing the results with other computational results and experimental results. The results of numerical simulations showed that the present developed code with the artificial compressibility method can be applied to slve steady and unsteady incompressible flows.

• Journal of computational fluids engineering
• /
• v.15 no.2
• /
• pp.55-61
• /
• 2010

A dependence of weighting parameter in preconditioning method for solving low Mach number flow with incompressible flow nature is investigated. The present preconditioning method employs a finite-difference method applied Roe‘s flux difference splitting approximation with the MUSCL-TVD scheme and 4th-order Runge-Kutta method in curvilinear coordinates. From the computational results of benchmark flows through a 2-D backward-facing step duct it is confirmed that there exists a suitable value of the weighting parameter for accurate and stable computation. A useful method to determine the weighting parameter is introduced. With this method, high accuracy and stable computational results were obtained for the flow with low Mach number in the range of Mach number less than 0.3.

• 한국전산유체공학회:학술대회논문집
• /
• 2000.05a
• /
• pp.166-171
• /
• 2000

A two-dimensional/axisymmetric CSCM upwind flux difference splitting Wavier-Stokes method has been developed to study the finite rate chemically react-ing invisicd and viscous hypersonic flows over blunt-body. A upwind method was chosen due to its robustness in capturing the strong bow shock waves. For the nonequilibrium chemically reacting air, NS-I species conservation equations were strongly coupled with flowfield equations through convection and species production terms. The nonequilibrium wall pressure and heat transfer rate distributions along the vehicle were compared with those from equilibrium and perfect gas calculations. The nonequilibrium species distribution shows the reduced concentrations of O and N species when compared with equilibrium species distribution. The solutions resolved strong bow shock waves md heat transfer rate very accurately when compared with central difference schemes.

• 한국전산유체공학회:학술대회논문집
• /
• 2005.10a
• /
• pp.169-177
• /
• 2005

A high resolution scheme for solving gas-liquid two-phase flows with cavitation is described. This scheme uses the curvilinear coordinate grid and solves the density based momentum equations for mixture of gas-liquid medium with a preconditioning method to treat both compressible and incompressible flow characteristics. The present preconditioned method is based on the Runge-Kutta explicit finite-difference scheme, and is improved by using the diagonalization, the flux difference splitting and the MUSCL-TVD schemes to save computational effort and to increase stability and resolvability, especially at gas-liquid contact surfaces. A homogeneous equilibrium cavitation model is used to treat the gas-liquid two-phase medium in cavitating flow as a locally homogeneous pseudo-single-phase medium. Therefore, it is easy to solve cavitating flow, including wave propagation, large density changes and incompressible flow characteristic at low Mach number. Some numerical results obtained by the present scheme are shown.

• Journal of computational fluids engineering
• /
• v.1 no.1
• /
• pp.123-141
• /
• 1996

In this paper the upwind flux difference splitting Navier-Stokes method has been applied to study the perfect gas and the equilibrium chemically reacting hypersonic flow over an axisymmetric sphere-cone(5°) geometry. The effective gamma(γ), enthalpy to internal energy ratio was used to couple chemistry with the fluid mechanics for equilibrium chemically reacting air. The test case condition was at altitude(30km) and Mach number(15). The equilibrium shock thickness over the blunt body region was much thinner than that of perfect gas shock. The pressure difference between perfect gas and equilibrium gas was about 3 ∼ 5 percent. The heat transfer coefficient were also calculated. The results were compared with VSL results in order to validate the current numerical analysis. The results from current method were compared well VSL results ; however, not well at near nose. The proper boundary condition and grid system will be studied to improve the solution quality.

• 한국전산유체공학회:학술대회논문집
• /
• 1995.10a
• /
• pp.203-212
• /
• 1995

In this paper the upwind flux difference splitting Navier-Stokes method has been applied to study the perfect gas and the equilibrium chemically reacting hypersonic flow over an axisymmetric sphere-cone($5^{\circ}$) geometry. The effective gamma($\bar{r}$), enthalpy to internal energy ratio was used to couple chemistry with the fluid mechanics for equilibrium chemically reacting air. The test case condition was at altitude(30Km) and Mach number(15). The equilibrium shock thickness over the blunt body region was much thinner than that of perfect gas shock. The pressure difference between perfect gas and equilibrium gas was about $3\sim5$ percent. The skin friction coefficient and heat transfer coefficient were also calculated.