Matlab代写 - MAE 376 Lab 5
2020-11-24
This problem emphasizes the importance of the choice of finite-difference rules when discretizing differential equations. Consider an example of the classical convection-diffusion transport equation, which
describes the transport of a fluid due to convection and diffusion:
νu00 0 au0 + 1 = 0, x ∈ [0, 1], u(0) = 0, u(1) = 0
Depending on the so-called Peclet number P e = a∆x 2ν
, where ∆x is the spacing between nodes in the
finite difference approximation, we can get spurious behavior in the numerical solution if we use a central
difference method for the convection (first-order derivative) term. In particular, if P e > 1 (convectiondominated), then a different scheme should be used.