### CFDTechniques

```CFD Techniques Quiz
What is the weight of an adult hippo
skin?
1. 0.5 tons
2. 1 ton
3. 2 tons
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10
What type of equation is this if the
flow is supersonic?
2
2




2
 M  1 x2  y2  0.
1. elliptic
2. parabolic
3. hyperbolic
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What is X in the definition below?
The X is the difference between the PDE and the finite
difference representation
1.
2.
3.
4.
5.
Rounding error
Goodness of fit
Truncation error
Convergence measure
Marching error
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10
Consider the finite difference approximation to the
first derivative below. Which statement is false?
 u  4u  x0  x, y0   3u  x0 , y0   u  x0  2x, y0 
2


O
(

x
)
 
2x
 x 0
1. If the grid spacing is halved
the error goes down by 1/4
2. This is a central difference
approximation
3. This form might be useful
close to a wall
4. This form might be useful
near the edge of the
simulation
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4
What is X in the description below?
A X is one for which errors from any source (round-off, truncation,
mistakes) are not permitted to grow in the sequence of numerical
procedures as the calculation proceeds from one marching step to
the next.
1. consistent numerical scheme
2. stable numerical scheme
3. convergent numerical
scheme
4. second-order numerical
scheme
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What is X in the description below?
A solution to a finite difference representation is said to be X if it
approaches the true solution to the PDE having the same initial
and boundary conditions as the mesh is refined.
1.
2.
3.
4.
consistent
stable
convergent
Ill-posed
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What is X in the description below?
By X, we mean those errors that arise as a result of the rounding
to a finite number of digits in the arithmetic operations.
1.
2.
3.
4.
truncation
round-off errors
systematic errors
happy accidents
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4
What is X in the definition below?
A finite difference representation is said to be X if we
can show that the difference between the PDE and its
finite difference representation vanishes as the mesh is
refined.
1.
2.
3.
4.
5.
consistent
convergent
stable
first order
most excellent
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10
1. Parabolic equations
have degenerate
Which statement is false?
characteristics
2. The initial value
problem is ill-posed
for elliptic problems
3. Discontinuities can
appear in elliptic
problems
conduction equation
is an example of a
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parabolic problem
1
2
3
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What is X in the definition below?
X error is the error in the solution to the PDE subject to the
given initial values and boundary conditions caused by
replacing the continuous problem by a discrete one and is
defined as the difference between the exact solution of the
PDE (round-off free) and the exact solution to the finite
difference equations (round-off free).
1.
2.
3.
4.
Discretisation
Truncation
Round-off
Integration
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10
1. The Courant number
has no units
2. If you double the
sound speed, the
Courant number
doubles
3. If you halve the space
grid the Courant
number doubles
4. If you halve the time
grid, the Courant
number doubles
Which statement is
false?
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10
Which term would NOT be required in a von
Neumann stability analysis of the equation below?
Hint: u nj  g n exp( 1 j )
u nj 1  u nj 1  r  u nj 1  u nj 1  u nj 1  u nj 1 
1.
2.
3.
4.
5.
g n1 exp( 1 j )
g n1 exp( 1 j )
g n exp( 1( j 1) )
g n exp( 1( j  1) )
g n1 exp( 1( j 1) )
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1.
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2.
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3.
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0%
4.
5.
10
The amplitude in a von Neumann stability test is found
to have the following modulus. What can we say about
the finite difference representation?
g  1  v 2 sin 2 
1. It’s unconditionally
stable
2. It’s conditionally stable
3. It’s conditionally
unstable
4. It’s unconditionally
unstable
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10
For what value of B in the equation below
does the equation become parabolic?
 2
 2
 2


2 2 B
8 2 3
 2x
 16 xy  0
x
xy
y
x
y
1.
2.
3.
4.
5.
2
4
8
16
32
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10
What is the equilibrium value
of A in the square grid used
to solve Laplace’s equation
in 2-d?
1.
2.
3.
4.
5.
0%
1.
0%
2.
2.3
2.4
2.5
2.6
2.7
0%
3.
10
0%
0%
4.
5.
What is the value of A in the grid below?
1.
2.
3.
4.
5.
1.5
0.5
1
0
-1
10
0%
1.
0%
2.
0%
3
0%
4
0%
5
What is the value of B in the grid below?
1.
2.
3.
4.
5.
1.5
0.5
1
0
-1
10
0%
1.
0%
2.
0%
3
0%
4
0%
5
What type are the boundary conditions in the previous
question?
1. Dirichlet
2. Neumann
3. Mixed
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10
Which of these is the correct expression for the
iteration at point 3 in an explicit (Jacobi) method?
1
1. ③   ② N  1.5  ④ N 
4
1
N 1
2. ③  ① N  1.5  ④ N
4
1
N 1
3. ③  ① N  1.0  ④ N
4
1
N 1
4. ③   ① N  0.5  ④ N 
4
N 1




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3.
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10
Which of these is the correct expression for the
iteration at point 2 in an implicit (Gauss-Seidel)
method?
1. ②
N 1
1
  FP2 +1.5 +④ N  ① N 
4
2. ② N 1 
3. ②
N 1
1
1.5 +2  ④ N  ① N 1 

4
1
  FP2 +1.5 +④ N  ① N 1 
4
4. ② N 1 
1
FP2 +1.5 +④ N 1  ① N 1 

4
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4.
 2
 2
 2


A 2 B
C 2  D
E
F 0
x
xy
y
x
y
B 
1 
2A
B 
2 
2A
  B 2  4 AC
Which of these is a characteristic of the (wave)
equation below?
 1

0
2
2
x
4 t
2
1.
2.
3.
4.
5.
2
  xt
  2x  t
  x  2t
  2x  t
  x  2t
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2.
3.
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4.
5.
10
A solution of this equation is
  3sin( x  2t )
1.
2.
3.
4.
Which way is the wave travelling and what is
its speed?
Left to right (toward
positive x) speed 2
Right to left (toward
negative x) speed 2
Left to right (toward
positive x) speed 0.5
Right to left (toward
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0%
0%
0%
positive x) speed 0.5
1
2
3
4
10
Which of these is not a solution of the equation?
1.   4sin  x  2t 
2.   4sin  x  2t   3sin( x  2t )


  4exp   x  2t   sin  x  2t 
  4exp   x  2t   cos  x  2t   sin  x  2t 
3.   4exp  x  2t  sin  x  2t 
2
4.
5.
2
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2
1.
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0%
2.
3.
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4.
5.
10
Which of the following statements is false?
1. Dispersion is caused by odd
derivative terms in a PDE
truncation
2. Diffusion is caused by odd
derivative terms in a PDE
truncation
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10
A CFD simulation of a shock develops
‘waviness’ as pictured below? This is evidence
for what in the solution?
1. Dispersion
2. Diffusion
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10
Which of these is NOT an implicit scheme?
1.
2.
3.
4.
 u nj 11  u nj 1 
 c
  0

t
 2x 
 u nj 1  u nj 1 
u nj 1  u nj
 c
  0

t
x


 u nj 11  u nj 11 
u nj 1  u nj
 c
  0

t
 2x 
 u nj 1  u nj 
u nj 1  u nj 1
 c
  0

2t
 x 
u nj 1  u nj
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3.
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10
Which of these is NOT a point at the entry to the
duct (x=0) joined to the point P by 45 degree
characteristics (i.e. lines of slope -1 and +1) ?
1.
2.
3.
4.
(0,0.6)
(0,-0.6)
(0,0.4)
(0,-0.4)
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```