+2 votes
in Finite Element Method by (110k points)
In the weak forms of the fluid flow model, as the weight functions (w1, w2) are virtual variations of the velocity components(vx, vy ),respectively, which relation is satisfied by the weight functions?

(a) \(\frac{\partial w1}{\partial x}+\frac{\partial w2}{\partial y}\)=0

(b) \(\frac{\partial w2}{\partial x}+\frac{\partial w1}{\partial y}\)=0

(c) \(\frac{\partial w1}{\partial x}-\frac{\partial w2}{\partial y}\)=0

(d) \(\frac{\partial w2}{\partial x}-\frac{\partial w1}{\partial y}\)=0

The question was posed to me at a job interview.

This key question is from Penalty in portion Flows of Viscous Incompressible Fluids of Finite Element Method

1 Answer

+2 votes
by (185k points)
selected by
Best answer
The correct answer is (a) \(\frac{\partial w1}{\partial x}+\frac{\partial w2}{\partial y}\)=0

Easy explanation: In the weak forms of the fluid flow model, suppose that the velocity field (vx, vy ) is such that the continuity equation \(\frac{\partial v_x}{\partial x}+\frac{\partial v_y}{\partial y}\)=0 is satisfied identically. Then the weight functions (w1, w2) being (virtual) variations of the velocity components, also satisfy the continuity equation. Thus the relation possessed by the weight functions is \(\frac{\partial w1}{\partial x}+\frac{\partial w2}{\partial y}=0\).

Related questions

We welcome you to Carrieradda QnA with open heart. Our small community of enthusiastic learners are very helpful and supportive. Here on this platform you can ask questions and receive answers from other members of the community. We also monitor posted questions and answers periodically to maintain the quality and integrity of the platform. Hope you will join our beautiful community