I want to solve the following set of coupled advection-diffusion equations: $$ \frac{\partial f}{\partial t}=\nabla\cdot(\kappa\nabla f)+\nabla\cdot(\boldsymbol{u}f)+s_f(g), $$ $$ \frac{\partial g}{\partial t}=\nabla\cdot(\kappa\nabla g)+\nabla\cdot(\boldsymbol{u}g)+s_g(f), $$ in polar coordinates $(r,\theta)$. Using finite elements is natural in that case. However, to help for stability and computation time, I would like to have a grid equally spaced in $\cos\theta$ and the zeros of Chebyshev polynomials for $r$. I never tried using finite volume methods so I am a bit unsure of what I am doing. My question is this: what is the best way to go about this? Can I simply use Chebyshev interpolation and derivation for values on volume faces? Or can I solve the system for the Chebyshev coefficients instead? I plan to use a fully explicit time stepping scheme (probably Runge-Kutta second order)



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.