Zur Lösung der Grundgleichungen des Fadens bei gleichförmiger Bewegung in einer Flüssigkeit

Hackmann, W. Kent

doi:10.1002/zamm.19820620305

Cited by 4 publications

(4 citation statements)

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“…As the next iteration starts, F ( k ∗) is inserted in (28), (24), and (25) to fill the system again. Convergence is formally proven in References 42,43 and typically reached within 100 iterations in the first time step and less than 50 afterward. The algorithm stops after reaching the residual criterion

\max_{j} | {| | {false({\vec{f}}^{(j)} false)}^{(k)} | |}_{2} - 1 | < tol, j = 1, \dots, N,

which corresponds to the conservation of all bar unit vectors within a tolerance typically chosen as 10 −4 .…”

Section: Numerical Modelsmentioning

confidence: 99%

“…An iterative method has to be chosen for solving the system because all components of (27) are related to each other. As proven by Hackmann, 42,43 a successive approximation can be found to ensure a converged solution. For this purpose, (27) is rearranged such that internal and external forces are separated

{\vec{f}}^{(j + 1)} F_{T}^{(j + 1)} - {\vec{f}}^{(j)} F_{T}^{(j)} = - false({\vec{F}}_{H}^{(j)} + {\vec{F}}_{G}^{(j)} false), j = 1, \dots, N - 1 .

…”

Section: Numerical Modelsmentioning

confidence: 99%

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Accurate modeling of the interaction of constrained floating structures and complex free surfaces using a new quasistatic mooring model

Martín

Kamath

Bihs

2020

Numerical Methods in Fluids

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SummaryA new approach for the coupled simulation of moored floating structures in a numerical wave tank using CFD is subject of this article. A quasistatic mooring model is derived by dividing the cable into finite elements and solve force equilibria in each time step. A successive approximation is applied to solve the problem most efficiently. Here, the unknown internal and external forces are separated, and the system is corrected iteratively using the intermediate results for the unit vectors until convergence is reached. An improved algorithm based on the directional ghost‐cell immersed boundary method is utilized for modeling floating objects in a three‐dimensional numerical wave tank. It is based on an implicit representation of the body on a stationary grid using a level set function. The motion of the rigid body is described using Euler parameters and Hamiltonian mechanics. Dynamic boundary conditions are enforced by modifying the ghost points in the vicinity of the structure. A special procedure for staggered grids is included in the article. The mooring model is coupled to the fluid‐structure interaction solver to simulate physically constrained floating bodies in waves. Several validation cases provide an overview of the accuracy of the mooring model and the floating algorithm. In addition, the comparison of the numerical results for the motion of a moored floating barge in regular waves with experiments is presented.

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\max_{j} | {| | {false({\vec{f}}^{(j)} false)}^{(k)} | |}_{2} - 1 | < tol, j = 1, \dots, N,

which corresponds to the conservation of all bar unit vectors within a tolerance typically chosen as 10 −4 .…”

Section: Numerical Modelsmentioning

confidence: 99%

{\vec{f}}^{(j + 1)} F_{T}^{(j + 1)} - {\vec{f}}^{(j)} F_{T}^{(j)} = - false({\vec{F}}_{H}^{(j)} + {\vec{F}}_{G}^{(j)} false), j = 1, \dots, N - 1 .

…”

Section: Numerical Modelsmentioning

confidence: 99%

Accurate modeling of the interaction of constrained floating structures and complex free surfaces using a new quasistatic mooring model

Martín

Kamath

Bihs

2020

Numerical Methods in Fluids

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“…The way of carrying out the calculation may be demonstrated using a very simple example although no evidences for its admissibility are shown (Leitzke, 1981;Hackmann, 1982).…”

Section: Mathematical-physical Modellingmentioning

confidence: 99%

“…For the calculation of complicated line systems at the Wilhelm-Pieck-University of Rostock a method of discretizing has been found, that makes a successive approximation of assessed initial values to the true solution possible (Litzke, 1981;Hackmann, 1982).…”

Section: Introductionmentioning

confidence: 99%

Calculation of fishing gear as discrete models

Leitzke¹,

Niedzwiedz²

1985

Acta Ichthyol. Piscat.

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Mathematische Begründung von Verfahren zur Berechnung von Form und Zugkraft in Fadenzugsystemen

Hackmann

1983

Z Angew Math Mech

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Diese Arbeit beschäftigt sich mit der Berechnung von Form und Zugkraft in Fadenzugsystemen, die in einer zähen Flüssigkeit gleichförmig bewegt werden. Hergeleitet werden zwei Möglichkeiten der Modellierung. Modell 1: Aufstellung eines Systems von gewöhnlichen Differentialgleichungen 1. Ordnung für Form und Zugkraft; Modell 2: Ermittlung eines Systems von Integralgleichungen für die Zugkraft. Weiter werden hinreichende Bedingungen angegeben zur Lösung von Modell 2 mittels der sukzessiven Approximation. Diskretisiert man Modell 2 auf der Grundlage der gemittelten Euler‐Formel und löst man das dadurch entstehende System ebenfalls durch sukzessive Approximation, so gelten weitgehend analoge hinreichende Bedingungen. Es werden Fehlerabschätzungen vom Typ O(h2) angegeben zur näherungsweisen Lösung von Modell 2 mittels des diskretisierten Systems. Schließlich werden Ergebnisse zur Anwendbarkeit des Newton‐Verfahrens auf das diskretisierte System hergeleitet.

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Zur Lösung der Grundgleichungen des Fadens bei gleichförmiger Bewegung in einer Flüssigkeit

Cited by 4 publications

References 1 publication

Accurate modeling of the interaction of constrained floating structures and complex free surfaces using a new quasistatic mooring model

Accurate modeling of the interaction of constrained floating structures and complex free surfaces using a new quasistatic mooring model

Calculation of fishing gear as discrete models

Mathematische Begründung von Verfahren zur Berechnung von Form und Zugkraft in Fadenzugsystemen

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