Aliasing Problem: Category 1, Problem 1, Analytical Solution

The exact analytical solution of the convective wave equation, satisfying initial condition t = 0 is shown. However, for ∆x = 1 and α = 4.6 > π (3) is not the exact computational solution. Because alpha is larger than pi, the solution is subjected to aliasing. In solving the above initial value problem, the computer code has, first, to sample the initial condition (2). For α > π ; i.e., waves with wavelength less than two mesh spacing, which is the Nyquist limit, the sampled initial condition is aliased into a wave with wavenumber (α - 2 π ). Thus the exact computational solution for case (b) is also shown.