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CFD Techniques Quiz

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  1. CFD Techniques Quiz

  2. What is the weight of an adult hippo skin? • 0.5 tons • 1 ton • 2 tons 10

  3. What type of equation is this if the flow is supersonic? • elliptic • parabolic • hyperbolic 10

  4. What is X in the definition below?The X is the difference between the PDE and the finite difference representation • Rounding error • Goodness of fit • Truncation error • Convergence measure • Marching error 10

  5. Consider 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

  6. 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. • consistent numerical scheme • stable numerical scheme • convergent numerical scheme • second-order numerical scheme 10

  7. 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. • consistent • stable • convergent • Ill-posed 10

  8. 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. • truncation • round-off errors • systematic errors • happy accidents 10

  9. 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. • consistent • convergent • stable • first order • most excellent 10

  10. Which statement is false? • Parabolic equations have degenerate characteristics • The initial value problem is ill-posed for elliptic problems • Discontinuities can appear in elliptic problems • The unsteady heat conduction equation is an example of a parabolic problem 10

  11. 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). • Discretisation • Truncation • Round-off • Integration 10

  12. Which statement is false? • The Courant number has no units • If you double the sound speed, the Courant number doubles • If you halve the space grid the Courant number doubles • If you halve the time grid, the Courant number doubles 10

  13. Which term would NOT be required in a von Neumann stability analysis of the equation below? Hint: 1. 2. 3. 4. 5. 10

  14. The 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

  15. For what value of B in the equation below does the equation become parabolic? • 2 • 4 • 8 • 16 • 32 10

  16. What 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

  17. What is the value of A in the grid below? • 1.5 • 0.5 • 1 • 0 • -1 10

  18. What is the value of B in the grid below? • 1.5 • 0.5 • 1 • 0 • -1 10

  19. What type are the boundary conditions in the previous question? • Dirichlet • Neumann • Mixed 10

  20. Which of these is the correct expression for the iteration at point 3 in an explicit (Jacobi) method? • 1. • 2. • 3. • 4. 10

  21. Which of these is the correct expression for the iteration at point 2 in an implicit (Gauss-Seidel) method? • 1. • 2. • 3. • 4. 10

  22. Which of these is a characteristic of the (wave) equation below? 1. 2. 3. 4. 5. 10

  23. A 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

  24. Which of these is not a solution of the equation? 1. 2. 3. 4. 5. 10

  25. Which of the following statements is false? • Dispersion is caused by odd derivative terms in a PDE truncation • Diffusion is caused by odd derivative terms in a PDE truncation 10

  26. A CFD simulation of a shock develops ‘waviness’ as pictured below? This is evidence for what in the solution? • Dispersion • Diffusion 10

  27. Which of these is NOT an implicit scheme? 1. 2. 3. 4. 10

  28. 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) ? • (0,0.6) • (0,-0.6) • (0,0.4) • (0,-0.4) 10