A new unconditionally stable and consistent quasi‐analytical in‐stream water quality solution scheme for CSTR‐based water quality simulators. Issue 6 (9th June 2017) - Woldegiorgis, Befekadu Taddesse; van Griensven, Ann; Pereira, Fernando; Bauwens, Willy
Abstract: Most common numerical solutions used in CSTR‐based in‐stream water quality simulators are susceptible to instabilities and/or solution inconsistencies. Usually, they cope with instability problems by adopting computationally expensive small time steps. However, some simulators use fixed computation time steps and hence do not have the flexibility to do so. This paper presents a novel quasi‐analytical solution for CSTR‐based water quality simulators of an unsteady system. The robustness of the new method is compared with the commonly used fourth‐order Runge‐Kutta methods, the Euler method and three versions of the SWAT model (SWAT2012, SWAT‐TCEQ, and ESWAT). The performance of each method is tested for different hypothetical experiments. Besides the hypothetical data, a real case study is used for comparison. The growth factors we derived as stability measures for the different methods and the R ‐factor—considered as a consistency measure—turned out to be very useful for determining the most robust method. The new method outperformed all the numerical methods used in the hypothetical comparisons. The application for the Zenne River (Belgium) shows that the new method provides stable and consistent BOD simulations whereas the SWAT2012 model is shown to be unstable for the standard daily computation time step. The new method unconditionally simulates robust solutions. Therefore, it is a reliable scheme for CSTR‐based water quality simulators that use first‐order reaction formulations. Key Points: The new quasi‐analytical solution method is unconditionally stable and its precision is unaffected by the size of the computation time step The new method is superior to the high order numerical schemes used in CSTR‐based water quality simulators The growth factor and the R ‐factor are good indicators of the stability and consistency of numerical solutions