The Peculiarity of Numerical Solving the Euler and Navier-Stokes Equations

• 作者: Ludmila Petrova
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: Solutions of TWO Types Nonintegrable MANIFOLDS and INTEGRABLE Structures Discrete TRANSITIONS TWO Different Frames of Reference
• 年，卷（期）: mgjssxqkyw_2014,（4）
• 页码范围: 304-310
• 页数: 7页
• 分类号: O1

摘要

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.