For the momentum equation with unbounded pressure gradient
- Title
- For the momentum equation with unbounded pressure gradient
- Authors
- 김지후
- Date Issued
- 2021
- Publisher
- 포항공과대학교
- Abstract
- We study the momentum equation with unbounded pressure gradient on
the interior curve starting at the non-convex vertex. The inflow boundary by the
horizontal directional vector U = (1, 0)^t on the L-shaped domain is not connected.
When the pressure is integrated along the streamline, it has a jump across the
interior curve. Hence the pressure gradient is not well-defined there. To handle
this we construct a vector field which lifts the pressure jump value on the curve
into the region. To find a precise structure for the solution we split from the
solution the lifting vector field, the contact singularity, the corner singularity and
the remainder part. The remainder one is shown to have the higher regularity.
The contact singularity is because the lifting vector show a non-smooth behavior
at the contact point where the interface curve meets the boundary. The corner
singularity is due to the non-convex vertex. Finally we give some numerical
examples confirming the critical roles of each part in the decomposition.
- URI
- http://postech.dcollection.net/common/orgView/200000369935
https://oasis.postech.ac.kr/handle/2014.oak/111220
- Article Type
- Thesis
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