One-Dimensional Surrogate Models for Advection-Diffusion Problems

Numerical solution of partial differential equations can be made more tractable by model reduction techniques. For instance, when the problem at hand presents a main direction of the dynamics (such as blood flow in arteries), it may be conveniently reduced to a 1D model. Here we compare two strategies to obtain this model reduction, applied to classical advection-diffusion equations in domains where one dimension dominates the others.