Diffusion Wave Model

Another simplified distributed routing model, known as the diffusion wave (zero inertia) model, is based on Eq. (1) along with an approximation of the momentum equation that retains only the last two terms in Eq. (2), i.e.,

Finite-difference approximation techniques, both explicit and implicit (Strelkoff and Katopodes, 1977), have been used to obtain simultaneous solutions to Eqs. (1) and (27). The diffusion-simplified routing model considers backwater effects; however, its accuracy is deficient for very fast rising hydographs, such as those resulting from dam failures, hurricane storm surges, or rapid reservoir releases, which propagate through mild to flat sloping waterways with medium to small Manning's n. The range of application (with expected modeling errors less than 5%) for the diffusion models, including the Muskingum-Cunge model, is given by the following (Fread, 1992):

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