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

DOI: 10.4236/ajcm.2014.44026   PDF   HTML     2,749 Downloads   3,135 Views   Citations

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.

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Petrova, L. (2014) The Peculiarity of Numerical Solving the Euler and Navier-Stokes Equations. American Journal of Computational Mathematics, 4, 304-310. doi: 10.4236/ajcm.2014.44026.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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[2] Petrova, L.I. (2009) Relationships between Discontinuities of Derivatives on Characteristics and Trajectories. Computational Mathematics and Modeling, 20, 367-372. http://dx.doi.org/10.1007/s10598-009-9043-0
[3] Smirnov, V.I. (1957) A Course of Higher Mathematics. Moscow, Tech. Theor. Lit., 4.
[4] Petrova, L.I. (2010) Role of Skew-Symmetric Differential Forms in Mathematics.
http://arxiv.org/abs/1007.4757

  
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