Research On Three Dimension Baroclinic Flow Numerical Model In Estuarine And Coastal Waters

The developments for 3-D flow numerical model are reviewed. Based on the equations of shallow water flow, 2-D and 3-D hydrodynamic models are established for estuarine and coastal waters by the use of Crank-Nicholson type of time averaging θ -method and predictor-corrector scheme in this dissertation. Moreover, the models are applied to numerical test in ideal topography and to current simulation of actual coastal waters. The main contents are as follows:1. The Crank-Nicholson type of time averaging implicit scheme, i.e., semi-implicit finite difference scheme, and predictor-corrector scheme are applied to the numerical solution of three-dimensional baroclinic flow model, which based on horizontal orthogonal curvilinear coordinate and on vertical single sigma coordinate. The Courant-Friedrich-Lewy (CFL) stability condition and inertial stability condition are avoided by above schemes. They make the numerical model stable, fast and accurate, so that the numerical model is more convenient to be applied in practical application.2. A new double sigma coordinates is introduced to keep the virtues of sigma coordinate in the vertical direction. The double sigma coordinates separate the simulation domain to upper and lower sigma domains. This dissertation presents a three-dimensional baroclinic and turbulence closure flow numerical model using horizontal orthogonal curvilinear coordinate and vertical double sigma coordinates system. The partitioned coefficient matrices neighboring the interface of upper and lower sigma domains are modified and are reconsolidated a linear, symmetric and positive definite five-diagonal system. Thus the existence and uniqueness of the numerical solution are assured. All prognostic variables are obtained through solving above linear system.3. Without loss of generality and based on the vertically two-dimensional topography following coordinate system, the density Jacobian formulation of horizontal pressure gradient force in both analytical and discrete forms are derived. The discrete analog of the Jacobian is the second-order central difference scheme. The truncation error of density Jacobian over vertical every single cell is estimated by substituting Taylor series expansion of buoyancy field into the finite difference...