Advection Diffusion
- Write the general PDE for an advection-diffusion problem
- For $\phi_t + u\phi_x$ with positive $u$, what direction does the wave travel (right or left)?
- What is the equation for the Pectlet number?
- How is it related to a Reynolds number?
- What is the Pe in terms of advection and diffusion rates?
- What is the value of the Pe (positive or negative) that results in unphysical behavior when using central differences or linear interpolation to evaluate terms?
- Why is using a central difference (or linear interpolation) not ideal for treating advective terms in advection-diffusion problems?
- How can this be remedied?
- How is a face value of a transported variable like $\phi$ evaluated using an upwind method with $u>0$?
- What is the spatial order of an upwind method for treating an advective term?
