The discretization error analysis for simulation of transient flow in a water reservoir

Resumo

The study of hydrodynamic and transport models that focus on their behavior and onexamining the results obtained with numerical and computational simulations seeks to ensurethe best performance in the analysis and decision-making process for real problems, such asthe dispersion of pollutants in two-dimensional (2D) transient flows in reservoirs and floodedregions with slopes and subject to resistance. Obtaining accurate and reliable numericalsolutions from models that involve interaction between advective and diffusive processes isa matter of great relevance due to the difficulties commonly experienced in solving thesemodels, but which can be reduced or eliminated by knowing the behavior of the solution andnumerical data, thus helping to understand the flow and dispersion patterns. This work presentsa simulation of a shallow water hydrodynamic model by means of a numerical solution thatuses the finite volume method (FVM) with a hybrid approximation scheme (central/upwind)for discretizing the advective-diffusive terms. A priori and a posteriori error analysis wereperformed to estimate discretization errors. The implemented code allows a temporal analysisof the level, volume, and flow in reservoirs that have devices at their outlets. An adequategraphical and numerical interpretation of the physical phenomenon studied was obtained witha high level of accuracy and a stable solution with low computational cost.