Advection diffusion flows arise in multiple areas of science and engineering.
Most numerical methods suffer from unphysical solution features like negative concentration fields when tracking sharp fronts. We developed a positivity-preserving h-adaptive space-time discontinuous Galerkin finite element method to overcome this issue.
The movie file shows how adaptive meshing resulting in an accurate resolution of the front.
A species injected into a converging diverging nozzle with oscillating flow in the background.
The flow characteristics are very distinct depending on the relative strengths of advection and diffusion.
Journal Publication:
Adaptive spacetime discontinuous Galerkin method for hyperbolic advection diffusion with a non-negativity constraint. International Journal for Numerical Methods in Engineering, 2015. R. K. Pal, R. Abedi, A. Madhukar, and R.B. Haber. pdf