Computational Characterization of Mixing in Flows
Författare och institution:
Erik D. Svensson (Institutionen för matematiska vetenskaper, Chalmers/GU)
Utgiven i serie vid Göteborgs universitet:
Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie, ISSN 0346-718X; nr 2453
Chalmers University of Technology
Datum för examination:
Tidpunkt för examination:
10.00 Pascal, the department of Mathematical Sciences, Chalmers University of Technology
Prof. Dr. Kunibert G. Siebert, Institut fur Mathematik, Universität Augsburg, Germany
The major theme of this thesis is mathematical aspects of fluid mixing in the case when diffusion is negligible, which is commonly refered to as mixing by stirring or mixing by chaotic advection in the engineering
literature. In this case the mixing is driven by a velocity field and is characterized by the flow generated by the velocity field. We propose a general methodology that can be used to characterize mixing in flows.
In this work we assume that the velocity field is modeled by the incompressible
Stokes equations but in principle we can choose to use any
other fluid model. We derive pointwise a posteriori error estimates for finite element approximations of the Stokes equations and investigate the flow generated by the velocity field by computing a large number of orbits
in the flow. We demonstrate that the computed orbits are close to exact orbits by deriving a shadowing error estimate. Principal to this estimate
is that we compute the orbits and the velocity field sufficiently accurately.
On the basis of notions from dynamical systems theory we devise a tractable mixing measure that resolves the mixing process both in space and time. We provide an error estimate for computed mixing measures
which relies on the error estimate for the computed orbits.
Finally, we discuss a few additional computational issues. (1) We suggest an optimal search algorithm that given a query point can locate the nsimplex in a finite element triangulation that contains the query point.
(2) We analyse and discuss finite element multigrid methods for quadratic
finite elements and for adaptively refined triangulations.
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
mixing, hyperbolicity, shadowing, finite elements, flow simulation, a priori error estimates, Stokes equations, point location, multigrid, refinements
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