1 Introduction</h5> The advection–diffusion (or convection–diffusion) equation in flow physics and heat transfer, also known as the drift-diffusion equation in semiconductor physics, is a second-order Partial Differential Equation (PDE) which governs transport phenomena. These processes are encountered in many engineering problems ranging from pollutant dispersal to semi-conductor modeling  . This PDE is also often used as a model problem for the incompressible Navier–Stokes equations. It describes the equilibrium between a transport process by advection, and one by diffusion. The problem it models is often characterized by the Péclet number Pe, which is defined as the ratio of the rate of advection and that of diffusion. In the advection-dominated regime, Pe ≫ 1 , and in the diffusion-dominated regime, Pe ≪ 1 . Many numerical methods have been designed originally for the solution of this PDE, then “upgraded” for the solution of the more challenging Navier–Stokes equations. In particular, the continuous, polynomial Galerkin finite element method has been successfully designed for addressing the diffusion-dominated regime. In the advection-dominated regime characterized by internal or boundary layers, this method delivers numerical solutions that are polluted by spurious oscillations whenever the mesh size is not sufficiently fine to capture the fine
Computer Methods in Applied Mechanics and Engineering – Elsevier
Published: Sep 1, 2013
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