What is it about?
It is known that an unsteady incompressible fluid flow can be approximated by minimizers of a certain energy functional if it is appropriately weighted in time. Within this approximation, one automatically obtains conditions for the flow behaviour also near the outlet or inlet boundaries. We show that this retrieves a kind of the celebrated do-nothing boundary condition that, however, includes the dynamic pressure. This represents the first of its kind mathematical justification of these conditions on the outflow.
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Why is it important?
Determination of outflow boundary conditions for a fluid flow is a longstanding problem in fluid mechanics that has serious consequences for computer simulations of the fluid flow. Indeed, it is rarely the case that the fluid is contained within an impermeable vessel; rather, one has to specify what happens on some artificial boundaries where the fluid leaves or enters the region of interest. How to do this exactly and correctly is a subject of an ongoing scientific debate and it still seems to be open to new and creative ideas.
Perspectives
This work highlights the general utility of variational methods; here in the case of natural boundary conditions.
PhD Michal Bathory
Charles University
Read the Original
This page is a summary of: Variational resolution of outflow boundary conditions for incompressible Navier–Stokes, Nonlinearity, September 2022, Institute of Physics Publishing,
DOI: 10.1088/1361-6544/ac8fd8.
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