Two-dimensional compact-finite-difference schemes for solving the bi-Laplacian operator with homogeneous wall-normal derivatives
[EN] In fluid mechanics, the bi-Laplacian operator with Neumann homogeneous boundary conditions emerges when transforming the Navier-Stokes equations to the vorticity-velocity formulation. In the case of problems with a periodic direction, the problem can be transformed into multiple, independent, t...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/186635 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/186635 |
| Access Level: | acceso abierto |
| Palabra clave: | DNS CFD Turbulence Bi-Laplacian Fourth-order elliptic INGENIERIA AEROESPACIAL MATEMATICA APLICADA 07.- Asegurar el acceso a energías asequibles, fiables, sostenibles y modernas para todos 11.- Conseguir que las ciudades y los asentamientos humanos sean inclusivos, seguros, resilientes y sostenibles |
| Sumario: | [EN] In fluid mechanics, the bi-Laplacian operator with Neumann homogeneous boundary conditions emerges when transforming the Navier-Stokes equations to the vorticity-velocity formulation. In the case of problems with a periodic direction, the problem can be transformed into multiple, independent, two-dimensional fourth-order elliptic problems. An efficient method to solve these two-dimensional bi-Laplacian operators with Neumann homogeneus boundary conditions was designed and validated using 2D compact finite difference schemes. The solution is formulated as a linear combination of auxiliary solutions, as many as the number of points on the boundary, a method that was prohibitive some years ago due to the large memory requirements to store all these auxiliary functions. The validation has been made for different field configurations, grid sizes, and stencils of the numerical scheme, showing its potential to tackle high gradient fields as those that can be found in turbulent flows. |
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