The numerical treatment of the NavierStokes equations
Abstract
The numerical calculation of the approximate solutions for flow velocity and pressure of the NavierStokes equations describing the time evolution of a viscous flow are treated. A method for the construction of approximate solutions for the equations in the case of conservative external forces (F=0) was developed. It allows to approximate equations using socalled particle methods; the solutions have a high degree of regularity; convergence predictions are demonstrated. A difference method, based on the Rothe method which takes into account external forces (F not = 0) and a general threedimensional flow was developed. Approximation theory, stability and convergence analysis, and numerical tests are presented. Examples for which the exact solutions are known were calculated showing agreement within 2% with the exact solutions.
 Publication:

Ph.D. Thesis
 Pub Date:
 1985
 Bibcode:
 1985PhDT.........9V
 Keywords:

 Finite Difference Theory;
 Flow Velocity;
 Fluid Pressure;
 NavierStokes Equation;
 Viscous Flow;
 Convergence;
 Flow Stability;
 Three Dimensional Flow;
 Fluid Mechanics and Heat Transfer