The Navier-Stokes equations are used to model fluid flow. Examples include fluid structure interactions in the heart, climate and weather modeling, and flow simulations in computer gaming and entertainment. The equations date back to the 1800s, but research and development of numerical approximation algorithms continues to be an active area. To numerically solve the Navier-Stokes equations we implement a least squares finite element algorithm based on work by Roland Glowinski and colleagues. We use the deal.II academic library , the C++ language, and the Linux operating system to implement the solver. We investigate convergence rates and apply the least squares solver to the lid driven cavity problem and discuss results.
K. Daniel Brauss
Lytch, Jada P.; Boatwright, Taylor; and Breeden, Ja'Nya
"Implementation of A Least Squares Method To A Navier-Stokes Solver,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 23:
1, Article 7.
Available at: https://scholar.rose-hulman.edu/rhumj/vol23/iss1/7