Relevant bibliographies by topics / Viscosity approximation methods

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Viscosity approximation methods'

Author: Grafiati
Published: 3 June 2025
Last updated: 13 July 2025

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Journal articles on the topic "Viscosity approximation methods"

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Xu, Hong-Kun. "Viscosity approximation methods for nonexpansive mappings." Journal of Mathematical Analysis and Applications 298, no. 1 (2004): 279–91. http://dx.doi.org/10.1016/j.jmaa.2004.04.059.

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Frimpong, K., and E. Prempeh. "Viscosity Approximation Methods in Reflexive Banach Spaces." British Journal of Mathematics & Computer Science 22, no. 2 (2017): 1–11. http://dx.doi.org/10.9734/bjmcs/2017/33396.

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Song, Yisheng, and Rudong Chen. "Viscosity approximation methods for nonexpansive nonself-mappings." Journal of Mathematical Analysis and Applications 321, no. 1 (2006): 316–26. http://dx.doi.org/10.1016/j.jmaa.2005.07.025.

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Wu, XianBing, and LeiNa Zhao. "Viscosity Approximation Methods for Multivalued Nonexpansive Mappings." Mediterranean Journal of Mathematics 13, no. 5 (2015): 2645–57. http://dx.doi.org/10.1007/s00009-015-0644-x.

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Lou, Jian, Li-juan Zhang, and Zhen He. "Viscosity approximation methods for asymptotically nonexpansive mappings." Applied Mathematics and Computation 203, no. 1 (2008): 171–77. http://dx.doi.org/10.1016/j.amc.2008.04.018.

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Moudafi, A. "Viscosity Approximation Methods for Fixed-Points Problems." Journal of Mathematical Analysis and Applications 241, no. 1 (2000): 46–55. http://dx.doi.org/10.1006/jmaa.1999.6615.

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K., Piesie Frimpong, and Prempeh E. "Viscosity Approximation Methods in Reflexive Banach Spaces." British Journal of Mathematics & Computer Science 22, no. 2 (2017): 1–11. https://doi.org/10.9734/BJMCS/2017/33396.

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In this paper, we study viscosity approximation methods in reflexive Banach spaces. Let X be a reflexive Banach space which admits a weakly sequentially continuous duality mapping <em>j : X → X<sup>*</sup>, C</em> a nonempty closed convex subset of <em>X, h<sub>n</sub></em>, where n ≥1 a sequence of contractions on C and Tn, n = 1; 2; 3; N, for N 2 N, a nite family of commuting nonexpansive mappings on C. We show that under appropriate conditions on n the explicit iterative sequence n de ned by n+1 = nhn(n) + (1 􀀀 n)Tnn; n 1; 1 2 C where n 2 (0; 1) converges strongly to a common xed point 2 NT k=1 Fk : We consequently show that the results is true for an in nite family Tn; n = 1; 2; 3; of commuting nonexpansive mapping on C.
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Ceng, Lu-Chuan, Ching-Feng Wen, and Chin-Tzong Pang. "Hierarchical Fixed Point Problems in Uniformly Smooth Banach Spaces." Abstract and Applied Analysis 2014 (2014): 1–15. http://dx.doi.org/10.1155/2014/173461.

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We propose some relaxed implicit and explicit viscosity approximation methods for hierarchical fixed point problems for a countable family of nonexpansive mappings in uniformly smooth Banach spaces. These relaxed viscosity approximation methods are based on the well-known viscosity approximation method and hybrid steepest-descent method. We obtain some strong convergence theorems under mild conditions.
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Kumari, Mandeep, and Renu Chugh. "Strong convergence for nonexpansive mappings by viscosity approximation methods in Hadamard manifolds." International Journal of Applied Mathematical Research 4, no. 2 (2015): 299. http://dx.doi.org/10.14419/ijamr.v4i2.4239.

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&lt;p&gt;In 2010, Victoria Martin Marquez studied a nonexpansive mapping in Hadamard manifolds using Viscosity approximation method. Our goal in this paper is to study the strong convergence of the Viscosity approximation method in Hadamard manifolds. Our results improve and extend the recent research in the framework of Hadamard manifolds.&lt;/p&gt;
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Aoyama, Koji, and Yasunori Kimura. "VISCOSITY APPROXIMATION METHODS WITH A SEQUENCE OF CONTRACTIONS." Cubo (Temuco) 16, no. 1 (2014): 09–20. http://dx.doi.org/10.4067/s0719-06462014000100002.

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Dissertations / Theses on the topic "Viscosity approximation methods"

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Sjösten, William, and Victor Vadling. "Finite Element Approximations of 2D Incompressible Navier-Stokes Equations Using Residual Viscosity." Thesis, Uppsala universitet, Institutionen för teknikvetenskaper, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-354590.

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Chorin’s method, Incremental Pressure Correction Scheme (IPCS) and Crank-Nicolson’s method (CN) are three numerical methods that were investigated in this study. These methods were here used for solving the incompressible Navier-Stokes equations, which describe the motion of an incompressible fluid, in three different benchmark problems. The methods were stabilized using residual based artificial viscosity, which was introduced to avoid instability. The methods were compared in terms of accuracy and computational time. Furthermore, a theoretical study of adaptivity was made, based on an a posteriori error estimate and an adjoint problem. The implementation of the adaptivity is left for future studies. In this study we consider the following three well-known benchmark problems: laminar 2D flow around a cylinder, Taylor-Green vortex and lid-driven cavity problem. The difference of the computational time for the three methods were in general relatively small and differed depending on which problem that was investigated. Furthermore the accuracy of the methods also differed in the benchmark problems, but in general Crank-Nicolson’s method gave less accurate results. Moreover the stabilization technique worked well when the kinematic viscosity of the fluid was relatively low, since it managed to stabilize the numerical methods. In general the solution was affected in a negative way when the problem could be solved without stabilization for higher viscosities.
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Debroux, Noémie. "Mathematical modelling of image processing problems : theoretical studies and applications to joint registration and segmentation." Thesis, Normandie, 2018. http://www.theses.fr/2018NORMIR02/document.

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Dans cette thèse, nous nous proposons d'étudier et de traiter conjointement plusieurs problèmes phares en traitement d'images incluant le recalage d'images qui vise à apparier deux images via une transformation, la segmentation d'images dont le but est de délimiter les contours des objets présents au sein d'une image, et la décomposition d'images intimement liée au débruitage, partitionnant une image en une version plus régulière de celle-ci et sa partie complémentaire oscillante appelée texture, par des approches variationnelles locales et non locales. Les relations étroites existant entre ces différents problèmes motivent l'introduction de modèles conjoints dans lesquels chaque tâche aide les autres, surmontant ainsi certaines difficultés inhérentes au problème isolé. Le premier modèle proposé aborde la problématique de recalage d'images guidé par des résultats intermédiaires de segmentation préservant la topologie, dans un cadre variationnel. Un second modèle de segmentation et de recalage conjoint est introduit, étudié théoriquement et numériquement puis mis à l'épreuve à travers plusieurs simulations numériques. Le dernier modèle présenté tente de répondre à un besoin précis du CEREMA (Centre d'Études et d'Expertise sur les Risques, l'Environnement, la Mobilité et l'Aménagement) à savoir la détection automatique de fissures sur des images d'enrobés bitumineux. De part la complexité des images à traiter, une méthode conjointe de décomposition et de segmentation de structures fines est mise en place, puis justifiée théoriquement et numériquement, et enfin validée sur les images fournies<br>In this thesis, we study and jointly address several important image processing problems including registration that aims at aligning images through a deformation, image segmentation whose goal consists in finding the edges delineating the objects inside an image, and image decomposition closely related to image denoising, and attempting to partition an image into a smoother version of it named cartoon and its complementary oscillatory part called texture, with both local and nonlocal variational approaches. The first proposed model addresses the topology-preserving segmentation-guided registration problem in a variational framework. A second joint segmentation and registration model is introduced, theoretically and numerically studied, then tested on various numerical simulations. The last model presented in this work tries to answer a more specific need expressed by the CEREMA (Centre of analysis and expertise on risks, environment, mobility and planning), namely automatic crack recovery detection on bituminous surface images. Due to the image complexity, a joint fine structure decomposition and segmentation model is proposed to deal with this problem. It is then theoretically and numerically justified and validated on the provided images
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Huang, Yun-ru, and 黃韻如. "Viscosity Approximation Methods for Generalized Equilibrium Problems and Fixed Point Problems." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/rrwzvc.

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碩士<br>國立中山大學<br>應用數學系研究所<br>96<br>The purpose of this paper is to investigate the problem of finding a common element of the set of solutions of a generalized equilibrium problem (for short, GEP) and the set of fixed points of a nonexpansive mapping in a Hilbert space. First, by using the well-known KKM technique we derive the existence and uniqueness of solutions of the auxiliary problems for the GEP. Second, on account of this result and Nadler''s theorem, we introduce an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of the GEP and the set of fixed points of the nonexpansive mapping. Furthermore, it is proven that the sequences generated by this iterative scheme converge strongly to a common element of the set of solutions of the GEP and the set of fixed points of the nonexpansive mapping.
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Book chapters on the topic "Viscosity approximation methods"

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Zaslavski, Alexander J. "Inexact Viscosity Approximation Methods in Hilbert Spaces." In Developments in Mathematics. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-70710-0_6.

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Dingping, Wu, and Xie Xuping. "Viscosity Approximation Methods for a Finite Family of Nonexpansive Non-Self-Mappings." In Proceedings of the 2012 International Conference on Communication, Electronics and Automation Engineering. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-31698-2_100.

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Öffner, Philipp. "Artificial Viscosity for SBP-FR Methods and the Construction of Fully Discrete Stable Schemes." In Approximation and Stability Properties of Numerical Methods for Hyperbolic Conservation Laws. Springer Fachmedien Wiesbaden, 2023. http://dx.doi.org/10.1007/978-3-658-42620-0_6.

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Popov, I. V., Yu A. Poveshchenko, and S. V. Polyakov. "Construction of Higher-Order Approximation Difference Scheme for Nonlinear Convection-Diffusion Equation Using Adaptive Artificial Viscosity in Case of Two-Phase Filtering Problems." In Finite Difference Methods. Theory and Applications. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11539-5_45.

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Deepho, Jitsupa, and Poom Kumam. "A Viscosity Approximation Method for the Split Feasibility Problems." In Transactions on Engineering Technologies. Springer Netherlands, 2014. http://dx.doi.org/10.1007/978-94-017-9588-3_6.

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Guermond, J. L., and R. Pasquetti. "Entropy Viscosity Method for High-Order Approximations of Conservation Laws." In Lecture Notes in Computational Science and Engineering. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-15337-2_39.

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Kumam, Poom, Somyot Plubtieng, and Phayap Katchang. "A New Viscosity Cesàro Mean Approximation Method for a General System of Finite Variational Inequalities and Fixed Point Problems in Banach Spaces." In Lecture Notes in Electrical Engineering. Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-94-007-7684-5_29.

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Miyake, Y., K. Tsujimoto, and Y. Kawanishi. "Performance of Eddy-viscosity Models for a Flow with Periodic Pressure Gradient." In Numerical Methods for Fluid Dynamics V. Oxford University PressOxford, 1996. http://dx.doi.org/10.1093/oso/9780198514800.003.0046.

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Abstract Modeling of turbulence is one of the most important problems in computational fluid dynamics of today. Although sharp rise of computer power is extending the possibility of doing turbulent flow prediction with large computational load such as LES, simulations based on Reynolds averaged equations, two-equation models in particular, are major in the practice of engineering. DNS database is a useful tool for validation of turbulence models including the group of k−ϵ c models. But since DNS can be applied only to simple canonical flows, it is needed to examine the validity of turbulence models more for a variety of complicated flows. Although test of turbulence model is mostly carried out in flows in which thin layer approximation is valid and as the consequence, problem is one-dimensional, but the flow fields in which two/three dimensional treatment is required should be tested.
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Tadmor, Eitan. "Super-viscosity and spectral approximations of nonlinear conservation laws." In Numerical Methods for Fluid Dynamics. Oxford University PressOxford, 1994. http://dx.doi.org/10.1093/oso/9780198536963.003.0005.

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Abstract Let PN stand for one of the standard spectral projections, such as Fourier, Chebyshev or Legendre. It is well known that such spectral projections, PNu , provide highly accurate approximations for sufficiently smooth u . This superior accuracy is destroyed if u contains discontinuities. Indeed, PNu produces 0(1) Gibbs oscillations in the local neighbourhoods of the discontinuities, and moreover, their global accuracy is deteriorated to first-order.
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Peraire, J., M. Vahdati, and J. Peiró. "The construction and behaviour of some unstructured grid algorithms for compressible flows." In Numerical Methods for Fluid Dynamics. Oxford University PressOxford, 1994. http://dx.doi.org/10.1093/oso/9780198536963.003.0014.

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Abstract The methods currently available for the solution of the equations of compressible flow have traditionally been classified as being of either centered or upwind type. Centered schemes are generally developed from the use of central difference type approximations to derivative operators [1], [2], [3], [4], [5]. Current upwind schemes, on the other hand, employ the solution of a one dimensional Riemann problem in the construction of the discrete form of the governing equations and are computationally more expensive [6], [7], [8], [9], [10]. Frequently, centered schemes rely on the explicit addition of artificial viscosity and this requires the empirical determination of the corresponding free parameters. Upwind methods are generally regarded as being parameter free.
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Conference papers on the topic "Viscosity approximation methods"

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Lin, Qiang. "Random Viscosity Approximation Methods for Nonexpansive Mappings in Banach Spaces." In 2009 International Workshop on Intelligent Systems and Applications. IEEE, 2009. http://dx.doi.org/10.1109/iwisa.2009.5073022.

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Wen, Dao-Jun, and Qian-Fen Gong. "Viscosity Approximation Methods for Asymptotically Nonexpansive Mappings in Banach Spaces." In 2011 International Conference on Intelligent Computation Technology and Automation (ICICTA). IEEE, 2011. http://dx.doi.org/10.1109/icicta.2011.85.

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Serna, Susana, Ilias Kotsireas, Roderick Melnik, and Brian West. "Analysis and numerical approximation of viscosity solutions with shocks: application to the plasma equation." In ADVANCES IN MATHEMATICAL AND COMPUTATIONAL METHODS: ADDRESSING MODERN CHALLENGES OF SCIENCE, TECHNOLOGY, AND SOCIETY. AIP, 2011. http://dx.doi.org/10.1063/1.3663455.

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Conrad, Daniel, Andreas Schneider, and Martin Böhle. "Numerical Investigation of an Extended Propeller Viscosimeter by Means of Lattice Boltzmann Methods." In ASME 2013 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/fedsm2013-16361.

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For the design of mixing and agitation facilities in process engineering it is of central importance to appraise the correct viscosity of fluids. This can be a challenging task when non-Newtonian and/or non-homogeneous fluids need to be processed. Since it is not always possible to analyze them in the classical ways, an propeller viscosimeter approach on the basis of the Rieger-Novak-Method is used. In recent years the Lattice Boltzmann Methods (LBM) are established as an alternative approach to classical computational fluid mechanics methods. The utilization of Cartesian grids avoids the need to discretize with boundary conform meshes. This makes the LBM suitable for complex geometries like a propeller in this case. Numerical simulations were carried out using a 3D in-house Lattice Boltzmann code called SAM-Lattice with our latest extension to non-Newtonian flow. We use a truncated form of the power-law approximation to accommodate the varying flow properties in non-Newtonian simulations, where the effective viscosity is a function of the shear rate. SAM-Lattice comprises the LBM solver and a highly automated grid generator for arbitrarily complex geometries. The code is capable of multi-domain grid refinement as well as multi reference frames and rotational boundaries. The post processing is done using an extension of the open source visualization tool Paraview. We compare results of experiments and LBM simulations for the Newtonian case (Glucose) to validate our Lattice Boltzmann solver. A study of the non-Newtonian, shear thinning case (Xanthan) is conducted to validate the generalized Newtonian model. The propeller viscosimeter is currently under development as a standalone solution for viscosity measurement. For calibration purposes the Metzner-Otto-constant of the propeller device has to be determined. While the constant is valid for the laminar region the numerical results for the agitator characteristics are presented. Different levels of grid refinement are tested to assure independence of the lattice resolutions.
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Saasen, Arild, Jan David Ytrehus, and Bjørnar Lund. "Annular Frictional Pressure Losses for Drilling Fluids." In ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/omae2020-18709.

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Abstract The most common viscosity models used in the drilling industry are the Bingham, the Power-Law and the Herschel-Bulkley models. In addition, it is common to refer to the low-shear yield-point. The scope of the present paper is to discuss numerical methods applicable for calculating annular frictional pressure losses. The topic of annular frictional pressure loss modelling has been treated in textbooks. None of these couple their models with the selection of viscosity data from measurements at the relevant shear rates. It is earlier shown how rotation of the inner string in an annulus can complicate the flow due to establishment of Taylor vortices. There are currently no analytical methods to handle such flow. The effect of the vortices depends strongly on the fluid’s composition in addition to the flow conditions. The practical way to handle these situations are by “fingerprinting” during circulation. In the paper examples will be presented showing how the Herschel-Bulkley fluid can be transferred to simple models for axial flow in an annulus where the inner cylinder does not rotate. It is common to use the narrow slot approximation. This method was used by Founargiotakis et al. In this paper both the modified Herschel-Bulkley model with dimensionless shear rates and the traditional model where the consistency depends on the shear rate will be presented. The dimensionless shear rate model can easily be translated back to the traditional form and vice-versa. Mathematical models will be presented. Hence a framework is given that is easier to use for digitalization and automation and in correlations including pressure, temperature and composition.
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Vetter, Daniel, Thomas Hagemann, and Hubert Schwarze. "Potentials and Limitations of an Extended Approximation Method for Nonlinear Dynamic Journal and Thrust Bearing Forces." In ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/gt2018-75662.

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Nonlinear dynamic journal bearing modeling within rotordynamic analyses requires the calculation of the nonlinear bearing forces particularly depending on shaft eccentricity and velocity. The bearing forces can be calculated properly using Reynolds differential equation and mass conserving cavitation algorithms, based for example on Elrod’s cavitation algorithm. This approach achieves high model accuracy and allows the consideration of additional effects like misalignment, variable viscosity and transient local oil distribution in the lubricant film. However, despite rising calculating capacity dynamic bearing analyses are still very CPU-time consuming and, consequently, approximation methods are commonly applied in multibody or rotordynamic analyses, especially in day-to-day business. While many approximation procedures are limited to special bearing geometries Glienicke et al. describe a method which is flexible to model different journal bearing geometries, as well as to consider many additional effects like oil supply pressure or starved lubrication conditions in a time averaged manner. It can be applied for both fixed-pad and tilting-pad journal bearings and its characteristic data is included in an a priori calculated map enabling a time-efficient call up of characteristic parameters of the bearing forces from a look-up table in dynamic simulations. Further, the data can be transferred to any other bearing if the requirements of the theory of similarity are supposed to be valid. In this investigation, the method is first successfully extended by the authors to consider misalignment. Secondly, the general idea of the procedure is transferred and applied to thrust bearings in order to enable a six degree of freedom rotordynamic modeling. In case of a simply lateral movement and rotation-symmetric bearing design the procedure is simple, though, in case of tilting movements it becomes more complicated. A misaligned thrust bearing provides tilting and cross-coupling moments. Cross coupling moments are smaller than the main moments, but have similar orders of magnitude and should therefore be considered. Strategies are investigated for a proper approximation of the nonlinear thrust bearing main and cross-coupling forces and moments. All steps are verified using a direct solution of Reynolds differential equation based on an extended mass conserving algorithm adapted from Elrod’s numerical implementation for the stationary case. Finally, the whole procedure and its application to rotordynamic analysis is verified by comparisons with results gained using direct online solution of Reynolds equation in rotordynamic simulation. While good simulation quality of this approximation approach is documented for selected rotor-bearing-systems in literature the range of validity is not clearly defined. Here, the influences of different parameters on the simulation error are investigated conducting different variation calculations for an overhung rotor with documented vibrational behavior from literature. It is shown that the simulation quality depends on the cavitation zone and decreases with rising vibrational velocity. The root cause for this upcoming error and a possible modification for the elimination of this limitation are presented.
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Amador, Carolina, Matthew W. Urban, Shigao Chen, and James F. Greenleaf. "Acoustic Radiation Force Creep and Shear Wave Propagation Method for Elasticity Imaging." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-87622.

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Elasticity imaging methods have been used to study tissue mechanical properties and have demonstrated that tissue elasticity changes with disease state. Quantitative mechanical properties can be measured in a model independent manner if both shear wave speed and attenuation are known. However, measuring shear wave speed attenuation is challenging in the field of elasticity imaging. Typically, only shear wave speed is measured and rheological models, such as Kelvin-Voigt, Maxwell and Standard Linear Solid, are used to solve for shear viscoelastic complex modulus. Acoustic radiation force has been used to study quasi-static viscoelastic properties of tissue during creep and relaxation conditions, however, as with shear wave propagation methods, a rheological model needs to be fit to the creep or relaxation experimental data to solve for viscoelastic parameters. This paper presents a method to quantify viscoelastic properties in a model-independent way by estimating complex shear elastic modulus over a wide frequency range using time-dependent creep response induced by acoustic radiation force. The acoustic radiation force induced creep (RFIC) method uses a conversion formula that is the analytic solution of the constitutive equation relating time dependent stress and time dependent strain. The RFIC method in combination with shear wave propagation is used to measure the complex shear modulus so that knowledge of the applied radiation force magnitude is not necessary. Numerical simulation of creep strain and compliance using the Kelvin-Voigt model shown that the conversion formula is sensitive to sampling frequency, the first reliable measure in time and the long term viscosity approximation. Experimental data are obtained in homogeneous tissue mimicking phantoms and excised swine kidneys.
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Da Fies, G., D. Peck, M. Dutko, and G. Mishuris. "On Averaging of Toughness Heterogeneity When Modelling Hydraulic Fracture Evolution." In 56th U.S. Rock Mechanics/Geomechanics Symposium. ARMA, 2022. http://dx.doi.org/10.56952/arma-2022-2135.

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ABSTRACT: In this paper we describe various approaches used to capture heterogeneity within the reservoir undergoing hydraulic fracturing treatment and their implication on modelling of fracture propagation. In highly laminated reservoirs with soft and/or weak layers, capturing heterogeneity at an appropriate resolution is the key for successful prediction fracture growth and other crucial treatment parameters. Our focus is on studying several strategies to average fracture toughness and assess their suitability for use in advanced computational methods such as FE/BEM. In practice the well log and petrophysical data deduced from various measurements and observations are upscaled and/or homogenized to the spatial approximation size. The fracture toughness is one of the most delicate physical parameters and application of the homogenization techniques are rather uncertain, hence any proposed averaging will depend on process conditions and the toughness distribution. We propose and analyse a notion of an average toughness and show that it is a process dependent variable and provide some recommendations how to implement the defined measure into the numerical modelling. As an example, we use periodic distributions and consider model without leak off that allows us straightforward handling different regimes (toughness/viscosity). 1. INTRODUCTION Typically, when using computational methods such as Finite Element Method, the well log and petrophysical data obtained from various measurements and observations are upscaled and/or "homogenized" to the element size. From all in-situ parameters, toughness is one of the most delicate physical parameters to handle, as application of the homogenization techniques are rather questionable here as commented on by Caiulo and Kachanov (2010) and Kachanos (1994). Compared to other types of fracture evolution, hydraulic fracturing is probably the most stable crack propagation process and thus, fortunately, some estimates can be provided here. We estimate errors introduced by various strategies to incorporate heterogeneous fracture toughness into numerical modelling (Dontsov and Suarez-Rivera (2021), Da Fies et al. (2021)). We use periodic distributions and consider model without leak off that allows us straightforward handling different regimes (toughness/viscosity). For the simulations, we use an extremely effective in house-built time – space adaptive solver utilizing main ideas from those reported by Wrobel and Mishuris (2015). The solver is capable to compute rather arbitrary distribution of the toughness.
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Yang, Jinguang, Yan Liu, Xiaofang Wang, and Hu Wu. "3D Viscous Inverse Design of Turbomachinery Using One-Equation Turbulence Model." In ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/gt2016-56332.

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Inverse method is a very efficient method in turbomachinery aerodynamic design. It takes blade aerodynamic loading as input, and the blade shape and the flow field are computed when calculation converged. However most current inverse methods model turbulent eddy viscosity by Baldwin-Lomax (BL) model or similar approximation, which does not involve local wall distance as a model parameter. Most one- and two-equation turbulence models are not that case, and local wall distance is needed in turbulent work variable(s) transport equation formulation. The usual wall distance computing procedure is the so called “exhaustive search method”, which is a time-consuming process. When a flow solver running in analysis mode, the wall distance calculation is not a problem, it can be computed once and stored for subsequent use. But for design mode, this computation intensive process becomes a big challenge. For an inverse design run, the blade shape is updated periodically for about 400 times, if wall distances is re-computed for each blade shape update, the time cost is very appreciable. That is the reason that prohibits the application of higher order (one- and two-equation, compared to BL model) turbulence models in inverse method. In this paper, a novel wall distance calculation method is proposed. The new method transforms the distance searching problem into a length optimization problem, and the steepest descent method is used to find the minimal length from a target point to a wall face. Numerical experiments show that the method can reduce the computing time to approximately 1/10 of the exhaustive search method. Based on this, together with an enhanced blade update method and Spalart-Allmaras turbulence model, a 3D viscous redesign of an axial fan rotor is conducted. Final results demonstrate the effectivity of the proposed method.
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Ouazzi, Abderrahim, Naheed Begum, and Stefan Turek. "Monolithic Finite Element Method for the simulation of thixo-viscoplastic flows." In VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València, 2021. http://dx.doi.org/10.4995/yic2021.2021.12250.

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This talk is concerned with the application of Finite Element Method (FEM) and Newton-Multigrid solver to simulate thixotropic flows.The thixotropy phenomena are introduced to yield stress material by taking into consideration the internal material micro structure using a structure parameter. Firstly, the viscoplastic stress is modified to include the thixotropic stress dependent on the structure parameter. Secondly, an evolution equation for the structure parameter is introduced to induce the time-dependent processof competition between the destruction (breakdown) and the construction (buildup) inhabited in the material. Substantially, this is done simply by introducing a structure-parameter-dependentviscosity into the rheological model for yield stress material, as for instance the Houska model based on a viscosity approach for the Bingham model [2].The modified viscoplastic stress w.r.t. the structure parameter which is integrated, in quasi-Newtonian manner or lagrangian multiplier manner, into the generalized Navier-Stokes equations and the evolution equation for the structure parameter constitutes the main core of full set of mod-eling equations, which are creditable as the privilege answer to incorporate thixotropy phenomena.The nonlinearity of the problem, related to the dependency of the diffusive stress on the material parameters, is treated with generalized Newton’s method w.r.t. the Jacobian’s singularities having a global convergence property. The linearized systems inside the outer Newton loops are solvedusing the geometrical multigrid methods with a Vanka-like smoother taking into account a stable FEM approximation pair for velocity and pressure with discontinuous pressure and biquadratic velocity spaces.We analyze the accuracy, robustness and efficiency of the Newton-Multigrid FEM solver [1] throughout the solution of thixotropic flow problems of benchmarking character in channel and Couette device [3].
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