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Special finite-difference methods for extremely anisotropic diffusion

Special finite-difference methods for extremely anisotropic ...

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6th european Congress on Computational methods in Applied Sciences and engineering, ECCOMAS 2012

作者： Van Es, Bram Koren, Barry De Blank, Hugo FOM Institute DIFFER - Dutch Institute for Fundamental Energy Research Edisonbaan 14 Nieuwegein Netherlands Centrum Wiskunde and Informatica Science Park 123 Amsterdam Netherlands Eindhoven University of Technology Den Dolech 2 Eindhoven Netherlands

ISBN: (纸本)9783950353709

In fusion plasmas there is extreme anisotropy due to the high temperature and large magnetic field strength. this causes diffusive processes, heat diffusion and energy/momentum loss due to viscous friction, to effectively be aligned with the magnetic field lines. this alignment leads to different values for the respective diffusive coefficients in the magnetic field direction and in the perpendicular direction, to the extent that heat diffusion coefficients can be up to 1012 times larger in the parallel direction than in the perpendicular direction. this anisotropy puts stringent requirements on the numerical methods used to approximate the MHD-equations since any misalignment of the grid may cause the perpendicular diffusion to be polluted by the numerical error in approximating the parallel diffusion. Currently the common approach is to apply magnetic field-aligned coordinates, an approach that automatically takes care of the directionality of the diffusive coefficients. this approach runs into problems in the case of crossing field lines, e.g., x-points and points where there is magnetic reconnection. It is therefore useful to consider numerical schemes that are more tolerant to the misalignment of the grid with the magnetic field lines, both to improve existing methods and to help open the possibility of applying regular non-aligned grids. To investigate this, several discretization schemes are applied to the unsteady anisotropic heat diffusion equation on a cartesian grid.

关键词： Diffusion

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numerical study on focusing of ultrasounds in microbubble-enhanced high intensity focused ultrasound therapy

Numerical study on focusing of ultrasounds in microbubble-en...

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6th european Congress on Computational methods in Applied Sciences and engineering, ECCOMAS 2012

作者： Okita, Kohei Takagi, Shu Matsumoto, Yoichiro Department of Mechanical Engineering College of Industrial Technology Nihon University 1-2-1 Izumi-cho Narashino Chiba 275-8575 Japan Department of Mechanical Engineering School of Engineering University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo 113-8654 Japan

ISBN: (纸本)9783950353709

the microbubble-enhanced high-intensity focused ultrasound (HIFU) therapy has been investigated through a numerical simulation. the equations for conservation of mass, momentum and energy are solved for a microbubble-infused mixture, and model HIFU therapy in the presence of microbubbles. the basic equations are discretized by finite difference method and are solved based on the FDTD method. the impacts of both the initial volume fraction and spatial distribution of microbubbles on the heat distribution are analyzed by using a two dimensional cylindrical simulation of the propagation of focused ultrasound (2.2MHz) through a mixture gel of bubbles 1.3μm in diameter. As the initial void fraction increased from 1×10-8 to 1×10-6, the temperature around a target increased due to the microbubble oscillation. However, at fG0=1×10-5, ultrasounds were too attenuated to heat the target. the heating region moved from the target to the transducer side. Next, the influence of spatial distributions of microbubbles on a localized heating was examined according to an experiment. the simulations could reproduce temperature rise distributions similar to those in the experimental observations. It was numerically confirmed that the localization of microbubble distribution was important to heat the target efficiently.

关键词： Spatial distribution

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Weakly enforced boundary conditions for the NURBS-based finite cell method

Weakly enforced boundary conditions for the NURBS-based fini...

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6th european Congress on Computational methods in Applied Sciences and engineering, ECCOMAS 2012

作者： Ruess, M. Bazilevs, Y. Schillinger, D. Zander, N. Rank, E. Department for Computation in Engineering Technische Universitt Mnchen Arcisstrasse 21 80333 Mnchen Germany Department of Structural Engineering University of California San Diego 9500 Gilman Drive San Diego CA 92093 United States Institute for Computational Engineering and Sciences University of Texas at Austin 201 East 24th Street Austin TX 78712 United States

ISBN: (纸本)9783950353709

In this paper, we present a variationally consistent formulation for the weak enforcement of essential boundary conditions as an extension to the finite cell method, a fictitious domain method of higher order. the absence of boundary fitted elements in fictitious domain or immersed boundary methods significantly restricts a strong enforcement of essential boundary conditions to models where the boundary of the solution domain coincides with the embedding analysis domain. Penalty methods and Lagrange multiplier methods are adequate means to overcome this limitation but often suffer from various drawbacks with severe consequences for a stable and accurate solution of the governing system of equations. In this contribution, we follow the idea of NITSCHE [29] who developed a stable scheme for the solution of the Laplace problem taking weak boundary conditions into account. An extension to problems from linear elasticity shows an appropriate behavior with regard to numerical stability, accuracy and an adequate convergence behavior. NURBS are chosen as a high-order approximation basis to benefit from their smoothness and flexibility in the process of uniform model refinement.

关键词： Boundary conditions

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numerical investigation of unsteady behavior of laminar separation bubble near stall conditions

Numerical investigation of unsteady behavior of laminar sepa...

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6th european Congress on Computational methods in Applied Sciences and engineering, ECCOMAS 2012

作者： Almutairi, Jaber H. AlQadi, Ibraheem M. College of Technological Studies Shuwaikh 70654 Kuwait King Abdulaziz University Jeddah 21589 Saudi Arabia

ISBN: (纸本)9783950353709

Large eddy simulation is performed to investigate the unsteady behavior of laminar separation bubble near stall conditions. the simulations is carried out for NACA-0012 airfoil at M∞ = 0.4, and Re = 50,000. Several angles of attack are considered within the low frequency range of 8.9° to 10° predicted by viscous-inviscid interaction. Near-stall low-frequency flow oscillation is captured. the self-sustained quasi-periodic oscillation is observed at several angles of attack. the bubble forming and bursting and the corresponding flow oscillations are in agreement with experimental observations. the oscillation frequency is found to dominate the flow field except in the wake region where no distinguishing frequency is observed. the current results represent the first successful large eddy simulation of bubble forming and bursting near stall conditions.

关键词： Large eddy simulation

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Developments in BEM-based finite element methods on polygonal and polyhedral meshes

Developments in BEM-based finite element methods on polygona...

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6th european Congress on Computational methods in Applied Sciences and engineering, ECCOMAS 2012

作者： Rjasanow, S. Weißer, S. Saarland University Campus Building E1.1 66041 Saarbrücken Germany

ISBN: (纸本)9783950353709

In the development of numerical methods for solving boundary value problems the requirement of flexible mesh handling gains more and more importance. the BEM-based finite element method is one of the new promising strategies which yields conforming approximations on polygonal and polyhedral meshes in 2D and 3D, respectively. For a two dimensional model problem the lowest order method is reviewed and extended with higher order basis functions on general meshes. these functions are defined implicitly as local solutions of the underlying homogeneous problem with constant coefficients. they are treated by means of boundary integral formulations and are approximated by the use of the boundary element methods in the numerics. Optimal rates of convergence can be proven with respect to the mesh size for the error measured in the H1- as well as the L2-norm in the case of uniform refinements for both, the lower and higher order method. Driven by applications with singular solutions for the BEM-based finite element method, the residual error estimate is stated which is reliable on polygonal meshes. A generalization to three space dimensions is discussed that copes with polyhedral elements having polygonal faces. All convergence rates for uniform and adaptive refinement in the two and three dimensional case are confirmed by numerical experiments.

关键词： Finite element method

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numerical analysis on asymmetrically combined glulam

Numerical analysis on asymmetrically combined glulam

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6th european Congress on Computational methods in Applied Sciences and engineering, ECCOMAS 2012

作者： Frese, Matthias Blaß, Hans J. Timber Structures and Building Construction R.-Baumeister-Platz 1 76131 Karlsruhe Germany

ISBN: (纸本)9783950353709

Glulam is used in particular as symmetrically combined glulam. Its cross section structure has lamellae of superior grade in the outer portions of the member and lamellae of lower grade in the inner one. Asymmetrically combined glulam (ACG), with lamellae of superior grade in the outer tension zone only, could be an economic alternative. However, the problem is the low nominal strength due to the minor strength class in the compression zone. Using a validated computer model the bending capacity of ACG is simulated. In doing so, the compressive stress is not limited by a nominal strength and, therefore, plastic strains are allowed to a certain extent. the influence of different cross section structures on the bending capacity is determined as well. Based on the results, the effective bending modulus of elasticity and the effective characteristic bending strength are calculated. Depending on the strength classes used in ACG, few lamellae of superior grade enhance the glulam strength significantly.

关键词： Bending strength

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Constitutive modelling of damage in adhesively bonded joints for static and cyclic sustained loadings with constant and variable amplitudes

Constitutive modelling of damage in adhesively bonded joints...

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6th european Congress on Computational methods in Applied Sciences and engineering, ECCOMAS 2012

作者： Matzenmiller, Anton Kroll, Ulrich University of Kassel Institute of Mechanics Department of Mechanical Engineering Mönchebergstraße 7 34125 Kassel Germany

ISBN: (纸本)9783950353709

In engineering structures with adhesively bonded joints, damage in the bonding layer takes place due to static and cyclic sustained loading as creep and fatigue damage. For the simulation of primary and secondary creep, a two-chain Maxwell model is used. A third chain is added to describe cyclic loading as well. In order to represent tertiary creep and damage due to fatigue, the viscoelastic model is combined with an additional damage approach, based on the effective stress concept, adapted to ductile adhesives. the creep and fatigue damage approach is based on a scalar damage variable driven by a suitable equivalent stress quantity in order to represent voidgrowth due to static and cyclic loading, respectively. For the numerical efficiency, the three-dimensional continuum theory is reduced to an interface model. As a result, the model predicts well the number of loading cycles up to fracture of a shear specimen in a test with combined static and cyclic loading as well as under an operating load.

关键词： Creep

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numerical simulations on piezoresistivity of nanofiller and polymer based nanocomposites

Numerical simulations on piezoresistivity of nanofiller and ...

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6th european Congress on Computational methods in Applied Sciences and engineering, ECCOMAS 2012

作者： Hu, B. Hu, N. Li, J. Alamusi Liu, Y. Ning, H. Wu, L. Chongqing University of Science and Technology Daxuecheng Chongqing 401331 China Chiba University 1-33 Yayoi Inage Chiba 263-8522 Japan

ISBN: (纸本)9783950353709

In this work, we propose a 3 dimensional (3D) resistor-network numerical model to predict the piezoresistivity behaviors of a nanocomposite material made from an insulating polymer filled by various conductive nanofillers, e.g., carbon nanotubes (CNTs) considered here. this material is very hopeful for its applications in highly sensitive resistance-type strain sensors by measuring its piezoresistivity, i.e., the resistance change ratio versus the applied strain. In this 3D numerical model, three main working mechanisms, which are wellknown to induce the piezoresistivity of the nanocomposite strain sensors to date, are considered. they are, a) the change of the internal conductive network formed by the CNTs;b) the tunneling effects among neighboring CNTs and c) the piezoresistivity of the CNTs themselves, respectively. Comparisons between the present numerical results with our previous experimental results are also performed to validate the present numerical model. the influence of the piezoresistivity of the CNTs on the piezoresistivity of the nanocomposite strain sensors is explored in detail by comparing it with the effects of the other two mechanisms. It is found that the main working mechanisms for the nanocomposite sensors should be the change of the internal conductive network and the tunneling effects. the contribution from the piezoresistivity of the CNTs to the total piezoresistivity of the nanocomposite sensors is very small.

关键词： Carbon nanotubes

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Generalised implementation of low-Mach preconditioning for arbitrary three-dimensional geometries (ECCOMAS 2012)

Generalised implementation of low-Mach preconditioning for a...

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6th european Congress on Computational methods in Applied Sciences and engineering, ECCOMAS 2012

作者： Fiedler, J. Di Mare, F. Linder Höhe 51147 Köln Germany

ISBN: (纸本)9783950353709

Turbomachinery flows involves a wide range of compressible and incompressible flow regimes. In the design process the application of various solvers for different flow speeds is cost- and time-intensive and mostly unattractive. therefore, low Mach preconditioning methods have become a powerful tool to improve the accuracy of the solution of the Navier-Stokes equations obtained by compressible solvers at low speeds, whilst accelerating convergence. Particulary in three-dimensional problems, such as in turbomachinery design practice preconditioning is an extremely difficult task, which has not been extensively treated in the literature. In this work an enhanced preconditioning method is presented in its full three-dimensional formulation and its implementation in the DLR-code TRACE discussed. Computations of classic academic testcases (e.g. GAMM bump series, flow in a cavity) are presented. the flow in a labyrinth seal of a LP gas turbine has also been investigated with excellent results, which will be also briefly illustrated.

关键词： numerical methods

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numerical investigation into mixed electroosmotic flow and pressure-driven flow in microchannels with wavy surfaces

Numerical investigation into mixed electroosmotic flow and p...

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6th european Congress on Computational methods in Applied Sciences and engineering, ECCOMAS 2012

作者： Cho, Ching-Chang Chang, Yu-Lin Liu, Kuo-Chi Department of Mechanical Engineering National Cheng Kung University Tainan Taiwan Department of Mechanical Engineering Far East University Tainan Taiwan

ISBN: (纸本)9783950353709

numerical investigations are performed into the flow characteristics of various electrokinetically- and pressure-driven flows within microchannels with complex-wavy surfaces. Four different flows are considered, namely (i) pure electroosmotic flow;(ii) pure pressure-driven flow;(iii) mixed electroosmotic / pressure-driven flow with the two flows in the same direction;and (iv) mixed electroosmotic / pressure-driven flow with the two flows in the opposite direction. the results have shown that the flow characteristics of the pure electroosmotic flow are significantly different from those of the pure pressure-driven flow given the same microchannel configuration. Specifically, flow recirculations are formed in the pure pressure-driven flow, but are absent in the pure electroosmotic flow. For the mixed electroosmotic / pressure-driven flow with the two flows in the same direction, the electrokinetic driving force generates a sufficient momentum to overcome the viscous effect near the microchannel walls, and therefore suppresses the formation of recirculation structures. For the mixed electroosmotic / pressure-driven flow with the two flows in the opposite direction, flow recirculations are induced near the wave crest rather those generated near the wave trough under pure pressure-driven flow conditions.

关键词： Microchannels

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