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\Large
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               the Institute for Theoretical and Engineering Science\\
		      Department of Mathematics\\
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                           University of Houston\\

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{{\Large\bf                Scientific Computing Seminar}}

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\large
Professor  Dmitri Kuzmin\\
Institute of Applied Mathematics\\ 
University of Dortmund, Germany

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\Large

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{\bf  High-Resolution Finite Element Schemes \\and Their
 Applications in Computational Fluid Dynamics }

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                         Monday, January 28, 2008$^*$ \\
                               10:00 AM- 11:00 AM\\
%                           Room 127  \  \  \  S\&R1 \\
                           Room 646  \   \  PGH \\
%                         Room 634  \  \  \  S\&R1 \\
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\noindent {\bf Abstract:} 

An algebraic approach to derivation of high-resolution schemes for
convection-dominated flow problems is introduced. In the first part of the
talk, the underlying design principles are explained in the context of a
scalar transport equation. The discretization in space is performed using
linear or bilinear finite elements. The standard Galerkin approximation is
shown to possess unfavorable properties which are responsible for
nonphysical oscillations that occur in the vicinity of steep gradients. A
nonoscillatory low-order scheme is constructed by adding a discrete
diffusion operator designed so as to enforce the algebraic positivity
constraint. The resulting error is decomposed into skew-symmetric internodal
fluxes, which makes it possible to remove excessive artificial diffusion.
A family of fully multidimensional flux limiters is developed building on
the flux-corrected transport (FCT) algorithm and total variation diminishing
(TVD) schemes. In the case of an implicit time-stepping method, the
nonlinearity of the discretized convective term is handled using iterative
defect correction. In the second part of the talk, the new methodology is
applied to nonlinear PDE systems including the compressible Euler equations,
the incompressible Navier-Stokes equations, the k-epsilon turbulence model,
and some advanced multiphase flow models. Two- and three-dimensional
simulation results are presented to give a flavor of practical applications.



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%\noindent {\bf Future talks in Scientific Computing Seminar}

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\noindent This seminar is easily accessible to persons with disabilities.
For more information or for assistance, please contact the Mathematics
Department at 743-3500.





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