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participant_pages:lsce [2014/05/16 14:08]
grenier 		participant_pages:lsce [2014/05/16 14:10]
grenier
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 The procedure developed for the complete set of equations relies upon the elementary time step resolution of the diffusive & advective equation provided in TRANGEOL. It offers MHFE and VF schemes, a theta method (from implicit to explicit) for diffusion and advection. These numerical schemes were originally designed for the resolution of the conductive heat transfer (equivalently diffusive transport). The extensions to advection were made expressing the advection as a source term for MHFE (Dabbene et al 1998) and using a modified version of the method by () for the FV (Le Potier 2004). The stability and accuracy of the resolution has to be controlled with the evaluation of Fourier and CFL numbers respectively. For high Peclet numbers (strong advection), some options are provided in TRANGEOL to obtain an automatic unconditional stability of the resolution. The procedure behind it is an upwind scheme, formally equivalent to the introduction of a dispersion coefficient equal to mesh size. This leads to the CFL value of 1 in the corresponding meshes.  The procedure developed for the complete set of equations relies upon the elementary time step resolution of the diffusive & advective equation provided in TRANGEOL. It offers MHFE and VF schemes, a theta method (from implicit to explicit) for diffusion and advection. These numerical schemes were originally designed for the resolution of the conductive heat transfer (equivalently diffusive transport). The extensions to advection were made expressing the advection as a source term for MHFE (Dabbene et al 1998) and using a modified version of the method by () for the FV (Le Potier 2004). The stability and accuracy of the resolution has to be controlled with the evaluation of Fourier and CFL numbers respectively. For high Peclet numbers (strong advection), some options are provided in TRANGEOL to obtain an automatic unconditional stability of the resolution. The procedure behind it is an upwind scheme, formally equivalent to the introduction of a dispersion coefficient equal to mesh size. This leads to the CFL value of 1 in the corresponding meshes. 
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 +//Resolution of the coupled set of equations//
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 +The resolution of the coupled set of equations is achieved iteratively, with a Picard scheme: the properties for both equations are computed from the values of the unknown at former iteration until convergence of both unknowns. The convergence criterion is expressed as the maximum value of the relative discrepancy between the two last computed pressure and temperature fields. For each time step, the convergence of the iteration scheme was considered achieved when the value of former criterion fell below a threshold. A threshold of 10-4 is commonly considered. 
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