Desenvolvimento de um modelo hidráulico computacional para o Complexo Estuarino de São Marcos (CESM) - Maranhão

Abstract

This work describes the numerical solution applied to the Navier-Stokes and Continuity equations when developing a computational model, using the FORTRAN language, to simulate the hydraulics of São Marcos Estuarine Complex (SMEC). The computational model governing equations were explicitly discretized using the finite difference method (FDM) and were divided into the spatial and temporal domains. In the spatial domain, the Leonard were employed to solve the advective terms and Smagorinsky schemes to estimate the horizontal diffusion coefficient. In the temporal domain, the Matsuno scheme were implemented to solve the local variation term at velocity field and free surface elevation and the Asselin filter to reduce the noise caused by numerical integrations. Two free surface oscillation time series were used as boundary conditions along the numerical grid northern boundary to simulate the free surface disturbance caused by the tide variation, obtained from the TPXO 6.2 model, and the zonal contribution of the velocity field related to the Northern Brazil Current (NBC) and the meridional contribution of the velocity field associated with the mean discharge of Mearim river was used as forcing at the southern boundary. The Berkhoff experiment was reproduced to test the numerical solution proposed here, simulating in a satisfactory way the wave propagation at the shoal in a confined area. The simulation of the SMEC hydraulics using the numerical solution proposed was validated and adjusted using a time series of high and low tide measurements collected within the harbor complex during January 1–11 2015. The measurements confirmed the skill of the computational model developed here in simulating the harbor complex region hydraulics and the occurrence of periodic inversions in the velocity field along the SMEC margins caused by potential vorticity.