Doctor of Philosophy / Department of Mathematics / Marianne Korten / Charles N. Moore / We start with linear single variable conservation laws and examine the conditions under
which a local extrapolation method (LEM) with upwinding underlying scheme is total
variation diminishing TVD. The results are then extended to non-linear conservation laws.
For this later case, we restrict ourselves to convex flux functions f, whose derivatives are
positive, that is, f A0 and f A0. We next show that the Goodman-LeVeque flux satisfies
the conditions for the LEM to be applied to it. We make heavy use of the CFL conditions,
the geometric properties of convex functions apart from the martingle type properties of
functions which are increasing, continuous, and differentiable.
| Identifer | oai:union.ndltd.org:KSU/oai:krex.k-state.edu:2097/886 |
| Date | January 1900 |
| Creators | Adongo, Donald Omedo |
| Publisher | Kansas State University |
| Source Sets | K-State Research Exchange |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation |
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