TY - CHAP A1 - Pastohr, Henry A1 - Kornadt, Oliver A1 - Gürlebeck, Klaus T1 - Numerische Untersuchungen zum Thermischen Strömungsverhalten im Aufwindkraftwerk T1 - Numerische und analytische Untersuchungen zum Strömungsverhalten im Aufwindkraftwerk N2 - Das Aufwindkraftwerk ist eine thermo- hydrodynamische Maschine zur Elektroenergiegewinnung, bestehend aus einem Treibhaus, einem Kamin und einer oder mehreren Turbinen. In dieser Studie wurden numerische Ergebnisse zum thermischen Strömungsverhalten in einem Aufwindkraftwerk unter der Berücksichtigung der Teilmodelle Erdboden, Kollektor, Atmosphäre, Umlenkung, Kamin und Turbine erhaltenden. Hierzu wurden die stationären Grundgleichungen der Thermofluiddynamik auf strukturierten, körperangepassten und rotationssymmetrischen Gittern unter Beachtung aller Rand- und Kopplungsbedingungen numerisch mit dem finite Volumenverfahren gelöst. Besonderes Augenmerk wurde dabei auf die Kalibrierung des Modells im Ruhezustand, auf die numerische Simulation, auf den Einfluss der Strahlung, auf die Betrachtung der Turbine, auf das Dichtemodell sowie auf den turbulenten Strömungszustand gelegt. Die erhaltenen Ergebnisse werden durch Approximationen 2. Ordnung, Gitterunabhängigkeit und durch einen sehr geringen Abbruchfehler charakterisiert. Für 4 verschiedene Einstrahlungen wurden die Verläufe von Temperatur und Geschwindigkeit im Aufwindkraftwerk erhalten. Zusätzlich sind für Vergleichszwecke der Massenstrom, der Temperaturhub, die Leistung an der Turbine und der Wirkungsgrad der Anlage bestimmt wurden. Aufbauend auf den Berechnungen in dieser Arbeit und den numerischen und analytischen Berechnungen in [1] können nun erweiterte Parameterstudien und instationäre Simulationen zum Aufwindkraftwerk durchgeführt werden. KW - Aufwindkraftwerk KW - Strömungsmechanik Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-3436 ER - TY - CHAP A1 - Nguyen, Manh Hung A1 - Gürlebeck, Klaus ED - Gürlebeck, Klaus ED - Lahmer, Tom ED - Werner, Frank T1 - ON M-CONFORMAL MAPPINGS AND GEOMETRIC PROPERTIES T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar N2 - Monogenic functions play a role in quaternion analysis similarly to that of holomorphic functions in complex analysis. A holomorphic function with nonvanishing complex derivative is a conformal mapping. It is well-known that in Rn+1, n ≥ 2 the set of conformal mappings is restricted to the set of Möbius transformations only and that the Möbius transformations are not monogenic. The paper deals with a locally geometric mapping property of a subset of monogenic functions with nonvanishing hypercomplex derivatives (named M-conformal mappings). It is proved that M-conformal mappings orthogonal to all monogenic constants admit a certain change of solid angles and vice versa, that change can characterize such mappings. In addition, we determine planes in which those mappings behave like conformal mappings in the complex plane. KW - Angewandte Informatik KW - Angewandte Mathematik KW - Computerunterstütztes Verfahren Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-27833 UR - http://euklid.bauing.uni-weimar.de/ikm2012 SN - 1611-4086 ER - TY - CHAP A1 - Legatiuk, Dmitrii A1 - Bock, Sebastian A1 - Gürlebeck, Klaus ED - Gürlebeck, Klaus ED - Lahmer, Tom ED - Werner, Frank T1 - THE PROBLEM OF COUPLING BETWEEN ANALYTICAL SOLUTION AND FINITE ELEMENT METHOD T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar N2 - This paper is focused on the first numerical tests for coupling between analytical solution and finite element method on the example of one problem of fracture mechanics. The calculations were done according to ideas proposed in [1]. The analytical solutions are constructed by using an orthogonal basis of holomorphic and anti-holomorphic functions. For coupling with finite element method the special elements are constructed by using the trigonometric interpolation theorem. KW - Angewandte Informatik KW - Angewandte Mathematik KW - Computerunterstütztes Verfahren Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-27730 UR - http://euklid.bauing.uni-weimar.de/ikm2012 SN - 1611-4086 ER - TY - CHAP A1 - Kraußhar, Rolf Sören A1 - Constales, Denis A1 - Gürlebeck, Klaus A1 - Sprößig, Wolfgang ED - Gürlebeck, Klaus ED - Könke, Carsten T1 - APPLICATIONS OF QUATERNIONIC ANALYSIS IN ENGINEERING N2 - The quaternionic operator calculus can be applied very elegantly to solve many important boundary value problems arising in fluid dynamics and electrodynamics in an analytic way. In order to set up fully explicit solutions. In order to apply the quaternionic operator calculus to solve these types of boundary value problems fully explicitly, one has 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. Recently the theory of quaternionic holomorphic multiperiodic functions and automorphic forms provided new impulses to set up explicit representation formulas for large classes of hyperbolic polyhedron type domains. These include block shaped domains, wedge shaped domains (with or without additional rectangular restrictions) and circular symmetric finite and infinite cylinders as particular subcases. In this talk we want to give an overview over the recent developments in this direction. KW - Architektur KW - CAD KW - Computerunterstütztes Verfahren Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-29128 UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html ER - TY - CHAP A1 - Hommel, Angela A1 - Gürlebeck, Klaus ED - Gürlebeck, Klaus ED - Lahmer, Tom T1 - THE RELATIONSHIP BETWEEN LINEAR ELASTICITY THEORY AND COMPLEX FUNCTION THEORY STUDIED ON THE BASIS OF FINITE DIFFERENCES T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar N2 - It is well-known that the solution of the fundamental equations of linear elasticity for a homogeneous isotropic material in plane stress and strain state cases can be equivalently reduced to the solution of a biharmonic equation. The discrete version of the Theorem of Goursat is used to describe the solution of the discrete biharmonic equation by the help of two discrete holomorphic functions. In order to obtain a Taylor expansion of discrete holomorphic functions we introduce a basis of discrete polynomials which fulfill the so-called Appell property with respect to the discrete adjoint Cauchy-Riemann operator. All these steps are very important in the field of fracture mechanics, where stress and displacement fields in the neighborhood of singularities caused by cracks and notches have to be calculated with high accuracy. Using the sum representation of holomorphic functions it seems possible to reproduce the order of singularity and to determine important mechanical characteristics. KW - Angewandte Informatik KW - Angewandte Mathematik KW - Building Information Modeling KW - Computerunterstütztes Verfahren KW - Data, information and knowledge modeling in civil engineering; Function theoretic methods and PDE in engineering sciences; Mathematical methods for (robotics and) computer vision; Numerical modeling in engineering; Optimization in engineering applications Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28010 SN - 1611-4086 ER - TY - CHAP A1 - Gürlebeck, Klaus A1 - Bock, Sebastian A1 - Falcao, M. Irene T1 - Applications of Bergman kernel functions N2 - In this paper we revisit the so-called Bergman kernel method (BKM) for solving conformal mapping problems. This method is based on the reproducing property of the Bergman kernel function. The main drawback of this well known technique is that it involves an orthonormalization process and thus is numerically unstable. This difficulty can be, in some cases, overcome by using the Maple system, which makes no use of numeric quadrature. We illustrate this implementation by presenting a numerical example. The construction of reproducing kernel functions is not restricted to real dimension 2. Results concerning the construction of Bergman kernel functions in closed form for special domains in the framework of hypercomplex function theory suggest that BKM can also be extended to mapping problems in higher dimensions, particularly 3-dimensional cases. We describe such a generalized BKM-approach and present numerical examples obtained by the use of specially developed software packages for quaternions. KW - Konforme Abbildung KW - Kernel Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-2994 ER - TY - CHAP A1 - Bock, Sebastian A1 - Gürlebeck, Klaus ED - Gürlebeck, Klaus ED - Könke, Carsten T1 - A Coupled Ritz-Galerkin Approach Using Holomorphic and Anti-holomorphic Functions N2 - The contribution focuses on the development of a basic computational scheme that provides a suitable calculation environment for the coupling of analytical near-field solutions with numerical standard procedures in the far-field of the singularity. The proposed calculation scheme uses classical methods of complex function theory, which can be generalized to 3-dimensional problems by using the framework of hypercomplex analysis. The adapted approach is mainly based on the factorization of the Laplace operator EMBED Equation.3 by the Cauchy-Riemann operator EMBED Equation.3 , where exact solutions of the respective differential equation are constructed by using an orthonormal basis of holomorphic and anti-holomorphic functions. KW - Architektur KW - CAD KW - Computerunterstütztes Verfahren Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-29281 UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html ER - TY - CHAP A1 - Al-Yasiri, Zainab A1 - Gürlebeck, Klaus ED - Gürlebeck, Klaus ED - Lahmer, Tom T1 - ON BOUNDARY VALUE PROBLEMS FOR P-LAPLACE AND P-DIRAC EQUATIONS T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar N2 - The p-Laplace equation is a nonlinear generalization of the Laplace equation. This generalization is often used as a model problem for special types of nonlinearities. The p-Laplace equation can be seen as a bridge between very general nonlinear equations and the linear Laplace equation. The aim of this paper is to solve the p-Laplace equation for 2 < p < 3 and to find strong solutions. The idea is to apply a hypercomplex integral operator and spatial function theoretic methods to transform the p-Laplace equation into the p-Dirac equation. This equation will be solved iteratively by using a fixed point theorem. KW - Angewandte Informatik KW - Angewandte Mathematik KW - Building Information Modeling KW - Computerunterstütztes Verfahren KW - Data, information and knowledge modeling in civil engineering; Function theoretic methods and PDE in engineering sciences; Mathematical methods for (robotics and) computer vision; Numerical modeling in engineering; Optimization in engineering applications Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-27928 SN - 1611-4086 ER -