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Hybrid grid–particle methods and Penalization: A Sherman–Morrison–Woodbury approach to compute 3D viscous flows using FFT

Robin Chatelin, Philippe Poncet
2014 Journal of Computational Physics  
This computational algorithm is based on the Sherman-Morrison-Woodbury formula coupled to a GMRES iterative method to reduce the computations to a sequence of Poisson problems: this allows to formulate  ...  The present applications focus mainly on a coupling between transport equation and 3D Stokes equations, for studying biological organisms motion in a highly viscous flows with variable viscosity.  ...  This work was granted access to the HPC resources of CALMIP under the allocation P0314.  ... 
doi:10.1016/j.jcp.2014.03.023 fatcat:cqucxzpzqbam7emaa76zcbf3be

Analysis of the penalized 3D variable viscosity stokes equations coupled to diffusion and transport

Robin Chatelin, David Sanchez, Philippe Poncet
2016 Mathematical Modelling and Numerical Analysis  
of the penalized 3D variable viscosity stokes equations coupled to diffusion and transport. Abstract.  ...  It models the interaction between a highly viscous fluid with variable viscosity and immersed moving and deformable obstacles.  ...  This work was granted access to the HPC resources of CALMIP under the allocation P0314.  ... 
doi:10.1051/m2an/2015056 fatcat:z3aawmlw55edpkmauzwm3gslzq

Develop Of Fast High-Order Numerical Methods For High Reynolds Number Environmental Flows

Sumedh Joshi
2016
These three factors conspire to make the numerical simulation of environmental flows difficult, and as such, a numerical method has to be carefully tailored to address all of these difficulties.  ...  This dissertation summarizes an effort to develop a high-order, element-based, parallel, deformed, discontinuous, spectral multi-domain penalty method (SMPM) model to simulate environmental flows.  ...  as an algebraic method closely related to past novel uses of the Sherman-Morrison-Woodbury identity to update the inverse of a matrix with the addition of a low-rank modification [48] .  ... 
doi:10.7298/x4ws8r63 fatcat:t2i4pb2ztnc2dctza74vgaxoyi