Coordinate Transformation Approach for Numerical Solution of Environmental Problems

We consider numerical solution of 1D and 2D advection-diffusion equations that arise, among others, in environmental modeling. Since the problems are posed on the unbounded domains we use coordinate transformations to confine the computational region. Well-posedness of the new problems and properties of the solution are studied. Finite volume difference schemes (FVDS) are discussed. Positive splitting numerical method is proposed.