TITLE:
The Peculiarity of Numerical Solving the Euler and Navier-Stokes Equations
AUTHORS:
Ludmila Petrova
KEYWORDS:
Solutions of Two Types, Nonintegrable Manifolds and Integrable Structures, Discrete Transitions, Two Different Frames of Reference
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.4 No.4,
September
5,
2014
ABSTRACT: The analysis of integrability of the Euler and Navier-Stokes equations shows that these equations have the solutions of two types: 1) solutions that are defined on the tangent nonintegrable manifold and 2) solutions that are defined on integrable structures (that are realized discretely under the conditions related to some degrees of freedom). Since such solutions are defined on different spatial objects, they cannot be obtained by a continuous numerical simulation of derivatives. To obtain a complete solution of the Euler and Navier-Stokes equations by numerical simulation, it is necessary to use two different frames of reference.