We are pleased to share a new publication from the Fluid Mechanics Laboratory:

“Analytical solution of the Stokes flow using the implicit potential method for the velocity-pressure coupling: Application to the lid-driven cavity flow”

by Emmanouil Kostas, Panayiotis Vafeas and Polycarpos K. Papadopoulos, now avaiable online in Applied Mathematics and Computation, Volume 533 (2027), Article 130308.

Understanding how velocity and pressure interact lies at the heart of fluid mechanics. In this work, we develop an analytical approach for the incompressible Stokes equations using the Implicit POTential (IPOT) method, providing an explicit treatment of the velocity–pressure coupling through a series representation of pressure variations.

The method is applied to the two-dimensional lid-driven cavity flow—a fundamental benchmark that continues to challenge and inspire the development of new computational and analytical techniques. Through separation of variables and Fourier-series expansions, the study derives the velocity and pressure fields and investigates their convergence as the number of retained modes increases.

The analytical predictions are compared with OpenFOAM simulations, showing close agreement and demonstrating the potential of the approach as an accurate and efficient tool for incompressible-flow analysis. Beyond this benchmark problem, the work opens promising directions for analytical and semi-analytical modelling of flows in which pressure–velocity coupling plays a decisive role.

Read the paper: https://doi.org/10.1016/j.amc.2026.130308