Wave Equation

Wave Equation a2u 2 a2u = CA ate az2 Symmetric Wave Equations auab ab au = = — , at CA az at CA az Initial Conditions u(z, 0) = 0 , b(z, 0) = 0 Boundary Conditions (0, t) = sin(2 u(0, u(zena, t) = 0 Givens At = 1 = 10 = c , cA , c cA Az Predictor Ste p 4 = ur – coin+, – br) hr = br _ c (nr+i — nr)
Corrector Step
f. I-1″J bri + _urci
The aim is to examine the behaviour of the system when a wave is driven from the left hand side and reflects off the right hand side.
Use MacCormack Technique to :

  1. Solve the symmetric wave equations. 2. Code a simulation that iterates through time plotting u(z) and b(z) for each timestep. J4. -or 3. Describe the time evolution of the system (make sure that you allow it to run for long enough to reach a steady state). ■■■ 4. It may be interesting to produce a movie of this
  2. What happens when you increase and decrease c by modifying its component parameters?
  3. Compare with an exact solution of wave equation

Sample Solution