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Two-Dimensional Compact-Finite-Difference Schemes for Solving the bi-Laplacian Operator with Homogeneous Wall-Normal Derivatives
Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Valencia 46022, Spain..
KTH, Skolan för teknikvetenskap (SCI), Centra, Linné Flow Center, FLOW. KTH, Skolan för teknikvetenskap (SCI), Teknisk mekanik, Strömningsmekanik och Teknisk Akustik.ORCID-id: 0000-0001-6570-5499
Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Valencia 46022, Spain..
Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Valencia 46022, Spain..
2021 (Engelska)Ingår i: Mathematics, E-ISSN 2227-7390, Vol. 9, nr 19, artikel-id 2508Artikel i tidskrift (Refereegranskat) Published
Abstract [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.

Ort, förlag, år, upplaga, sidor
MDPI AG , 2021. Vol. 9, nr 19, artikel-id 2508
Nyckelord [en]
DNS, CFD, turbulence, bi-Laplacian, fourth-order elliptic
Nationell ämneskategori
Matematisk analys
Identifikatorer
URN: urn:nbn:se:kth:diva-304686DOI: 10.3390/math9192508ISI: 000709847800001Scopus ID: 2-s2.0-85116718671OAI: oai:DiVA.org:kth-304686DiVA, id: diva2:1613316
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QC 20211122

Tillgänglig från: 2021-11-22 Skapad: 2021-11-22 Senast uppdaterad: 2022-06-25Bibliografiskt granskad

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Vinuesa, Ricardo

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Linné Flow Center, FLOWStrömningsmekanik och Teknisk Akustik
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