The Finite Volume Method in point of view of Finite Element Method
- The best-known discretization methods for solving engineering problems formulated as partial differential equations are finite difference method (FDM), finite element method (FEM) and finite volume method (FVM). While the finite volume method is used in fluid mechanics, the finite element method is predominant in solid state mechanics. At first glance, FVM and FEM are two highly specialized methods. However, both methods can solve problems of both solid mechanics and fluid mechanics well. Since experimental mechanics deals not only with solid state physics but also with fluid mechanics problems, we want to understand FVM in the sense of FEM in this work. In the long term, we want to use the variational calculus to unify many important numerical methods in engineering science into a common framework. In this way, we expect that experiences can be better exchanged between different engineering sciences and thus innovations in the field of experimental mechanics can be advanced. But inThe best-known discretization methods for solving engineering problems formulated as partial differential equations are finite difference method (FDM), finite element method (FEM) and finite volume method (FVM). While the finite volume method is used in fluid mechanics, the finite element method is predominant in solid state mechanics. At first glance, FVM and FEM are two highly specialized methods. However, both methods can solve problems of both solid mechanics and fluid mechanics well. Since experimental mechanics deals not only with solid state physics but also with fluid mechanics problems, we want to understand FVM in the sense of FEM in this work. In the long term, we want to use the variational calculus to unify many important numerical methods in engineering science into a common framework. In this way, we expect that experiences can be better exchanged between different engineering sciences and thus innovations in the field of experimental mechanics can be advanced. But in this work, we limit ourselves to the understanding of the FVM with the help of the variational calculus already known in FEM. We use a simple 1D Poisson equation to clarify the point. First, we briefly summarize the FVM and FEM. Then we will deal with the actual topic of this paper, as we establish the FEM and the FVM on a common basis by variation formulation. It is shown here that the FVM can be understood in terms of the finite element method with the so-called Galerkin-Petrov approach.…
Autor*innen: | Cheng-Chieh Wu |
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Weitere Person: | Daniel Völker, S. Weisbrich, F. Neitzel |
Dokumenttyp: | Posterpräsentation |
Veröffentlichungsform: | Präsentation |
Sprache: | Englisch |
Jahr der Erstveröffentlichung: | 2021 |
Organisationseinheit der BAM: | 8 Zerstörungsfreie Prüfung |
8 Zerstörungsfreie Prüfung / 8.1 Sensorik, mess- und prüftechnische Verfahren | |
DDC-Klassifikation: | Naturwissenschaften und Mathematik / Chemie / Analytische Chemie |
Freie Schlagwörter: | Computational physics; Finite element method; Finite volume method; Simulation; Variational calculation |
Themenfelder/Aktivitätsfelder der BAM: | Umwelt |
Umwelt / Sensorik | |
Veranstaltung: | 37th Danubia Adria Symposium on Advances in Experimental Mechanics |
Veranstaltungsort: | Linz, Austria |
Beginndatum der Veranstaltung: | 21.09.2021 |
Enddatum der Veranstaltung: | 24.09.2021 |
Verfügbarkeit des Dokuments: | Datei im Netzwerk der BAM verfügbar ("Closed Access") |
Datum der Freischaltung: | 30.09.2021 |
Referierte Publikation: | Nein |