Resolution of the Computational Diffusion Hydrodynamic Model into Partial Differential Equation Form

Computational modeling continues to evolve in applications of hydrology and hydraulics, and the field of Computational Hydrology and Hydraulics has grown into a significant technology in both engineering and computational mathematics. In this paper, the fundamental issue of assessment of computational error is addressed by determination of an “equivalent” mathematical statement, as a partial differential equation (“PDE”) that describes the original mathematical PDE statement and computational solution of it. In other words, given that the computational model does not exactly solve the governing PDE and that the computational processes used to approximate the governing PDE further moves the computational outcome away from the exact solution, what “alternate” or “equivalent” PDE does the resulting computational model exactly solve? In this paper it is shown that development of such an equivalent PDE enables an assessment of computational error by direct comparison of the equivalent PDE to the original PDE targeted to being solved. As an example, the USGS Diffusion Hydrodynamic Model (“DHM”) is examined as to development of an equivalent PDE that describes the DHM computational modeling outcome, which is then compared to the actual outcomes resulting from application of the DHM model.