Numerical extraction of a macroscopic pde and a lifting operator from a lattice Boltzmann model

Lifting operators play an important role in starting a lattice Boltzmann model from a given initial density. The density, a macroscopic variable, needs to be mapped to the distribution functions, mesoscopic variables, of the lattice Boltzmann model. Several methods proposed as lifting operators have been tested and discussed in the literature. The most famous methods are an analytically found lifting operator, like the Chapman-Enskog expansion, and a numerical method, like the Constrained Runs algorithm, to arrive at an implicit expression for the unknown distribution functions with the help of the density. This paper proposes a lifting operator that alleviates several drawbacks of these existing methods. In particular, we focus on the computational expense and the analytical work that needs to be done. The proposed lifting operator, a numerical Chapman-Enskog expansion, obtains the coefficients of the Chapman-Enskog expansion numerically. Another important feature of the use of lifting operators is found in hybrid models. There the lattice Boltzmann model is spatially coupled with a model based on a more macroscopic description, for example an advection-diffusion-reaction equation. In one part of the domain, the lattice Boltzmann model is used, while in another part, the more macroscopic model. Such a hybrid coupling results in missing data at the interfaces between the different models. A lifting operator is then an important tool since the lattice Boltzmann model is typically described by more variables than a model based on a macroscopic partial differential equation.Comment: submitted to SIAM MM

A Unified Analysis of Balancing Domain Decomposition by Constraints for Discontinuous Galerkin Discretizations

The BDDC algorithm is extended to a large class of discontinuous Galerkin (DG) discretizations of second order elliptic problems. An estimate of C(1 + log(H/h))2 is obtained for the condition number of the preconditioned system where C is a constant independent of h or H or large jumps in the coefficient of the problem. Numerical simulations are presented which confirm the theoretical results. A key component for the development and analysis of the BDDC algorithm is a novel perspective presenting the DG discretization as the sum of element-wise “local” bilinear forms. The element-wise perspective allows for a simple unified analysis of a variety of DG methods and leads naturally to the appropriate choice for the subdomain-wise local bilinear forms. Additionally, this new perspective enables a connection to be drawn between the DG discretization and a related continuous finite element discretization to simplify the analysis of the BDDC algorithm.Boeing CompanyMassachusetts Institute of Technology (Zakhartchenko Fellowship

A comparison of homogenization and standard mechanics analyses for periodic porous composites

Composite material elastic behavior has been studied using many approaches, all of which are based on the concept of a Representative Volume Element (RVE). Most methods accurately estimate effective elastic properties when the ratio of the RVE size to the global structural dimensions, denoted here as ν, goes to zero. However, many composites are locally periodic with finite ν. The purpose of this paper was to compare homogenization and standard mechanics RVE based analyses for periodic porous composites with finite ν. Both methods were implemented using a displacement based finite element formulation. For one-dimensional analyses of composite bars the two methods were equivalent. Howver, for two- and three-dimensional analyses the methods were quite different due to the fact that the local RVE stress and strain state was not determined uniquely by the applied boundary conditions. For two-dimensional analyses of porous periodic composites the effective material properties predicted by standard mechanics approaches using multiple cell RVEs converged to the homogenization predictions using one cell. In addition, homogenization estimates of local strain energy density were within 30% of direct analyses while standard mechanics approaches generally differed from direct analyses by more than 70%. These results suggest that homogenization theory is preferable over standard mechanics of materials approaches for periodic composites even when the material is only locally periodic and ν is finite.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47812/1/466_2004_Article_BF00369853.pd

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Nouvelles données (présence du canal bucco-œsophagien et du canal génito-intestinal, position des vitellogènes et du testicule) sur Eupolystoma alluaudi, parasite de l’Amphibien africain Bufo regularis

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Description de Polystoma galamensis Monogène nouveau de la vessie urinaire de Rana galamensis au Togo. Ce parasite se caractérise par la faible valeur du rapport hapteur-corps, la taille importante des hamulis et le développement des caecums axiaux avec possibilité d’anastomose