CFD Techniques Quiz

What is the weight of an adult hippo skin?

1 2 3

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1. 0.5 tons2. 1 ton3. 2 tons

10

What type of equation is this if the flow is supersonic?

1 2 3

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1. elliptic2. parabolic3. hyperbolic

2 2

22 2

1 0.Mx y

10

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

0% 0% 0%0%0%

1. Rounding error2. Goodness of fit3. Truncation error4. Convergence measure5. Marching error

10

Consider the finite difference approximation to the first derivative below . Which statement is false?

1 2 3 4

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0 0 0 0 0 0 2

0

4 , 3 , 2 ,( )

2

u x x y u x y u x x yuO x

x x

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 10

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 2 3 4

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1. consistent numerical scheme2. stable numerical scheme3. convergent numerical

scheme4. 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.

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1. consistent 2. stable3. convergent 4. 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

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1. truncation2. round-off errors3. systematic errors4. happy accidents

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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

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1. consistent2. convergent3. stable4. first order5. most excellent

10

Which statement is false?

1 2 3 4

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1. Parabolic equations have degenerate characteristics

2. The initial value problem is ill-posed for elliptic problems

3. Discontinuities can appear in elliptic problems

4. The unsteady heat conduction equation is an example of a parabolic problem 10

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

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1. Discretisation2. Truncation3. Round-off4. Integration

10

Which statement is false?

1 2 3 4

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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

10

Which term would NOT be required in a von Neumann stability analysis of the equation below? Hint:

1. 2. 3. 4. 5.

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1 1 1 11 1

n n n n n nj j j j j ju u r u u u u

exp( 1 )n nju g j

1 exp( 1 )ng j 1.2.3.4.5.

1 exp( 1 )ng j

exp( 1 )( 1)ng j exp( 1 )( 1)ng j 1 exp( 1 )( 1)ng j

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?

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2 21 sing v

1. It’s unconditionally stable

2. It’s conditionally stable3. It’s conditionally

unstable4. It’s unconditionally

unstable10

For what value of B in the equation below does the equation become parabolic?

1 2 3 4 5

0% 0% 0%0%0%

2 2 2

2 22 8 3 2 16 0B x xyx x y y x y

1. 22. 43. 84. 165. 32

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.

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1. 2.32. 2.43. 2.54. 2.65. 2.7

10

What is the value of A in the grid below?

1. 2. 3 4 5

0% 0% 0%0%0%

1. 1.52. 0.53. 14. 05. -1

10

What is the value of B in the grid below?

1. 2. 3 4 5

0% 0% 0%0%0%

1. 1.52. 0.53. 14. 05. -1

10

What type are the boundary conditions in the previous question?

1 2 3

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1. Dirichlet2. Neumann3. Mixed

10

Which of these is the correct expression for the iteration at point 3 in an explicit (Jacobi) method?

1. 2. 3. 4.

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1 11.5

4N N N ③ ② ④

1 11.0

4N N N ③ ① ④

1 11.5

4N N N ③ ① ④

1.

2.

3.

4. 1 10.5

4N N N ③ ① ④

10

Which of these is the correct expression for the iteration at point 2 in an implicit (Gauss-Seidel) method?

1. 2. 3. 4.

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1 1

4N N N ② FP2+1.5+④ ①1.

2.

3.

4.

1 11

4N N N ② 1.5+2 ④ ①

1 11

4N N N ② FP2+1.5+④ ①

1 1 11

4N N N ② FP2+1.5+④ ①

10

1 22 2

B B

A A

2 4B AC

2 2 2

2 20A B C D E F

x x y y x y

Which of these is a characteristic of the (wave) equation below?

1. 2. 3. 4. 5.

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2 2

2 2

10

4x t

x t 1.2.3.4.5.

2x t

2x t

2x t

2x t 10

A solution of this equation is

Which way is the wave travelling and what is its speed?

1 2 3 4

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3sin( 2 )x t

1. Left to right (toward positive x) speed 2

2. Right to left (toward negative x) speed 2

3. Left to right (toward positive x) speed 0.5

4. Right to left (toward positive x) speed 0.5 10

Which of these is not a solution of the equation?

1. 2. 3. 4. 5.

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4sin 2x t 1.

2.

3.

4.

5.

4sin 2 3sin( 2 )x t x t

24exp 2 sin 2x t x t

24exp 2 sin 2x t x t

24exp 2 cos 2 sin 2x t x t x t

10

Which of the following statements is false?

1 2

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1. Dispersion is caused by odd derivative terms in a PDE truncation

2. Diffusion is caused by odd derivative terms in a PDE truncation

10

A CFD simulation of a shock develops ‘waviness’ as pictured below? This is evidence for what in the

solution?

1 2

0%0%

1. Dispersion2. Diffusion

10

Which of these is NOT an implicit scheme?

1. 2. 3. 4.

0% 0%0%0%

1 11 1 02

n n n nj j j ju u u u

ct x

1 1

1 0n n n nj j j ju u u u

ct x

1 1 1

1 1 02

n n n nj j j ju u u u

ct x

1 1

1 02

n n n nj j j ju u u u

ct x

1.

2.

3.

4.10

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

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1. (0,0.6)2. (0,-0.6)3. (0,0.4)4. (0,-0.4)

10