A Three-Dimensional Environmental Fluid Dynamics Computer Code : Theoretical and computational aspects

This report describes and documents the theoretical and computational aspects of a three-dimensional computer code for environmental fluid flows. The code solves the three-dimensional primitive variable v1ertically hydrostatic equations of motion for turbulent flow in a coordinate system which is curvilinear and orthogonal in the horizontal plane and stretched to follow bottom topography and free surface displacement in the vertical direction which is aligned with the gravitational vector. A second moment turbulence closure scheme relates turbulent viscosity and diffusivity to the turbulence intensity and a turbulence length scale. Transport equations for the turbulence intensity and length scale as well as transport equations for and a dye tracer are also to pressure, salinity, concentration. salinity, temperature, suspended sediment solved. An equation of state relates density temperature and suspended sediment The computational scheme utilizes an external-internal mode splitting to solve the horizontal momentum equations and the continuity equation on a staggered grid. The external mode, associated with barotropic long wave motion, is solved using a semiimplicit three time level scheme with a periodic two time level correction. A multi-c:olor successive over relaxation scheme is used to solve the resulting system of equations for the free surface displacement. The internal mode, associated with vertical shear of the horizontal velocity components is solved using a fractional step scheme combining an implicit step for the vertical shear terms, with an explicit step for all other terms. The transport equations for the turbulence intensity, turbulence length scale, salinity, temperature, suspended sediment and dye tracer are also solved using a fractional step scheme with implicit vertical diffusion and explicit advection and horizontal diffusion. A number of alternate advection schemes are implemented in th1e code.

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