MAE 290C HOMEWORK 4 Solved

35.00 $ 17.50 $

Category:
Click Category Button to View Your Next Assignment | Homework

You'll get a download link with a: . zip solution files instantly, after Payment

Description

5/5 - (1 vote)

Integrate numerically the linear wave equation

tu + c∂xu = 0,

in the domain 0 ≤ x < 10 with homogeneous initial conditions and u(x = 0,t) = sin(At) Solve using secondorder centered finite difference schemes with N = 200 grid points, ∆t = 0.01 and the following boundary conditions at the artificial exit:

  1. Homogeneous boundary conditions, uN = 0.
  2. Linear extrapolating boundary conditions, uN = 2uN−1uN−2.
  3. Quadratic extrapolating boundary conditions, uN = 3uN−1− 3uN−2 + uN−3.
  4. Homogeneous Neumann boundary conditions, uN = uN−1.
  5. Antisymmetric boundary conditions, uN = −uN−1.
  6. First-order upwinding convective boundary conditions,

.

  1. Second-order upwinding convective boundary conditions,

.

Perform an analytical study of the reflection of waves generated by the each scheme at the artificial boundary and discuss the results obtained for A = 0.1 and A = 3. Compare your numerical results with the analysis of each boundary condition.

  • HW4-qekbff.zip