Method-of-lines solution of time-dependent two-dimensional Navier-Stokes equations

Oymak, O
Selçuk, Nevin
A novel approach to the development of a code for the solution of the time-dependent two-dimensional Navier-Stokes equations is described. The code involves coupling between the method of lines (MOL) for the solution of partial differential equations and a parabolic algorithm which removes the necessity of iterative solution on pressure and solution of a Poisson-type equation for the pressure. The code is applied to a test problem involving the solution of transient laminar flow in a short pipe for an incompressible Newtonian fluid. Comparisons show that the MOL solutions are in good agreement with the previously reported values. The proposed method described in this paper demonstrates the ease with which the Navier-Stokes equations can be solved in an accurate manner using sophisticated numerical algorithms for the solution of ordinary differential equations (ODEs).


Method of lines for transient flow fields
Tarhan, T; Selçuk, Nevin (2001-01-01)
A computational fluid dynamics (CFD) code based on the method of lines (MOL) approach was developed for the solution of transient, two-dimensional Navier-Stokes equations for incompressible separated internal flows in complex rectangular geometries. The predictive accuracy of the code was tested by applying it to the prediction of flow fields in both laminar and turbulent channel flows with and without sudden expansion, and comparing its predictions with either measured data or numerical results available i...
Numerical simulation of transient turbulent flow in a heated pipe
Uygur, Ahmet Bilge; Selçuk, Nevin; Oymak, Olcay; Department of Chemical Engineering (2002)
A computational fluid dynamics (CFD) code based on direct numerical simulation (DNS) and the method of lines MOL approach developed previously for the solution of transient two-dimensional Navier-Stokes equations for turbulent, incompressible, internal, non-isothermal flows with constant wall temperature was applied to prediction of turbulent flow and temperature fields in flows dominated by forced convection in circular tubes with strong heating. Predictive ability of the code was tested by comparing its r...
Transient simulation of radiating flows
Selçuk, Nevin; Ayranci, I; Tarhan, T (2005-06-01)
Time-dependent Navier-Stokes equations are solved in conjunction with the radiative transfer equation by coupling a previously developed direct numerical simulation-based computational fluid dynamics code to an existing radiation code, both based on the method of lines approach. The temperature profiles predicted by the coupled code are validated against steady-state solutions available in the literature for laminar, axisymmetric, hydrodynamically developed flow of a gray, absorbing, emitting fluid in a hea...
Transient simulation of reacting radiating flows
Uygur, A. Bilge; Tarhan, Tanil; Selçuk, Nevin (2006-10-01)
Laminar methane-air diffusion flame was simulated by coupling a method of lines based parallel direct numerical simulation code with a radiation code based on method of lines solution of discrete ordinates method. The predictions of the code are validated against experimental data as well as numerical results of the same code without radiation model. Comparisons show that incorporation of radiation code to the computational fluid dynamics code results in a significant improvement in the predicted temperatur...
Computation of multi-passage cascade flows with overset and deforming grids
Tuncer, İsmail Hakkı (null; 1997-12-01)
An overset grid method is applied to the solution of single and multi-passage cascade flows with a compressible Navier-Stokes solver. C-type grids around individual blades are overset onto a Cartesian background grid. Overset grids are allowed to move in time relative to each other as prescribed by the oscillatory plunging motion. The overset grid method uses a simple, robust numerical algorithm to localize moving boundary points and to interpolate solution variables across intergrid boundaries. Computation...
Citation Formats
O. Oymak and N. Selçuk, “Method-of-lines solution of time-dependent two-dimensional Navier-Stokes equations,” INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, pp. 455–466, 1996, Accessed: 00, 2020. [Online]. Available: