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.