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Etude de schémas numériques d'ordre élevé pour la simulation de dispersion de polluants dans des géométries complexes

Abstract : The prevention of industrial risks requires simulating turbulent dispersion of pollutants. However, the tools mostly used so far do not allow near fields treated in the case of complex geometries, and it is necessary to utilize the tools of CFD (Computational Fluid Dynamics ") more suitable but more expensive. To simulate atmospheric flows with dispersion of pollutants, the CFD models must correctly model the one hand, the effects of buoyancy, and secondly the effects of turbulence. Several approaches exist, including taking into account the effects of buoyancy and turbulence modeling, and require numerical methods adapted to the specific mathematics of each, and accurate numerical schemes to avoid pollution modeling. A formulation of high order finite volume on unstructured meshes, parallelized, is proposed to simulate the atmospheric flows with dispersion of pollutants. The use of high order schemes allow one hand to reduce the number of cells and decrease the simulation time to achieve a given accuracy, and secondly to better control the viscosity numerical schemes for simulation LES (Large Eddy Simulation), for which the numerical viscosity patterns may mask the effects of modeling. Two high-order schemes have been studied and implemented in a 3D Navier Stokes solver on unstructured mesh finite volume. We developed the first high-order scheme, corresponding to a Padé finite volume scheme, and we have extended the scheme of reconstruction polynomial Carpentier (2000) for incompressible flows. The numerical properties of the various schemes implemented in the same computer code are studied different two-dimensional test cases (calculation of diffusive and convective flow on a solution a priori, a task Gaussian convection, decay of a vortex of Taylor and driven cavity) and tri-dimensional (flow past an obstacle cubic). Particular attention has been paid to the study of the accuracy and treatment of boundary conditions. The implementation of the polynomial allows to obtain quasi identical simulation time compared to a classical upwind scheme of order 2, but with higher accuracy. The compact layout gives the best accuracy. Using a Jacobi method without calculation implied matrix to calculate the gradient, the simulation time becomes interesting only when the required accuracy is important. An alternative is the resolution of linear system by an algebraic multigrid method. This method significantly reduces the computation time of the gradient and the Padé scheme is effective even for coarse meshes. Finally, to reduce simulation time, the parallelization schemes of high order is achieved by a decomposition into subdomains. The assembly flow occurs naturally and different solvers provided by PETSc libraries and HYORE (algebraic multigrid solver and preconditioned Krylov method) used to solve linear systems from our problem. The work was to identify and determine the parameters that lead to lowest time resolution simulation. Various tests of speed-up and scale-up were used to determine the most effective and optimal parameters for solving linear systems in parallel from our problem. The results of this work have been the subject of a communication in an international conference "Parallel CFD 2008" and an article submitted to "International Journal for Numerical Methods in Fluids" (Analysis of high-order finite volume schemes for the incompressible Navier Stokes equations)
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  • HAL Id : tel-00842988, version 1

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Julien Montagnier. Etude de schémas numériques d'ordre élevé pour la simulation de dispersion de polluants dans des géométries complexes. Autre [cond-mat.other]. Université Claude Bernard - Lyon I, 2010. Français. ⟨NNT : 2010LYO10118⟩. ⟨tel-00842988⟩

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