Publication
Very high-order accurate finite volume scheme for the steady-state incompressible Navier-Stokes equations with polygonal meshes on arbitrary curved boundaries
| Summary: | The numerical solution of the incompressible Navier-Stokes equations raises challenging numerical issues on the development of accurate and robust discretisation techniques due to the div-grad duality. Significant advances have been achieved in the context of high-order of convergence methods, but many questions remain unsolved in the quest of practical, accurate, and efficient approaches. In particular, the discretisation of problems with arbitrary curved boundaries has been the subject of intensive research, where the conventional practice consists in employing curved meshes to avoid accuracy deterioration. The present work proposes a novel approach, the reconstruction for off-site data method, which employs polygonal meshes to approximate arbitrary smooth curved boundaries with linear piecewise elements. The Navier-Stokes equations are discretised with a staggered finite volume method, and the numerical fluxes are computed on the polygonal mesh elements. Boundary conditions are taken into account via polynomial reconstructions with specific linear constraints defined for a set of points on the physical boundary. The very-high order of convergence is preserved without relying on the full curve parametrisation, avoiding the limitations of curved mesh approaches, such as sophisticated mesh generation algorithms, cumbersome quadrature rules, and complex non-linear transformations. A comprehensive verification benchmark is provided, with numerical test cases for several fluid flow problems, to demonstrate the capability of the proposed approach to achieve very high-orders of convergence.(c) 2022 Elsevier B.V. All rights reserved. |
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| Main Authors: | Costa, Ricardo Daniel Pereira da |
| Other Authors: | Clain, Stéphane; Machado, Gaspar J.; Nóbrega, J. M. |
| Subject: | Incompressible fluid flows Navier-Stokes equations Arbitrary curved boundaries Reconstruction for off-site data method Very high-order of convergence Staggered polygonal meshes |
| Year: | 2022 |
| Country: | Portugal |
| Document type: | article |
| Access type: | restricted access |
| Associated institution: | Universidade do Minho |
| Language: | English |
| Origin: | RepositóriUM - Universidade do Minho |
| Summary: | The numerical solution of the incompressible Navier-Stokes equations raises challenging numerical issues on the development of accurate and robust discretisation techniques due to the div-grad duality. Significant advances have been achieved in the context of high-order of convergence methods, but many questions remain unsolved in the quest of practical, accurate, and efficient approaches. In particular, the discretisation of problems with arbitrary curved boundaries has been the subject of intensive research, where the conventional practice consists in employing curved meshes to avoid accuracy deterioration. The present work proposes a novel approach, the reconstruction for off-site data method, which employs polygonal meshes to approximate arbitrary smooth curved boundaries with linear piecewise elements. The Navier-Stokes equations are discretised with a staggered finite volume method, and the numerical fluxes are computed on the polygonal mesh elements. Boundary conditions are taken into account via polynomial reconstructions with specific linear constraints defined for a set of points on the physical boundary. The very-high order of convergence is preserved without relying on the full curve parametrisation, avoiding the limitations of curved mesh approaches, such as sophisticated mesh generation algorithms, cumbersome quadrature rules, and complex non-linear transformations. A comprehensive verification benchmark is provided, with numerical test cases for several fluid flow problems, to demonstrate the capability of the proposed approach to achieve very high-orders of convergence.(c) 2022 Elsevier B.V. All rights reserved. |
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