Computational Fluid Dynamics Practice Test 4

1. Which of these schemes guarantee boundedness?

Central difference schemes.

Forward difference schemes

High-resolution schemes

First order schemes

2. Express the 2-dimensional continuity equation in cylindrical coordinates.

\(\frac{\partial(\rho v_r)}{\partial r}+\frac{1}{r}\frac{\partial(\rho v_\theta)}{\partial\theta}+\rho \frac{v_r}{r}+\frac{\partial\rho}{\partial t}=0 \)

\(\frac{\partial(\rho v_r)}{\partial r}+\frac{1}{r}\frac{\partial(\rho v_\theta)}{\partial\theta}+\frac{\rho v_r}{r}=0\)

\(\frac{\partial(\rho v_r)}{\partial r}+\frac{1}{r}\frac{\partial(\rho v_\theta)}{\partial\theta}+\frac{\partial\rho}{\partial t}=0\)

\(\frac{\partial(\rho v_r)}{\partial r}+\frac{1}{r}\frac{\partial(\rho v_\theta)}{\partial\theta}+\rho \frac{v_r}{r}+\frac{\partial\rho}{\partial t}=0\)

3. Preconditioners improve ____________ of the coefficient matrix.

sparsity

Singularity

rank

spectral properties

4. Consider the global matrix AΦ=b. If my coefficient matrix A is the same for different b vectors, which of these methods is economic?

Gauss elimination

PDMA

TDMA

LU decomposition

5. In solving non-linear systems, there is a trade-off between ___________ and ___________

speed and security

stability and convergence

speed and stability

stability and error

6. The multi-grid approach is used to assist __________

gradient solvers

iterative solvers

pre-conditioned solvers

direct solvers

7. For a system to be bounded, the coefficients of the nodes should ___________

have different signs everywhere

be different everywhere

be the same

have the same sign

8. Tolerance for iteration errors is usually based on _______________

stability

convergence

round-off error

residuals

9. When the Peclet number is large, the isolines are ___________

parabolic

elliptic

circular

hyperbolic

10. While changing the coordinates from Cartesian to non-orthogonal in the Finite Difference Method, which of the following remains the same?

all the terms in the equation

source terms of the equation

conservation properties of the equation

number of terms in the equation