2
$\begingroup$

I would like to know whether anyone has seen a boundary condition used in a fluid flow problem, of the following type. Suppose viscous incompressible fluid is to the left of a plane $x_1=a$, so the outer normal to the fluid region is $n=(1,0,0)$. The condition specifies that the $x_1$ momentum flux is a nonnegative multiple of the velocity: $$ m\begin{bmatrix} u_1\cr u_2\cr u_3\end{bmatrix} = \begin{bmatrix}\rho u_1^2+p-2\mu u_{1,1} \cr \rho u_2u_1-\mu(u_{1,2}+u_{2,1}) \cr \rho u_3u_1-\mu(u_{1,3}+u_{3,1}) \end{bmatrix} $$ where $m$ could be a number $\ge0$ or even a nonnegative 3 by 3 matrix. (This is connected with my question at http://www.mathoverflow.net/q/163772/) Thanks for any references.

$\endgroup$
  • $\begingroup$ Your notation confuses me. Are you actually mixing subscript for components AND derivatives? Please don't do that. $\endgroup$ – Bernhard Apr 21 '14 at 16:12
  • $\begingroup$ Can you clarify this with an edit to your question? $\endgroup$ – Bernhard Apr 26 '14 at 10:01

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.