Alternating direction implicit method with exponential upwinding

We consider a two-dimensional diffusive transport model with convection. This model is studied numerically using an alternating direction implicit (ADI) method with exponential upwinding. It is known that the exponential upwinding technique can perform really well on one-dimensional steady transport problems. So, we are interested to find out how good exponential upwinding will be on a two-dimensional problem when coupled to locally one-dimensional methods, i.e., ADI methods. Our numerical simulations show that an ADI method with exponential upwinding can be a very useful method even in two dimensions. Especially, when there are no systematic ways of choosing the upwinding parameters in the conventional upwinding methods, one can confidently employ an ADI method with exponential upwinding on a convection dominated diffusion problem and expect good answers