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- W3199235554 abstract "Due to computational complexity, fluid flow problems are mostly defined on a bounded domain. Hence, capturing fluid outflow calls for imposing an appropriate condition on the boundary where the said outflow is prescribed. Usually, the Neumann-type boundary condition called do-nothing condition is the go-to description for such outflow phenomenon However, such condition does not ensure an energy estimate for the Navier--Stokes equations - let alone establish the existence of solutions. In this paper, we analyze a convective boundary condition that will capture outflow and establish the existence of solutions to the governing equation. We shall show existence and uniqueness results for systems with mixed boundary conditions - Dirichlet condition and the convective boundary condition. The first system is a stationary equation where the Dirichlet condition is purely homogeneous, the other is where an input function is prescribed, and lastly a dynamic system with prescribed input function. We end by showing numerical examples to illustrate the difference between the current outflow condition and the usual do-nothing condition." @default.
- W3199235554 created "2021-09-27" @default.
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- W3199235554 date "2021-09-21" @default.
- W3199235554 modified "2023-09-24" @default.
- W3199235554 title "A Convective Boundary Condition for the Navier-Stokes Equations: Existence Analysis and Numerical Implementations" @default.
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- W3199235554 doi "https://doi.org/10.48550/arxiv.2109.10025" @default.
- W3199235554 hasPublicationYear "2021" @default.
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