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タイトル Semi-Lagrangian methods for diffusion problems
開催日時 2015年9月11日 16:45 ~
主催者
講演者 Luca Bonaventura 氏(Politecnico di Milano)
場所 慶應義塾大学理工学部 14棟 733 (創想館 7階 ミーティング3)
内容 Semi-Lagrangian methods have traditionally been developed in the framework of hyperbolic equations, but several extensions of the semi-Lagrangian approach to diffusion and advection-diffusion problems have been proposed recently. These extensions are mostly based on probabilistic arguments and share the common feature of treating second-order operators in trace form, which makes them unsuitable for mass conservative models like the classical formulations of turbulent diffusion employed in computational fluid dynamics. I will present some joint work with R. Ferretti (University of Roma 3) in which we have proposed approaches treating second-order operators in divergence form. A general framework for constructing consistent schemes in one space dimension is presented, and specific cases of conservative and nonconservative discretization are discussed in detail and analyzed. Finally, an extension to (possibly nonlinear) problems in an arbitrary number of dimensions is proposed. Although the resulting discretization approach is only of first order in time, numerical results in a number of test cases highlight the advantages of these methods for applications to computational fluid dynamics and their superiority over to more standard low order time discretization approaches, for both the advection dominated and the stiff diffusion regimes.
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