Nonparametric solution of the Euler equations for steady flow
Abstract
A theory is presented for formulating wellposed boundary value problems for the Euler equations for steady rotational flow. It is shown that the Euler equations of motion are equivalent to a variational principle, which is used to define a finite difference scheme for numerically solving the Euler equations. The principle is extended to MHD problems in terms of a potential energy of a perfectly conducting plasma having a minimum number of stable configurations. The flow around a cylinder is considered, noting that timeindependent solutions of the Euler equations can be used to provide limits to solutions of the NavierStokes equations. A sample is worked out in terms of the motion of vortices inside a circle.
 Publication:

Communications in Pure Applied Mathematics
 Pub Date:
 July 1983
 Bibcode:
 1983CPAM...36..529G
 Keywords:

 Computational Fluid Dynamics;
 Euler Equations Of Motion;
 Rotating Fluids;
 Steady Flow;
 Vortices;
 Boundary Value Problems;
 Convergence;
 Flow Theory;
 Iterative Solution;
 Variational Principles;
 Fluid Mechanics and Heat Transfer