This paper presents eigensolution and non-modal analyses for immersedboundary methods (IBMs) based on volume penalization for the linear advectionequation . This approach is used to analyze the behavior of flux reconstruction(FR) discretization, including the influence of polynomial order andpenalization parameter on numerical errors and stability . Numerical experiments show that the penalization term needs to be increased to damp oscillations inside the solid (i.e. porous region), which leads to undesirable time steprestrictions. As an alternative, we propose to include a second-order term inthe solid for the no-slip wall boundary condition . Results show that by adding a second order term we improve the overall accuracy with relaxed time step restriction. This indicates that the optimal value of the penalizingparameter and the second order damping can be carefully chosen to obtain a more accurate scheme. Finally, the approximated relationship between these twoparameters is used as a guideline to select the optimum penaltyterms in a Navier-Stokes solver, to simulate flow past a cylinder .

Author(s) : Jiaqing Kou, Aurelio Hurtado-de-Mendoza, Saumitra Joshi, Soledad Le Clainche, Esteban Ferrer

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Keywords : order - penalization - term - eigensolution - boundary -

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