Numerical Solution of the Navier-Stokes Equations for the Entrance Region of Suddenly Accelerated Parallel Plates, 1967

(1967) Numerical Solution of the Navier-Stokes Equations for the Entrance Region of Suddenly Accelerated Parallel Plates, 1967. Iowa State University

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Abstract

The difficulties associated with the mathematical solution of the hydrodynamic equations for a viscous fluid are such that in the two hundred fifty years since these equations were first derived, only a very small number of particular cases have been solved exactly. This is true despite the fact that many great mathematicians have studied the problem. The development of fast digital computers in the middle 1950's made the numerical methods much more feasible and a number of studies have been reported. This dissertation reviews several of these investigations and describes a new study of the time dependent Navier-Stokes equations by numerical techniques. The particular example considered is the unsteady laminar flow of a viscous fluid in the inlet section between two semi-infinite parallel plates. Results are compared with other available data.