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arXiv · 2409.07037

A Reynolds-semi-robust and pressure robust Hybrid High-Order method for the time dependent incompressible Navier--Stokes equations on general meshes

Daniel Castanon Quiroz·Daniele A. Di Pietro
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Abstract

In this work we develop and analyze a Reynolds-semi-robust and pressure-robust Hybrid High-Order (HHO) discretization of the incompressible Navier--Stokes equations. Reynolds-semi-robustness refers to the fact that, under suitable regularity assumptions, the right-hand side of the velocity error estimate does not depend on the inverse of the viscosity. This property is obtained here through a penalty term which involves a subtle projection of the convective term on a subgrid space constructed element by element. The estimated convergence order for the $L^\infty(L^2)$- and $L^2(\text{energy})$-norm of the velocity is $h^{k+\frac12}$, which matches the best results for continuous and discontinuous Galerkin methods and corresponds to the one expected for HHO methods in convection-dominated regimes. Two-dimensional numerical results on a variety of polygonal meshes complete the exposition.

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Daniel Castanon Quiroz, Daniele A. Di Pietro. 2024-09-11. A Reynolds-semi-robust and pressure robust Hybrid High-Order method for the time dependent incompressible Navier--Stokes equations on general meshes. https://arxiv.org/abs/2409.07037

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