55046
2022
eng
2679
2683
62
article
Elsevier Ltd.
Amsterdam
1
--
--
--
The finite volume method in the context of the finite element method
The finite volume method (FVM), like the finite element method (FEM), is a numerical method for determining an approximate solution for partial differential equations. The derivation of the two methods is based on very different considerations, as they have historically evolved from two distinct engineering disciplines, namely solid mechanics and fluid mechanics. This makes FVM difficult to learn for someone familiar with FEM. In this paper we want to show that a slight modification of the FEM procedure leads to an alternative derivation of the FVM. Both numerical methods are starting from the same strong formulation of the problem represented by differential equations, which are only satisfied by their exact solution. For an approximation of the exact solution, the strong formulation must be converted to a so-called weak form. From here on, the two numerical methods differ. By appropriate choice of the trial function and the test function, we can obtain different numerical methods for solving the weak formulation of the problem. While typically in FEM the basis functions of the trial function and test function are identical, in FVM they are chosen differently. In this paper, we show which trial and test function must be chosen to derive the FVM alternatively: The trial function of the FVM is a “shifted” trial function of the FEM, where the nodal points are now located in the middle of an integration interval rather than at the ends. Moreover, the basis functions of the test function are no longer the same as those of the trial function as in the FEM, but are shown to be a constant equal to 1. This is demonstrated by the example of a 1D Poisson equation.
Materials Today: Proceedings
2214-7853
10.1016/j.matpr.2022.05.460
publish
18.07.2022
Cheng-Chieh Wu
Daniel Völker
S. Weisbrich
F. Neitzel
eng
uncontrolled
Finite Volume Method
eng
uncontrolled
Finite Element Method
eng
uncontrolled
Variational Calculation
eng
uncontrolled
Numerical Methods
Analytische Chemie
8 Zerstörungsfreie Prüfung
8.1 Sensorik, mess- und prüftechnische Verfahren
Umwelt
Chemie und Prozesstechnik
Verlagsliteratur
Datei im Netzwerk der BAM verfügbar ("Closed Access")
Sensorik
53422
2021
eng
12
13
conferenceobject
Johannes Kepler University
0
--
--
--
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 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.
Book of Abstracts 37th Danubia Adria Symposium on Advances in Experimental Mechanics
978-3-9504997-0-4
37th Danubia Adria Symposium on Advances in Experimental Mechanics
Linz, Österreich
21.09.2021
24.09.2021
publish
false
true
Cheng-Chieh Wu
Daniel Völker
S. Weisbrich
F. Neitzel
eng
uncontrolled
Finite element method
eng
uncontrolled
Finite volume method
eng
uncontrolled
Variational calculation
eng
uncontrolled
Simulation
eng
uncontrolled
Computational physics
Analytische Chemie
8 Zerstörungsfreie Prüfung
8.1 Sensorik, mess- und prüftechnische Verfahren
Umwelt
Datei im Netzwerk der BAM verfügbar ("Closed Access")
Graue Literatur
Sensorik
53424
2021
eng
poster
0
--
--
--
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 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.
37th Danubia Adria Symposium on Advances in Experimental Mechanics
Linz, Austria
21.09.2021
24.09.2021
publish
false
true
Cheng-Chieh Wu
eng
uncontrolled
Finite volume method
eng
uncontrolled
Finite element method
eng
uncontrolled
Variational calculation
eng
uncontrolled
Simulation
eng
uncontrolled
Computational physics
Analytische Chemie
8 Zerstörungsfreie Prüfung
8.1 Sensorik, mess- und prüftechnische Verfahren
Umwelt
Datei im Netzwerk der BAM verfügbar ("Closed Access")
Präsentation
Sensorik
37529
2016
eng
52
53
conferenceobject
Ljubljana
Narodna in univerzitetna knjižnica, Ljubljana
0
--
--
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Approximate model for geometrical complex structures
Many engineering structures are made of composite materials or metal foam. To simulate the deformational behaviour of these structures often requires a high number of discretisation elements. This in turn yields a very large system of linear equations that are extremely time and memory consuming or practically impossible to solve. It is therefore desirable to find an approach to overcome this obstacle.
33rd Danubia- Adria Symposium on Advances in Experimental Mechanics - BOOK OF ABSTRACTS
978-961-94081-0-0
33rd Danubia- Adria Symposium on Advances in Experimental Mechanics
Portorož, Slovenia
20.09.2016
23.09.2016
Cheng-Chieh Wu
S. Weisbrich
F. Neitzel
eng
uncontrolled
Inverse analysis
eng
uncontrolled
Finite element method
eng
uncontrolled
Least-squares adjustment
Analytische Chemie
Ingenieurwissenschaften und zugeordnete Tätigkeiten
Datei im Netzwerk der BAM verfügbar ("Closed Access")
Graue Literatur
37521
2016
eng
poster
0
--
--
--
Determination of an approximate anisotropic model for a given geometrical complex isotropic structure by means of finite element method and least-squares adjustment
Many engineering structures are made of composite materials or metal foam. To simulate the deformational behaviour of these structures often requires a high number of discretisation elements. This in turn yields a very large system of linear equations that are extremely time and memory consuming or practically impossible to solve. It is therefore desirable to find an approach to overcome this obstacle.
PhD Day 2016
Berlin, Germany
01.09.2016
Cheng-Chieh Wu
eng
uncontrolled
Least-Squares Adjustment
eng
uncontrolled
Inverse Analysis
eng
uncontrolled
Finite Element Method
Analytische Chemie
Ingenieurwissenschaften und zugeordnete Tätigkeiten
Datei im Netzwerk der BAM verfügbar ("Closed Access")
Präsentation
37523
2016
eng
poster
0
--
--
--
Approximate model for geometrical complex structures
Many engineering structures are made of composite materials or metal foam. To simulate the deformational behaviour of these structures often requires a high number of discretisation elements. This in turn yields a very large system of linear
equations that are extremely time and memory consuming or practically impossible to solve. It is therefore desirable to find an approach to overcome this obstacle.
33rd Danubia- Adria Symposium on Advances in Experimental Mechanics
Portorož, Slovenia
20.09.2016
23.09.2016
Cheng-Chieh Wu
eng
uncontrolled
Inverse analysis
eng
uncontrolled
Finite element method
eng
uncontrolled
Least-squares adjustment
Analytische Chemie
Ingenieurwissenschaften und zugeordnete Tätigkeiten
Datei im Netzwerk der BAM verfügbar ("Closed Access")
Präsentation
37524
2016
eng
lecture
0
--
--
--
Approximate model for geometrical complex structures
Many engineering structures are made of composite materials or metal foam. To simulate the deformational behaviour of these structures often requires a high number of discretisation elements. This in turn yields a very large system of linear equations that are extremely time and memory consuming or practically impossible to solve. It is therefore desirable to find an approach to overcome this obstacle.
33rd Danubia- Adria Symposium on Advances in Experimental Mechanics
Portorož, Slovenia
20.09.2016
23.09.2016
0
Cheng-Chieh Wu
eng
uncontrolled
Inverse analysis
eng
uncontrolled
Finite element method
eng
uncontrolled
Least-squares adjustment
Analytische Chemie
Ingenieurwissenschaften und zugeordnete Tätigkeiten
Datei im Netzwerk der BAM verfügbar ("Closed Access")
Präsentation
30913
2014
eng
46
47
conferenceobject
Bergische Universität Wuppertal
0
--
--
--
On optimal measurement set-ups for parameter identification from an integrated structural analysis of hybrid measurements and finite element model
One major ambition in Structural Health Monitoring (SHM) is to develop the ability to detect, identify and localize damage as well as to predict the lifespan of civil structures (Worden et al. 2007). This would allow well-informed decision on whether to repair or to demolish these structures. The word monitoring in SHM brings up several frequently ignored questions: What type of sensors and accuracies are needed to monitor a given structure? Where are the optimal sensor placements? How many sensors are necessary? How to analyse spatially distributed hybrid measurements? Or, in short: What is the sensor configuration best suited for structural health monitoring? If these questions are not explicitly addressed, the usefulness of the measurement data for an evaluation is left to coincidence.
XIVth Bilateral Czech/German Symposium 'Experimental methods and numerical simulation in engineering science'
33898
XIVth Bilateral Czech/German Symposium 'Experimental methods and numerical simulation in engineering science'
Wuppertal, Germany
04.06.2014
07.06.2014
S. Weisbrich
Cheng-Chieh Wu
F. Neitzel
Datei im Netzwerk der BAM verfügbar ("Closed Access")
Graue Literatur
31728
2014
eng
191
192
conferenceobject
Verein Deutscher Ingenieure (VDI)
1
--
--
--
Integrated structural analysis of hybrid measurement and finite element method for damage detection within a slender beam
One major ambition in Structural Health Monitoring (SHM) is to develop the ability to detect, identify and localize damage as well as to predict the lifespan of civil structures. This would allow well-informed decision on whether to repair or to demolish these structures. We want to focus on the issues of detection and localisation of damage caused by material degradation within a slender beam - a structure that is often used as a construction carrier.
31st Danubia-Adria Symposium on advances in experimental mechanics (Proceedings)
34774
978-3-00-046740-0
31st Danubia-Adria Symposium on advances in experimental mechanics
Kempten, Germany
24.09.2014
27.09.2014
30.10.2014
Cheng-Chieh Wu
S. Weisbrich
F. Neitzel
Verlagsliteratur
Datei im Netzwerk der BAM verfügbar ("Closed Access")
34485
2015
eng
78
79
conferenceobject
Zilina
Faculty of Mechanical Engineering, Univerzity of Zilina, Slovakia
1
--
--
--
Inverse finite element adjustment of material parameters from integrated analysis of displacement field measurement
32nd Danubia-Adria Symposium on advances in experimental mechanics (Proceedings)
37619
978-80-554-1094-4
Sonderstandort: Publica-Schrank
32nd Danubia-Adria Symposium on advances in experimental mechanics
Starý Smokovec, Slovakia
2015-09-22
2015-09-25
12.10.2015
Cheng-Chieh Wu
S. Weisbrich
F. Neitzel
Verlagsliteratur
Physisches Exemplar in der Bibliothek der BAM vorhanden ("Hardcopy Access")