Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

A Mathematical Interpretation and Validation of the Streamline's Shape Theory for Inviscid-Incompressible Flows & Viscid-Compressible Flows of the Newtonian Fluids

Version 1 : Received: 9 December 2020 / Approved: 10 December 2020 / Online: 10 December 2020 (13:06:39 CET)

How to cite: George, Y. A Mathematical Interpretation and Validation of the Streamline's Shape Theory for Inviscid-Incompressible Flows & Viscid-Compressible Flows of the Newtonian Fluids. Preprints 2020, 2020120262 (doi: 10.20944/preprints202012.0262.v1). George, Y. A Mathematical Interpretation and Validation of the Streamline's Shape Theory for Inviscid-Incompressible Flows & Viscid-Compressible Flows of the Newtonian Fluids. Preprints 2020, 2020120262 (doi: 10.20944/preprints202012.0262.v1).

Abstract

This article objectively assesses, the hypothesis of the streamline's shape theory and its formulated equation. The deduction of proof uses algebra rather than first-order partial differential equations to address the specific hypothesis of "Streamline's shape theory" from the fundamental perspective of applied mathematics and scientifically derives mathematical relations of the axioms and corollaries in the field of fluid dynamics. The algebraic methods employed provide progressively more distinct and precise solutions compared to first-order partial differential equations. The foremost objective of this work is to evaluate if the formulations of the streamline's shape theory can have solutions for inviscid-incompressible and viscid-compressible flows of Newtonian fluids and to identify their nature. Secondly, to understand how the topology of the body and the free-stream conditions affect these solutions with due regards to the shape and size of the body interacting with the fluid flow. Finally, to explore the possibility of this theory to develop a CFD solver for streamline simulation to reduce the experimentation in the analysis of flow-structure interactions of Newtonian fluids and also to identify its scope of applications and limitations.

Supplementary and Associated Material

Subject Areas

Fluid-Structure interactions; Topological fluid dynamics; General fluid mechanics; Mathematical fluid dynamics; Applied mathematics

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