Abstract
In this work we propose a novel Hybrid High-Order method for the incompressible Navier–Stokes equations based on a formulation of the convective term including Temam's device for stability. The proposed method has several advantageous features: it supports arbitrary approximation orders on general meshes including polyhedral elements and non-matching interfaces; it is inf-sup stable; it is locally conservative; it supports both the weak and strong enforcement of velocity boundary conditions; it is amenable to efficient computer implementations where a large subset of the unknowns is eliminated by solving local problems inside each element. Particular care is devoted to the design of the convective trilinear form, which mimicks at the discrete level the non-dissipation property of the continuous one. The possibility to add a convective stabilisation term is also contemplated, and a formulation covering various classical options is discussed. The proposed method is theoretically analysed, and an energy error estimate in hk+1 (with h denoting the meshsize) is proved under the usual data smallness assumption. A thorough numerical validation on two and three-dimensional test cases is provided both to confirm the theoretical convergence rates and to assess the method in more physical configurations (including, in particular, the well-known two- and three-dimensional lid-driven cavity problems).
| Language | English |
|---|---|
| Pages | 786-816 |
| Number of pages | 31 |
| Journal | Journal of Computational Physics |
| Volume | 376 |
| DOIs | |
| Publication status | Published - 1 Jan 2019 |
Keywords
- A priori error estimate
- Hybrid High-Order methods
- Incompressible Navier–Stokes equations
- Polyhedral element methods
Cite this
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A Hybrid High-Order method for the incompressible Navier–Stokes equations based on Temam's device. / Botti, Lorenzo; Di Pietro, Daniele A.; Droniou, Jérôme.
In: Journal of Computational Physics, Vol. 376, 01.01.2019, p. 786-816.Research output: Contribution to journal › Article › Research › peer-review
TY - JOUR
T1 - A Hybrid High-Order method for the incompressible Navier–Stokes equations based on Temam's device
AU - Botti, Lorenzo
AU - Di Pietro, Daniele A.
AU - Droniou, Jérôme
PY - 2019/1/1
Y1 - 2019/1/1
N2 - In this work we propose a novel Hybrid High-Order method for the incompressible Navier–Stokes equations based on a formulation of the convective term including Temam's device for stability. The proposed method has several advantageous features: it supports arbitrary approximation orders on general meshes including polyhedral elements and non-matching interfaces; it is inf-sup stable; it is locally conservative; it supports both the weak and strong enforcement of velocity boundary conditions; it is amenable to efficient computer implementations where a large subset of the unknowns is eliminated by solving local problems inside each element. Particular care is devoted to the design of the convective trilinear form, which mimicks at the discrete level the non-dissipation property of the continuous one. The possibility to add a convective stabilisation term is also contemplated, and a formulation covering various classical options is discussed. The proposed method is theoretically analysed, and an energy error estimate in hk+1 (with h denoting the meshsize) is proved under the usual data smallness assumption. A thorough numerical validation on two and three-dimensional test cases is provided both to confirm the theoretical convergence rates and to assess the method in more physical configurations (including, in particular, the well-known two- and three-dimensional lid-driven cavity problems).
AB - In this work we propose a novel Hybrid High-Order method for the incompressible Navier–Stokes equations based on a formulation of the convective term including Temam's device for stability. The proposed method has several advantageous features: it supports arbitrary approximation orders on general meshes including polyhedral elements and non-matching interfaces; it is inf-sup stable; it is locally conservative; it supports both the weak and strong enforcement of velocity boundary conditions; it is amenable to efficient computer implementations where a large subset of the unknowns is eliminated by solving local problems inside each element. Particular care is devoted to the design of the convective trilinear form, which mimicks at the discrete level the non-dissipation property of the continuous one. The possibility to add a convective stabilisation term is also contemplated, and a formulation covering various classical options is discussed. The proposed method is theoretically analysed, and an energy error estimate in hk+1 (with h denoting the meshsize) is proved under the usual data smallness assumption. A thorough numerical validation on two and three-dimensional test cases is provided both to confirm the theoretical convergence rates and to assess the method in more physical configurations (including, in particular, the well-known two- and three-dimensional lid-driven cavity problems).
KW - A priori error estimate
KW - Hybrid High-Order methods
KW - Incompressible Navier–Stokes equations
KW - Polyhedral element methods
UR - http://www.scopus.com/inward/record.url?scp=85054870631&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2018.10.014
DO - 10.1016/j.jcp.2018.10.014
M3 - Article
VL - 376
SP - 786
EP - 816
JO - Journal of Computational Physics
T2 - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
ER -