AERO 455 - Computational Fluid Dynamics Assignment 1: Due Beginning of Class on February 3rd, 2020 Information You need to submit a hard copy of your report in class on the due date. Your report should include a clear description of any equations, procedures, derivations, algorithms, etc. that you used to solve each problem. It should also include all the requested plots, tables, answers, etc. that are requested for each case. 5% penalty per day late. You also need to submit a single .zip file containing all of your computer codes to brian.vermeire@concordia.ca with the subject AERO 455 - Assignment 1 before the in-class due date. Your submission is not considered complete until both the report and this email are received. Question 1 - Linear Advection (10 Marks) The linear advection equation is where a is the advection velocity, u is a scalar, x is the spatial coordinate, and t is time. As derived in class, one suitable scheme is u+l - u uy U;-1 = 0, (2) t where At is the time step size, Ar is the grid spacing, and u is the solution at node i and time level t. Write a computer code using this finite difference scheme to advance the linear advection equation to a final time T = 1 on a periodic domain of length L = 1, using advection velocity a = 1, grid spacings Ax = 1/10, 1/20, 1/40, 1/80,1/160, corresponding time steps of size At = 1/20, 1/40, 1/80,1/160, 1/320, and the initial condition uo = sin(270). (a) Create a single plot showing the exact solution (identical to the initial condition in this case) and the final solution for each level of grid refinement. Discuss the behaviour as you refine the grid. (b) Create an error table showing the error norm E1 = DAU; - ueil/N for each value of Ar, where we is the exact solution (c) Create a Log-Log plot of Ei vs. Ar. Comment on the slope of this line with respect to the expected order of accuracy. AERO 455 - Computational Fluid Dynamics Assignment 1: Due Beginning of Class on February 3rd, 2020 Information You need to submit a hard copy of your report in class on the due date. Your report should include a clear description of any equations, procedures, derivations, algorithms, etc. that you used to solve each problem. It should also include all the requested plots, tables, answers, etc. that are requested for each case. 5% penalty per day late. You also need to submit a single .zip file containing all of your computer codes to brian.vermeire@concordia.ca with the subject AERO 455 - Assignment 1 before the in-class due date. Your submission is not considered complete until both the report and this email are received. Question 1 - Linear Advection (10 Marks) The linear advection equation is where a is the advection velocity, u is a scalar, x is the spatial coordinate, and t is time. As derived in class, one suitable scheme is u+l - u uy U;-1 = 0, (2) t where At is the time step size, Ar is the grid spacing, and u is the solution at node i and time level t. Write a computer code using this finite difference scheme to advance the linear advection equation to a final time T = 1 on a periodic domain of length L = 1, using advection velocity a = 1, grid spacings Ax = 1/10, 1/20, 1/40, 1/80,1/160, corresponding time steps of size At = 1/20, 1/40, 1/80,1/160, 1/320, and the initial condition uo = sin(270). (a) Create a single plot showing the exact solution (identical to the initial condition in this case) and the final solution for each level of grid refinement. Discuss the behaviour as you refine the grid. (b) Create an error table showing the error norm E1 = DAU; - ueil/N for each value of Ar, where we is the exact solution (c) Create a Log-Log plot of Ei vs. Ar. Comment on the slope of this line with respect to the expected order of accuracy
