05 tons 1 ton 2 tons 10 What type of equation is this if the flow is supersonic elliptic parabolic hyperbolic 10 What is X in the definition below The X is the difference between the PDE and the finite difference representation ID: 780392
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Slide1
CFD Techniques Quiz
Slide2What is the weight of an adult hippo skin?
0.5 tons
1 ton
2 tons
10
Slide3What type of equation is this if the flow is supersonic?
elliptic
parabolic
hyperbolic
10
Slide4What is
X in the definition below
?The X is the difference between the PDE and the finite difference representation
Rounding error
Goodness of fitTruncation errorConvergence measureMarching error
10
Slide5Consider the finite difference approximation to the first derivative below
. Which statement is
false?
If the grid spacing is halved the error goes down by 1/4
This is a central difference approximation
This form might be useful close to a wall
This form might be useful near the edge of the simulation
10
Slide6What 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.
consistent numerical scheme
stable numerical scheme
convergent numerical scheme
second-order numerical scheme
10
Slide7What 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.
consistent
stable
convergent
Ill-posed
10
Slide8What 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.
truncation
round-off errors
systematic errors
happy accidents
10
Slide9What 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.
consistent
convergent
stable
first order
most excellent
10
Slide10Which statement is
false?
Parabolic equations have degenerate characteristics
The initial value problem is ill-posed for elliptic problems
Discontinuities can appear in elliptic problemsThe unsteady heat conduction equation is an example of a parabolic problem
10
Slide11What 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).
DiscretisationTruncation
Round-off
Integration
10
Slide12Which statement is
false?
The Courant number has no unitsIf you double the sound speed, the Courant number doublesIf you halve the space grid the Courant number doublesIf you halve the time grid, the Courant number doubles
10
Slide13Which term would
NOT
be required in a von Neumann stability analysis of the equation below? Hint:
1.
2.
3.
4.
5.
10
Slide14The amplitude in a von Neumann stability test is found to have the following modulus. What can we say about the finite difference representation?
It’s unconditionally stable
It’s conditionally stable
It’s conditionally unstable
It’s unconditionally unstable
10
Slide15For what value of B in the equation below does the equation become parabolic?
2
4
8
16
32
10
Slide16What is
the equilibrium value of A in the square grid used to solve Laplace’s equation in 2-d?
2.3
2.4
2.5
2.6
2.7
10
Slide17What is the value of A in the grid below?
1.5
0.5
1
0
-1
10
Slide18What is the value of B in the grid below?
1.5
0.5
1
0
-1
10
Slide19What type are the boundary conditions in the previous question?
Dirichlet
Neumann
Mixed
10
Slide20Slide21Which of these is the correct expression for the iteration at point 3 in an explicit (Jacobi) method?
1.
2.
3.
4.
10
Slide22Which of these is the correct expression for the iteration at point 2 in an implicit (Gauss-Seidel) method?
1.
2.
3.
4.
10
Slide23Slide24Which of these is a characteristic of the (wave) equation below?
1.
2.
3.
4.
5.
10
Slide25A solution of this equation is
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 positive x) speed 0.5
10
Slide26Which of these is
not a solution of the equation?
1.
2.
3.
4.
5.
10
Slide27Which of the following statements is
false
?
Dispersion is caused by odd derivative terms in a PDE truncationDiffusion is caused by odd derivative terms in a PDE truncation
10
Slide28A CFD simulation of a shock develops ‘waviness’ as pictured below? This is evidence for what in the solution?
Dispersion
Diffusion
10
Slide29Which of these is NOT an implicit scheme?
1.
2.
3.
4.
10
Slide30Which 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) ?
(0,0.6)
(0,-0.6)
(0,0.4)
(0,-0.4)
10