Solutions of the Navier-Stokes equations by group methods
Abstract
Using the machinery of Lie theory (groups and algebras) applied to the Navier-Stokes equations a number of exact solutions for the steady state are derived in (two) three dimensions. It is then shown how each of these generates an infinite number of time dependent solutions via (three) four arbitrary functions of time. This algebraic structure also provides the mechanism to search for other solutions since its character is inferred from the basic equations.
- Publication:
-
IN: World Congress on System Simulation and Scientific Computation
- Pub Date:
- 1983
- Bibcode:
- 1983sssc....3...31B
- Keywords:
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- Computational Fluid Dynamics;
- Lie Groups;
- Navier-Stokes Equation;
- Steady Flow;
- Algebra;
- Three Dimensional Flow;
- Time Dependence;
- Two Dimensional Flow;
- Fluid Mechanics and Heat Transfer