# Questions tagged [advection-diffusion]

Questions related to solving the advection-diffusion equation using numerical methods, including derivation and implementation of boundary conditions.

9 questions
Filter by
Sorted by
Tagged with
2k views

### Does the finite element method impose any restrictions on the Peclet number for numerical stability?

Background on finite volume method When discretising the flux with a central difference stencil of the the advection-diffusion equation restriction $\frac{ah}{d} < 2$ must be observed for the ...
1k views

### BDF vs implicit Runge Kutta time stepping

Are there any reasons for why one should choose high order implicit Runge Kutta (IMRK) over BDF time stepping? BDF seems much easier to me as $q$ stage IMRK needs $q$ linear solves per time step. ...
687 views

Following Hundsdorfer approach the finite volume discretisation of the advection-diffusion equation (conservative form) on non-uniform cell centered grid can be written as, $$w_j^{\prime} = \frac{w_{... 2answers 1k views ### Finite-volume method: can Dirichlet boundary conditions be applied to the integral form? I would like to apply Dirichlet conditions to the advection-diffusion equation using the finite-volume method. This answer, "How should boundary conditions be applied when using finite-volume method?" ... 1answer 853 views ### How do you debug numerical code, what could be source of this oscillatory error? Quiet a lot of insight can be gained form experience, I was just wondering if anybody has seen something similar to this before. The plot shows the initial condition (green) for the advection-... 3answers 762 views ### What are the basic principles behind generating a moving mesh? I am interested in implementing an moving mesh for an advection-diffusion problem. Adaptive Moving Mesh Methods gives a good example of how to do this for Burger's equation in 1D using finite-... 2answers 1k views ### Does the time-dependent advection-diffusion equation have an analytical solution? The advection-diffusion problem, where 0<x<1,$$u_t = (-au + du_x)_x$$with Dirichlet boundary conditions,  u(0)=1,~u(1)=0  , has the steady-state solution,$$ u(x) = \frac{e^{\lambda} - ...
I'm looking at the analytical solution of the convection-diffusion equation $$\frac{\partial C}{\partial t} = D\frac{\partial ^2 C}{\partial x^2}-v\frac{\partial C}{\partial x}$$ with initial ...