Figure 3 shows the numerical solution of the advection equation for a scalar u along x at three consecutive timesteps. 1.0 0.8 0.6 0.4 0.2- 0.0 -0.2 -0.4 -0.6 T 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Figure 3: Advection equation, solution for three different timesteps. a) Provide an explanation what conditions and numerical setup could explain the curves. Identify which of the three curves is the first, second and third timestep.

Figure 3 shows the numerical solution of the advection equation for a scalar u along x at three consecutive timesteps. 1.0 0.8 0.6 0.4 0.2- 0.0 -0.2 -0.4 -0.6 T 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Figure 3: Advection equation, solution for three different timesteps. a) Provide an explanation what conditions and numerical setup could explain the curves. Identify which of the three curves is the first, second and third timestep.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question 2 Figure 3 shows the numerical solution of the advection equation for a scalar u along x at three consecutive timesteps. 1.0 0.8- 0.6- 0.4- 0.2- 0.0- -0.2- -0.4- -0.6 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Figure 3: Advection equation, solution for three different timesteps. a) Provide an explanation what conditions and numerical setup could explain the curves. Identify which of the three curves is the first, second and third timestep. b) Consider explicit schemes with central and upwind discretisations. Explain how each of these candidate discretisations could produce the behaviour shown in Figure 3. c) Determine the CFL number that was used in the simulation for each of the candidate schemes for all possible updates. Assume that the timestep and mesh-width used are constant. Read the data to two digits of accuracy from Figure 4 shown at the end of the question, which is an enlarged version of Figure 3. Demonstrate your method and input data for one calculation, but then use a…
Figure 3 shows the numerical solution of the advection equation for a scalar u along x at three consecutive timesteps. 1.0- 0.8- 0.6- 0.4- 0.2 0.0- -0.2- -0.4- -0.6 T T T 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Figure 3: Advection equation, solution for three different timesteps. a) Provide an explanation what conditions and numerical setup could explain the curves. Identify which of the three curves is the first, second and third timestep.
9) A merry-go-round is set up at a local fair. The merry-go-round moves continuously at a rate slow enough for riders to step on and off the ride. The pink horse, P, moves along the circumference of the ride. Hal used a coordinate grid to make a rough sketch of the merry-go-round, with the center at the origin. Initially, P is at P(5,0). It takes 30 seconds for P to return to the same place. What would be the coordinate of P on Hal's sketch after 8.25 minutes? P(5,0)
0.8 m wo B D E 0.8 m 1.0 m Bar AB rotates about the fixed point A with constant angular velocity wo. The system starts with bar AB horizontal. 1) Use the relative velocity equation to find the velocity of C in terms of the angles 0 and > and their derivatives. 2) Determine the lengths of bars AB and BC so that as bar AB rotates, the collar C moves back and forth between the positions D and E. A design constraint is that bar BC must be longer than bar AB (as shown in sketch). 3) You are given the design constraint that the magnitude of the acceleration of collar C must not exceed 200 m/s². What is the maximum allowable value of wo? 4) Create the following plots for a complete revolution of bar AB using the values for lengths and angular velocity determined above: о о e and > versus time as 2 sub-plots. Position, velocity, and acceleration of C versus time as 3 sub-plots. Velocity and acceleration of C versus its position as 2 sub-plots. - 5) Use your plotted results to describe the…
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Do not actually solve the problem numerically or algebraically, just pick the one equation and define the relevant knowns and single unknown. Don’t forget to include direction when called for by a vector variable 12) The air conditioner removes 2.7 kJ of heat from inside a house with 450 m3 of air in it. At a typical air density of 1.3 kg/m3 that means 585 kg of air. If the specific heat of air is 1.01 kJ/(kg oC), by how much would this cool the house if no heat got in through the rest of the house during that time?
Using the Method of Undetermined Coefficients, determine the form of a particular solution for the differential equation. (Do not evaluate coefficients.) 3 y" + 64y = 9t³ sin 8t The root(s) of the auxiliary equation associated with the given differential equation is/are (Use a comma to separate answers as needed.) Write the form of a particular solution. Choose the correct answer below. OA. Yp(t)=t(A3t³ + A₂t² + A₁t+ A₁) e¹ cos 8t + t ¹ cos 8t+t(B3t³ + B₂t² + B₁t+Bo) e' sin 8t O B. Yp(t) = (A3t¹ + A₂t³ +A₁t² + A₁t) e' cos 8t + (B3tª + B₂t³ + B₁t² + Bo) e' sin 8t OC. Yp(t)=t[(A3t³ +A₂t² +A₁t+A₁) cos &t+t(B3t³ + B₂t² + B₁t+ B₁) sin 8t OD. Yp(t) = (A3t³ + A₂t² +A₁t+A₁) cos &t+ (B3t³ + B₂t² + B₁t+Bo) sin 8t
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