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SUMMARYWe are interested in solving second-order PDEs with multigrid and unstructured meshes. The multigrid strategy we present here is adapted from the generalized finite volume agglomeration multigrid algorithm we have developed recently for the solution of the Euler equations. We now focus on Poisson's equation. A strategy is defined by introducing a correction factor for the diffusive terms, and some illustrating results are given.
International audienceA multiphase hyperbolic model for dynamic and irreversible powder compactionis built. Four important points have to be addressed in this case. The first one isrelated to the irreversible character of powder compaction. When a granular media issubjected to a loading–unloading cycle, the final volume is lower than the initial one.To deal with this hysteresis phenomenon, a multiphase model with relaxation is built.During loading, mechanical equilibrium is assumed corresponding to stiff mechanicalrelaxation, while during unloading non-equilibrium mechanical transformation isassumed. Consequently, the sound speed of the limit models are very different duringloading and unloading. These differences in acoustic properties are responsible forirreversibility in the compaction process. The second point is related to dynamiceffects, where pressure and shock waves play an important role. Wave dynamics isguaranteed by the hyperbolic character of the equations. Phase compressibility aswell as configuration energy are taken into account. The third point is related tomulti-dimensional situations that involve material interfaces. Indeed, most processeswith powder compaction entailfree surfaces.Consequently, the model should be ableto solve interfaces separating pure fluids and granular mixtures. Finally, the fourthpoint is related to gas permeation that may play an important role in some specificpowder compaction situations. This poses the difficult question of multiple-velocitydescription. These four points are considered in a unique model fitting the frameof multiphase theory of diffuse interfaces . The ability of the model to deal with thesevarious effects is validated on basic situations, where each phenomenon is consideredseparately. Except for the material EOS (hydrodynamic and granular pressures andenergies), which are determined on the basis of separate experiments found in theliterature, the model is free of adjustable parameter
Abstract. Analytical and experimental convergence results are presented for a novel pseudo-unsteady solution method for higher-order accurate upwind discretizations of the steady Euler equations. Comparisons are made with an existing pseudo-unsteady solution method. Both methods make use of nonlinear multigrid for acceleration and nested iteration for the fine-grid initialization. The new method uses iterative defect correction. Analysis shows that it not only has better stability but it also has better smoothing properties. The analytical results are confirmed by numerical experiments, which show better convergence and efficiency.
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