Wyniki wyszukiwania - BazTech

1

Simultaneous shape and mesh quality optimization using pre-shape calculus

Luft Daniel, Schulz Volker

Control and Cybernetics

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2021

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Vol. 50, No. 4

473--520

EN

Computational meshes arising from shape optimization routines commonly suffer from decrease of mesh quality or even destruction of the mesh. In this work, we provide an approach to regularize general shape optimization problems to increase both shape and volume mesh quality. For this, we employ pre-shape calculus as established in Luft and Schulz (2021). Existence of regularized solutions is guaranteed. Further, consistency of modified pre-shape gradient systems is established. We present pre-shape gradient system modifications, which permit simultaneous shape optimization with mesh quality improvement. Optimal shapes to the original problem are left invariant under regularization. The computational burden of our approach is limited, since additional solution of possibly larger (non-)linear systems for regularized shape gradients is not necessary. We implement and compare pre-shape gradient regularization approaches for a 2D problem, which is prone to mesh degeneration. As our approach does not depend on the choice of metrics representing shape gradients, we employ and compare several different metrics.

2

Pre-shape calculus and its application to mesh quality optimization

Luft Daniel, Schulz Volker

Control and Cybernetics

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2021

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Vol. 50, No. 3

263--301

EN

Deformations of the computational mesh, arising from optimization routines, usually lead to decrease of mesh quality or even destruction of the mesh. We propose a theoretical framework using pre-shapes to generalize the classical shape optimization and calculus. We define pre-shape derivatives and derive corresponding structure and calculus theorems. In particular, tangential directions are featured in pre-shape derivatives, in contrast to classical shape derivatives, featuring only normal directions. Techniques from classical shape optimization and calculus are shown to carry over to this framework. An optimization problem class for mesh quality is introduced, which is solvable with the use of pre-shape derivatives. This class allows for simultaneous optimization of the classical shape objectives and mesh quality without deteriorating the classical shape optimization solution. The new techniques are implemented and numerically tested for 2D and 3D.

3

Effect of the numerical grid density on the modelling of fluid flow in a stirred tank with a PMT impeller

Story A., Jaworski Z.

Czasopismo Techniczne. Chemia

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2014

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R. 111, z. 2-Ch

115--123

EN

The paper present the results of numerical simulations performed for a stirred tank equipped with a PMT type impeller, filled up with a Newtonian fluid. The effects of the grid density and mesh quality and also of the simulation mode on the modelling of fluid flow in a stirred tank were studied. The results are compared with literature data obtained from LDA measurements. It was found that denser numerical grids give more detailed information about generated flow field near the impeller blades. Additionally, better compatibility of predicting and experimental results was obtained in the case of the transient mode simulation, what also demonstrates a significant effect of the angular position of the impeller against baffles on the generated velocity field.

PL

W artykule przedstawiono wyniki symulacji numerycznych prowadzonych dla mieszalnika z mieszadłem typu PMT, wypełnionego cieczą newtonowską. Zbadano wpływ gęstości i jakości siatki numerycznej oraz trybu prowadzenia symulacji numerycznych na modelowanie pola prędkości cieczy w mieszalniku. Wyniki porównano z literaturowymi danymi eksperymentalnymi z pomiarów LDA. Stwierdzono, że gęstsza siatka numeryczna daje bardziej szczegółowe informacje o generowanym polu prędkości w pobliżu łopatek mieszadła. Dodatkowo lepszą zgodność wyników przewidywanych z doświadczalnymi otrzymano w przypadku prowadzenia symulacji w trybie nieustalonym, co świadczy o dużym wpływie kątowego położenia mieszadła względem przegród na generowane pole prędkości.

4

Improved GETMe by adaptive mesh smoothing

Vartziotis D., Papadrakakis M.

Computer Assisted Methods in Engineering and Science

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2013

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Vol. 20, no. 1

55--71

EN

Mesh smoothing improves mesh quality by node relocation without altering mesh topology. Such methods play a vital role in finite element mesh improvement with a direct consequence on the quality of the discretized solution. In this work, an improved version of the recently proposed geometric element transformation method (GETMe) for mesh smoothing is presented. Key feature is the introduction of adaptive concepts, which improve the resulting mesh quality, reduce the number of parameters, and enhance the parallelization capabilities. Implementational aspects are discussed and results of a more efficient version are presented, which demonstrate that GETMe adaptive smoothing yields high quality meshes, is particularly fast, and has a comparably low memory profile. Furthermore, results are compared to those of other state-of-the-art smoothing methods.