Computational Fluid Dynamics Multiple Choice Questions on “Incompressible Flows – Special Features of Navier Stokes Equation”.
1. Which of these statements is correct?
a) Body force term in the momentum equation is non-linear
b) Rate of change term in the momentum equation is non-linear
c) Convective term in the momentum equation is linear
d) Convective term in the momentum equation is non-linear
Answer: d
Clarification: The convective term in the momentum equation is given by (frac{partial(rho u_i u_j)}{partial x_j}). Where, ρ and u are density and velocity respectively. This term is a non-linear term. The rate of change and the body force terms are linear.
2. For the incompressible flows, which of these terms will be zero?
a) Pressure force
b) Body force
c) Bulk viscosity
d) Shear force
Answer: c
Clarification: A part of the viscous terms in the momentum equation is present in the diffusive term. Among these comes the bulk viscosity terms. These terms will be non-zero only for the compressible flows.
3. In which of these approaches is the pressure force treated as a body force?
a) Finite volume method – non-conservative approach
b) Finite volume method – conservative approach
c) Finite difference method – conservative approach
d) Finite difference method – non-conservative approach
Answer: b
Clarification: In the general integral form of the conservation equations, the pressure force is taken as a volume integral. While using the finite volume method, this is changed into a surface force by using the Gauss-Divergence theorem.
4. If the pressure force is not treated as a surface force in the finite volume method, what will happen?
a) Non-conservative error
b) Stability issues
c) Boundedness problems
d) Convergence issues
Answer: a
Clarification: Without using the Gauss-Divergence theorem, the pressure force can be treated as a volume integral itself. But, this will lead to a non-conservative form of equations which, in turn, will result in non-conservative errors.
5. The difference between the conservative and the non-conservative approaches occurs in the ___________
a) finite difference method
b) finite volume method
c) finite element method
d) spectral element method
Answer: b
Clarification: The conservative and non-conservative approaches gives rise to a considerable difference only in the finite volume method. In the finite difference approach, they do not result in any variation.
6. Which of these is correct for extra viscous terms in cylindrical coordinates?
a) The implicit and explicit treatments do not depend on the sign of the coefficients
b) It is treated implicitly when its contribution to the coefficient of the central node is negative
c) It is treated implicitly when its contribution to the coefficient of the central node is positive
d) It is treated explicitly when its contribution to the coefficient of the central node is positive
Answer: c
Clarification: While using the non-Cartesian coordinate systems, extra terms occur such as that of the extra viscous term in the momentum equation. This term is treated implicitly when it leads to a positive coefficient for the central node. Otherwise, it is treated explicitly.
7. Which of these changes do not contribute to a change in momentum in the momentum equation?
a) Surface fluxes
b) Surface forces
c) Body forces
d) Rate of change term