Conservation and Accuracy in Meshfree Generalized Finite Difference Methods
Pratik Suchde
Hrsg.: Fraunhofer ITWM, Kaiserslautern
2018, 145 S., num., mostly col. illus. and tab., Softcover
Sprache: Englisch
Kaiserslautern, TU, Diss., 2017
Fraunhofer Verlag
ISBN 978-3-8396-1325-2

zur Open Access Version

Inhalt
The goal of this PhD is to improve various aspects of meshfree Generalized Finite Difference Methods (GFDMs). In this thesis, different meshfree GFDMs are compared, and their potential to solve over-determined problems is presented. A new method is presented that introduces conservation of fluxes in a meshfree setting, which reduces the problem of lack of conservation that has plagued meshfree methods. Special attention is paid on the application of meshfree GFDMs to simulate fluid flow modeled by the incompressible Navier - Stokes equations. A new meshfree GFDM scheme for the same is presented which improves local accuracy, and shows better approximations to the mass conservation condition. Further, different aspects of meshfree Lagrangian frameworks are studied, and new methods to improve accuracy in the Lagrangian movement process are also presented.

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