Graduate Thesis Or Dissertation
 

A predictor-corrector method for the transient motion of a nonhomogeneous incompressible, viscous fluid

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  • The system of partial differential equations which governs the motion of a Newtonian fluid has been known for over a century. Yet, due to the complexity of the equations, an analytical solution is known only for a few simple geometries or a few special cases such as very slow motion. No general analytical solution is known. The development of the digital computer has led to sophisticated numerical techniques for solving systems of partial differential equations. This paper develops a predictor- corrector numerical method which solves simultaneously the Navier- Stokes equation, the continuity equation, the incompressibility equation and the energy equation - -first law of thermodynamics - -for a nonhomogeneous, viscous fluid. As an example of the potential of this method, the problem of finding the transient flow from a density stratified reservoir is solved. In addition a FORTRAN IV listing for this problem is included.
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