Question

Which option is correct regarding constraints in the viscous flow problems governed by the continuity and momentum equation?

(a) Constrains are readily available

(b) Constraints are created by the elimination of pressure

(c) Constraints are created by the elimination of velocity

(d) No constraints are dealt with in penalty formulation

The question was asked in unit test.

This intriguing question comes from Penalty in chapter Flows of Viscous Incompressible Fluids of Finite Element Method

Answer 1

Correct choice is (b) Constraints are created by the elimination of pressure

Easiest explanation: In viscous flow problems, constrains are not readily available from the presented equations. Since pressure is not present in all the governing equations, we eliminate it from the given other equations. The constraints are created on velocity by the elimination of pressure, and thus, the penalty method is applied.