A result of existence and uniqueness for a cavity driven flow. Analytical expression of the solution

TL;DR

This paper proves the existence and uniqueness of a steady cavity-driven flow using an analytical approach, providing explicit solutions and examples, including a shear-forced flow with eddies, typically obtained numerically.

Contribution

It introduces an analytical method to derive explicit solutions for cavity-driven flows, demonstrating existence and uniqueness with elementary mathematical techniques.

Findings

Explicit symbolic solutions for cavity flows.

Illustration of shear-forced flow with eddies.

Analytical approach replaces numerical methods.

Abstract

In this work a result of existence and uniqueness for a plane cavity driven steady flow is deduced using an analytical method for the resolution of a linear partial differential problem on a triangular domain. The solution admits a symbolic expression based on integration over the domain. Some examples of flow are computed and graphed. In particular, it is shown a realistic example of a shear-forced flow with two eddies, usually computed only by numerical methods. The mathematical techniques used for the demonstration of the main result are elementary.