Numerical Methods
Not all CFD methods are
created equal ...
Discrete Calculus Approach
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Those who refuse to
read the papers won't believe it - but this is an approach
to discretizes PDEs exactly. The equations are exact -
but not closed (or solvable).
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Closure occurs in
the constitutive equations (where the physics is also
approximated) so all the calculus operators and the physics
remains exact.
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We have explored how
to construct higher-order versions of these methods.
Moving Mesh Adaptation
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Mesh smoothing and
mesh flipping. This keeps positions and connectivity
optimal. These algorithms are nontrivial in 3D.
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Mesh motion for
adaptation is fully parallel. It is very fast (< 2% of
the solution time) , and it does not alter the CPU load
balance.
Unstructured Staggered Mesh
Methods
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These are a subclass
of the methods described above that are well suited for the
Navier-Stokes equations.
-
We have
demonstrated: their conservation properties, how to use
median rather than dual meshes, and how to use moving meshes
(using Reynolds Transport Theorem - NOT ALE methods).
Fractional Step Methods
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Matrix analysis of
these methods makes them easier to understand. In
particular - there are no boundary condition issues.
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Exact Fractional
Step Methods. Splitting errors can become large when
the implicit terms are large (implicit convection, low Re,
etc). This is a pressure removal method with no errors
for incompressible flows.
-
When iterative
solution methods are used, exact fractional step requires
far fewer iterations and is therefore also faster even for
regular applications.
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