1. A pressure-robust HHO method for the solution of the incompressible Navier–Stokes equations on general meshes.
- Author
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Quiroz, Daniel Castanon and Pietro, Daniele A Di
- Abstract
In a recent work (Castanon Quiroz & Di Pietro (2020) A hybrid high-order method for the incompressible Navier–Stokes problem robust for large irrotational body forces. Comput. Math. Appl. , 79 , 2655–2677), we have introduced a pressure-robust hybrid high-order method for the numerical solution of the incompressible Navier–Stokes equations on matching simplicial meshes. Pressure-robust methods are characterized by error estimates for the velocity that are fully independent of the pressure. A crucial question was left open in that work, namely whether the proposed construction could be extended to general polytopal meshes. In this paper, we provide a positive answer to this question. Specifically, we introduce a novel divergence-preserving velocity reconstruction that hinges on the solution inside each element of a mixed problem on a subtriangulation, then use it to design discretizations of the body force and convective terms that lead to pressure robustness. An in-depth theoretical study of the properties of this velocity reconstruction, and their reverberation on the scheme, is carried out for arbitrary polynomial degrees |$k\geq 0$| and meshes composed of general polytopes. The theoretical convergence estimates and the pressure robustness of the method are confirmed by an extensive panel of numerical examples. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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