A single-node characteristic collocation method for unsteady-state convection-diffusion equations in three-dimensional spaces

We develop a nonconventional single-node characteristic collocation method with piecewise-cubic Hermite polynomials for the numerical simulation to unsteady-state advection-diffusion transport partial differential equations. This method greatly reduces the number of unknowns in the conventional collocation method, and generates accurate numerical solutions even if very large time steps are taken. The reduction of number of nodes has great potential for problems defined on high space dimensions, which appears in such problems as quantification of uncertainties in subsurface porous media. The method developed here is easy to formulate. Numerical experiments are presented to show the strong potential of the method. © 2009 Wiley Periodicals, Inc