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DOI: 10.1615/ICHMT.2010.RAD-6.340
page 2

Nevin Selcuk
Chemical Engineering Department, Middle East Technical University, 06531 Ankara, Turkey


Solution of the time-dependent conservation equations of mass, momentum, energy and species in conjunction with the radiative transfer equation (RTE) is indispensable for the complete simulation of turbulent, reacting and radiating flows and understanding the interactions among these complicated phenomena. Accurate modeling of turbulent flows necessitates implementation of direct numerical simulation (DNS) in which all space and time scales are resolved and computed directly without using any turbulence models. On the other hand, this rigorous, accurate and straightforward treatment requires a lot of grid points and time steps and hence the computational effort is highly intensive. Moreover, coupling a transient computational fluid dynamics (CFD) code based on DNS with an RTE solver is expected to increase the computational cost enormously. Therefore, it is essential to develop efficient codes based on accurate models as well as efficient coupling strategies to overcome this difficulty. Applying compatible solution methods for the CFD and radiation codes is a promising approach to maintain computational efficiency. The method of lines (MOL) is an alternative approach that meets this requirement for time dependent problems. The MOL consists of two stages. First, the dependent variables are kept continuous in time and the partial differential equations (PDEs) are discretized only in space on a dimension by dimension basis using any readily available 1-D spatial discretization package such as finite difference, finite volume or finite element based schemes. This leads to a system of ordinary differential equations (ODEs) to be integrated in time using any readily available explicit or implicit ODE solver, constituting the second stage. By this way, MOL not only offers accurate and stable solutions but also flexibility to incorporate any desired package with ease.

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