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ON THE NAVIER-STOKES EQUATION WITH FREE CONVECTION IN STRIP DOMAINS AND 3D TRIANGULAR CHANNELS

  • The Navier-Stokes equations and related ones can be treated very elegantly with the quaternionic operator calculus developed in a series of works by K. Guerlebeck, W. Sproeossig and others. This study will be extended in this paper. In order to apply the quaternionic operator calculus to solve these types of boundary value problems fully explicitly, one basically needs to evaluate two types ofThe Navier-Stokes equations and related ones can be treated very elegantly with the quaternionic operator calculus developed in a series of works by K. Guerlebeck, W. Sproeossig and others. This study will be extended in this paper. In order to apply the quaternionic operator calculus to solve these types of boundary value problems fully explicitly, one basically needs to evaluate two types of integral operators: the Teodorescu operator and the quaternionic Bergman projector. While the integral kernel of the Teodorescu transform is universal for all domains, the kernel function of the Bergman projector, called the Bergman kernel, depends on the geometry of the domain. With special variants of quaternionic holomorphic multiperiodic functions we obtain explicit formulas for three dimensional parallel plate channels, rectangular block domains and regular triangular channels. The explicit knowledge of the integral kernels makes it then possible to evaluate the operator equations in order to determine the solutions of the boundary value problem explicitly.show moreshow less

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Metadaten
Document Type:Conference Proceeding
Author: Denis Constales, Prof. Dr. Rolf Sören Kraußhar
URN (Cite-Link):https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20170327-29387Cite-Link
URL:http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html
DOI (Cite-Link):https://doi.org/10.25643/bauhaus-universitaet.2938Cite-Link
Editor: Klaus GürlebeckGND, Carsten KönkeORCiDGND
Language:English
Date of Publication (online):2017/03/24
Date of first Publication:2006/07/14
Release Date:2017/03/27
Publishing Institution:Bauhaus-Universität Weimar
Creating Corporation:Bauhaus-Universität Weimar
Institutes and partner institutions:Bauhaus-Universität Weimar / In Zusammenarbeit mit der Bauhaus-Universität Weimar
Page Number:12
GND Keyword:Architektur <Informatik>; CAD; Computerunterstütztes Verfahren
Dewey Decimal Classification:500 Naturwissenschaften und Mathematik / 510 Mathematik
BKL-Classification:56 Bauwesen / 56.03 Methoden im Bauingenieurwesen
Collections:Bauhaus-Universität Weimar / Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen, IKM, Weimar / Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen, IKM, Weimar, 17. 2006
Licence (German):License Logo Creative Commons 4.0 - Namensnennung-Nicht kommerziell (CC BY-NC 4.0)