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Mikhail Sizov
| Speaker: |
Mikhail Sizov
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| Date: |
Wednesday June 10, 2003 |
| Title: |
Use of the LDC technique for convection-diffusion equations
(Master's Thesis Presentation)
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Abstract
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Partial differential equations with solutions that
have highly localized properties appear in many industrial problems like combustion,
shock hydrodynamics, turbulence. For boundary value problems with solutions
that have one or a few small regions with high activity, a fine grid is needed
in the regions with high activity, whereas a coarser grid would suffice in
the rest of the domain. We consider a discretization method for elliptic
boundary value problems called the local defect correction (LDC) method.
This method was first developed for diffusion problems. Since we want to
use LDC technique for flow problems (which are mostly convection dominated),
we need additional testing. We apply the LDC technique to convection-diffusion
problems. First we consider a simple one dimensional convection-diffusion
equation and we study (both theoretically and numerically) the convergence
behavior of the LDC technique for such type of problems. Next we combine high
order compact finite difference schemes (which are very popular nowadays in
Direct Numerical Simulation (DNS) of turbulent flows) with the LDC technique
and study convergence behavior as well as the computational efficiency of
the resulting method. Finally, we consider LDC method for convection
dominated and pure convection problems.
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