Numerical results for advection-dominated heat transfer in a moving fluid with a non-slip boundary condition

This paper is concerned with the laminar transfer of heat by forced convection where the velocity profile is taken to be parabolic. In the advection dominated case the problem is described mathematically by a singularly perturbed boundary value problem with a non-slip condition. It has been established both theoretically and computationally that numerical methods composed of upwind finite difference operators on special piecewise uniform meshes have the property that they behave uniformly well, regardless of the magnitude of the ratio of the advection term to the diffusion term. A variety of choices of special piecewise uniform mesh is examined and it is shown computationally that these lead to numerical methods also sharing this property. These results validate a previous theoretical result which is quoted.