WAF Method and Splitting Procedure for Simulating Hydro- and Thermal-Peaking Waves in Open-Channel Flows

Hydro- and thermal-peaking waves, generated by hydroelectric power generation, have a strong impact on the ecological integrity of aquatic ecosystems. In order to reduce such effects, mitigation procedure must be studied and implemented. To this end a one-dimensional model which solves the coupling of hydrodynamics with heat transport is developed. The solution is obtained advancing simultaneously the hydrodynamic and thermal module with the same accuracy. For the numerical solution of the governing advection-reaction/diffusion problem a splitting procedure is adopted: the advection-reaction part is solved by means of the weight average flux (WAF) finite volume explicit method, while the diffusion part is solved using a nonlinear version of the implicit Crank-Nicolson method. The WAF method is extended to second-order in the presence of reaction terms. Numerical results are presented for different test examples, which demonstrate the accuracy and robustness of the scheme and its applicability in predicting temperature transport by shallow water flows. Application to the Adige River (Northern Italy) of this framework proves that the model is an effective tool for designing hydro- and thermal-peaking waves mitigation procedures.