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Field equations for incompressible non-viscous fluids using artificial intelligence

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Abstract

In this article, we introduce new field equations for incompressible non-viscous fluids, which can be treated similarly to Maxwell’s electromagnetic equations based on artificial intelligence algorithms. Lagrangian and Hamiltonian formulations are used to arrive at field equations that are solved using convolutional neural networks. Four linear differential equations, which describe the two fields, namely, the dynamic pressure and the vortex fields, are derived, and these can be used in place of Euler’s equation. The only assumption while deriving this equation is that the dynamic pressure and vortex fields obey the superposition principle. The important finding to be noted is that Euler’s fluid equations can be converted into field equations analogous to Maxwell’s electromagnetic equations. We solve the flow problem for laminar flow past a cylinder, sphere, and cone in two dimensions similar to the conduction in a uniform electric field and arrive at closed-form expressions. These closed-form expressions, which are obtained for the potentials of fluid flow, are similar to the streamline potential functions in the case of fluid dynamics.

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Abbreviations

\(\vec{v}\) :

Velocity

\(\frac{{d\vec{v}}}{dt}\) :

Total differential of velocity

\(p\) :

Pressure

\(\phi\) :

Dynamic pressure potential

\(\vec{\omega }\) :

Vortex field

\(\overrightarrow {J}\) :

Current density

\(\rho\) :

Mass density

\(\overrightarrow {A}\) :

Vortex potential

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Acknowledgements

The authors would like to thank the editor-in-chief, the associate editor, and the reviewers for their insightful comments and suggestions. The author also wishes to thank Prof. E. Poovammal for providing constant guidance and support throughout the making of the article. The author also wishes to thank his brother P.C. Vijay and father P.S. Chandrasekaran for fruitful discussions.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, School of Computing, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Chengalpattu , Tamilnadu, 603203, India

    P. C. Karthik, M. Baskar & E. Poovammal

  2. Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Chengalpattu, Tamilnadu, 603203, India

    J. Sasikumar

  3. Institute of Electronics and Communication Engineering, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai, Tamilnadu, 602105, India

    P. Kalyanasundaram

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  1. P. C. Karthik
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  2. J. Sasikumar
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  3. M. Baskar
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  4. E. Poovammal
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  5. P. Kalyanasundaram
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Correspondence to M. Baskar.

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Karthik, P.C., Sasikumar, J., Baskar, M. et al. Field equations for incompressible non-viscous fluids using artificial intelligence. J Supercomput 78, 852–867 (2022). https://doi.org/10.1007/s11227-021-03917-y

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