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Journal Articles IMA Journal of Numerical Analysis Year : 2023

A pressure-robust HHO method for the solution of the incompressible Navier-Stokes equations on general meshes

Abstract

In a recent work [11], 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 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.
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Dates and versions

hal-03608248 , version 1 (14-03-2022)
hal-03608248 , version 2 (11-10-2022)

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Daniel Castanon Quiroz, Daniele Di Pietro. A pressure-robust HHO method for the solution of the incompressible Navier-Stokes equations on general meshes. IMA Journal of Numerical Analysis, 2023, 44 (1), pp.397-434. ⟨10.1093/imanum/drad007⟩. ⟨hal-03608248v2⟩
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