@article{BADIA2025118343,
title = {A velocity-vorticity-pressure formulation for the steady Navier–Stokes–Brinkman–Forchheimer problem},
journal = {Comput. Methods in Appl. Mech. Engrg.},
volume = {447},
pages = {118343},
year = {2025},
issn = {0045-7825},
doi = {https://doi.org/10.1016/j.cma.2025.118343},
url = {https://www.sciencedirect.com/science/article/pii/S0045782525006152},
author = {Badia, S. and Carstensen, C. and Martín, A. F. and Ruiz-Baier, R. and Villa-Fuentes, S.},
keywords = {Navier–Stokes–Brinkman–Forchheimer equations, Pressure robustness, Nonconforming finite elements, Banach fixed-point theory, A priori and a posteriori error estimates},
abstract = {The flow of incompressible fluid in highly permeable porous media in vorticity - velocity - Bernoulli pressure form leads to a double saddle-point problem in the Navier–Stokes–Brinkman–Forchheimer equations. The paper establishes, for small sources, the existence of solutions on the continuous and discrete level of lowest-order piecewise divergence-free Crouzeix–Raviart finite elements. The vorticity employs a vector version of the pressure space with normal and tangential velocity jump penalisation terms. A simple Raviart–Thomas interpolant leads to pressure-robust a priori error estimates. An explicit residual-based a posteriori error estimate allows for efficient and reliable a posteriori error control. The efficiency for the Forchheimer nonlinearity requires a novel discrete inequality of independent interest. The implementation is based upon a light-weight forest-of-trees data structure handled by a highly parallel set of adaptive mesh refining algorithms. Numerical simulations reveal robustness of the a posteriori error estimates and improved convergence rates by adaptive mesh-refining.}
}