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On the Mathematical Analysis and Physical Implications of the Principle of Minimum Pressure Gradient
Haithem Taha
In this paper, we establish a two-way equivalence between the incompressible Navier- Stokes equation (INSE) and the principle of minimum pressure gradient (PMPG). We prove that a c…
Variational Projection of Navier-Stokes: Fluid Mechanics as a Quadratic Programming Problem
Haithem Taha, Kshitij Anand
Gauss's principle of least constraint transforms a dynamics problem into a pure minimization problem, where the total magnitude of the constraint force is the cost function, minimi…
On the Separating Flow Behind a Cylinder: Insights from the Principle of Minimum Pressure Gradient
Mohamed Shorbagy, Haithem Taha
We study the separating flow over a circular cylinder with two objectives: (i) to demonstrate the validity of the condition of matching curvature, and (ii) to obtain a reasonable e…
Minimizing Nature's Cost: Exploring Data-Free Physics-Informed Neural Network Solvers for Fluid Mechanics Applications
Abdelrahman Elmaradny, Ahmed Atallah, Haithem Taha
In this paper, we present a novel approach for fluid dynamic simulations by harnessing the capabilities of Physics-Informed Neural Networks (PINNs) guided by the newly unveiled pri…