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J. Málek
Charles University, Faculty of Mathematics and Physics, Mathematical Institute, Sokolovská 83, Prague 186 75, Czech Republic

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Journal article
Published: 11 February 2021 in Applications in Engineering Science
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We consider flows of an incompressible Navier-Stokes fluid in a tubular domain with Navier’s slip boundary condition imposed on the impermeable wall. We focus on several implementational issues associated with this type of boundary conditions within the framework of the standard Taylor-Hood mixed finite element method and present the computational results for flows in a tubular domain of finite length with one inlet and one outlet. In particular, we present the details regarding variants of the Nitsche method concerning the incorporation of the impermeability condition on the wall. We also find that the manner in which the normal to the boundary is numerically implemented influences the nature of the computational results. As a benchmark, we set up steady flows in a tube of finite length and compare the computational results with the analytical solutions. Finally, we identify various quantities of interest, such as the dissipation, wall shear stress, vorticity, pressure drop, and provide their precise mathematical definitions. We document how well these quantities are computationally approximated in the case of the benchmark. Although the geometry of the benchmark is simple, the correct computational results require careful selection of numerical methods and surprisingly non-trivial computational resources. Our goal is to test, using the setting with a known analytical solution, a robust computational tool that would be suitable for computations on real complex geometries that have relevance to problems in engineering and medicine. The model parameters in our computations are chosen based on flows in large arteries.

ACS Style

R. Chabiniok; J. Hron; A. Jarolímová; J. Málek; K.R. Rajagopal; H. Švihlová; K. Tůma. A benchmark problem to evaluate implementational issues for three-dimensional flows of incompressible fluids subject to slip boundary conditions. Applications in Engineering Science 2021, 6, 100038 .

AMA Style

R. Chabiniok, J. Hron, A. Jarolímová, J. Málek, K.R. Rajagopal, H. Švihlová, K. Tůma. A benchmark problem to evaluate implementational issues for three-dimensional flows of incompressible fluids subject to slip boundary conditions. Applications in Engineering Science. 2021; 6 ():100038.

Chicago/Turabian Style

R. Chabiniok; J. Hron; A. Jarolímová; J. Málek; K.R. Rajagopal; H. Švihlová; K. Tůma. 2021. "A benchmark problem to evaluate implementational issues for three-dimensional flows of incompressible fluids subject to slip boundary conditions." Applications in Engineering Science 6, no. : 100038.

Article
Published: 28 November 2020 in Zeitschrift für angewandte Mathematik und Physik
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We investigate mathematical properties of the system of nonlinear partial differential equations that describe, under certain simplifying assumptions, evolutionary processes in water-saturated granular materials. The unconsolidated solid matrix behaves as an ideal plastic material before the activation takes place and then it starts to flow as a Newtonian or a generalized Newtonian fluid. The plastic yield stress is non-constant and depends on the difference between the given lithostatic pressure and the pressure of the fluid in a pore space. We study unsteady three-dimensional flows in an impermeable container, subject to stick-slip boundary conditions. Under realistic assumptions on the data, we establish long-time and large-data existence theory.

ACS Style

Anna Abbatiello; Miroslav Bulíček; Tomáš Los; Josef Málek; Ondřej Souček. On unsteady flows of pore pressure-activated granular materials. Zeitschrift für angewandte Mathematik und Physik 2020, 72, 1 -18.

AMA Style

Anna Abbatiello, Miroslav Bulíček, Tomáš Los, Josef Málek, Ondřej Souček. On unsteady flows of pore pressure-activated granular materials. Zeitschrift für angewandte Mathematik und Physik. 2020; 72 (1):1-18.

Chicago/Turabian Style

Anna Abbatiello; Miroslav Bulíček; Tomáš Los; Josef Málek; Ondřej Souček. 2020. "On unsteady flows of pore pressure-activated granular materials." Zeitschrift für angewandte Mathematik und Physik 72, no. 1: 1-18.

Journal article
Published: 11 August 2020 in Fluids
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We revisit some classical models for dilute polymeric fluids, and we show that thermodynamically consistent models for non-isothermal flows of these fluids can be derived in a very elementary manner. Our approach is based on the identification of energy storage mechanisms and entropy production mechanisms in the fluid of interest, which, in turn, leads to explicit formulae for the Cauchy stress tensor and for all of the fluxes involved. Having identified these mechanisms and derived the governing equations, we document the potential use of the thermodynamic basis of the model in a rudimentary stability analysis. In particular, we focus on finite amplitude (nonlinear) stability of a stationary spatially homogeneous state in a thermodynamically isolated system.

ACS Style

Mark Dostalík; Josef Málek; Vít Průša; Endre Süli. A Simple Construction of a Thermodynamically Consistent Mathematical Model for Non-Isothermal Flows of Dilute Compressible Polymeric Fluids. Fluids 2020, 5, 133 .

AMA Style

Mark Dostalík, Josef Málek, Vít Průša, Endre Süli. A Simple Construction of a Thermodynamically Consistent Mathematical Model for Non-Isothermal Flows of Dilute Compressible Polymeric Fluids. Fluids. 2020; 5 (3):133.

Chicago/Turabian Style

Mark Dostalík; Josef Málek; Vít Průša; Endre Süli. 2020. "A Simple Construction of a Thermodynamically Consistent Mathematical Model for Non-Isothermal Flows of Dilute Compressible Polymeric Fluids." Fluids 5, no. 3: 133.

Journal article
Published: 01 January 2020 in SIAM Journal on Mathematical Analysis
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In the first part of the paper we provide a new classification of incompressible fluids characterized by a continuous monotone relation between the velocity gradient and the Cauchy stress. The considered class includes Euler fluids, Navier--Stokes fluids, classical power-law fluids as well as stress power-law fluids, and their various generalizations including the fluids that we refer to as activated fluids, namely, fluids that behave as an Euler fluid prior activation and behave as a viscous fluid once activation takes place. We also present a classification concerning boundary conditions that are viewed as the constitutive relations on the boundary. In the second part of the paper, we develop a robust mathematical theory for activated Euler fluids associated with different types of the boundary conditions ranging from no-slip to free-slip and include Navier's slip as well as stick-slip. Both steady and unsteady flows of such fluids in three-dimensional domains are analyzed.

ACS Style

Jan Blechta; Josef Málek; K. R. Rajagopal. On the Classification of Incompressible Fluids and a Mathematical Analysis of the Equations That Govern Their Motion. SIAM Journal on Mathematical Analysis 2020, 52, 1232 -1289.

AMA Style

Jan Blechta, Josef Málek, K. R. Rajagopal. On the Classification of Incompressible Fluids and a Mathematical Analysis of the Equations That Govern Their Motion. SIAM Journal on Mathematical Analysis. 2020; 52 (2):1232-1289.

Chicago/Turabian Style

Jan Blechta; Josef Málek; K. R. Rajagopal. 2020. "On the Classification of Incompressible Fluids and a Mathematical Analysis of the Equations That Govern Their Motion." SIAM Journal on Mathematical Analysis 52, no. 2: 1232-1289.

Journal article
Published: 21 October 2019 in Nonlinearity
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We develop a mathematical theory for a class of compressible viscoelastic rate-type fluids with stress diffusion. Our approach is based on the concepts used in the nowadays standard theory of compressible Newtonian fluids as renormalization, effective viscous flux identity, compensated compactness. The presence of the extra stress, however, requires substantial modification of these techniques, in particular, a new version of the effective viscous flux identity is derived. With help of these tools, we show the existence of global-in-time weak solutions for any finite energy initial data.

ACS Style

Miroslav Bulíček; Eduard Feireisl; Josef Málek. On a class of compressible viscoelastic rate-type fluids with stress-diffusion. Nonlinearity 2019, 32, 4665 -4681.

AMA Style

Miroslav Bulíček, Eduard Feireisl, Josef Málek. On a class of compressible viscoelastic rate-type fluids with stress-diffusion. Nonlinearity. 2019; 32 (12):4665-4681.

Chicago/Turabian Style

Miroslav Bulíček; Eduard Feireisl; Josef Málek. 2019. "On a class of compressible viscoelastic rate-type fluids with stress-diffusion." Nonlinearity 32, no. 12: 4665-4681.

Journal article
Published: 18 July 2019 in Entropy
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Thermodynamical arguments are known to be useful in the construction of physically motivated Lyapunov functionals for nonlinear stability analysis of spatially homogeneous equilibrium states in thermodynamically isolated systems. Unfortunately, the limitation to isolated systems is essential, and standard arguments are not applicable even for some very simple thermodynamically open systems. On the other hand, the nonlinear stability of thermodynamically open systems is usually investigated using the so-called energy method. The mathematical quantity that is referred to as the “energy” is, however, in most cases not linked to the energy in the physical sense of the word. Consequently, it would seem that genuine thermo-dynamical concepts are of no use in the nonlinear stability analysis of thermodynamically open systems. We show that this is not the case. In particular, we propose a construction that in the case of a simple heat conduction problem leads to a physically well-motivated Lyapunov type functional, which effectively replaces the artificial Lyapunov functional used in the standard energy method. The proposed construction seems to be general enough to be applied in complex thermomechanical settings.

ACS Style

Miroslav Bulíček; Josef Málek; Vít Průša. Thermodynamics and Stability of Non-Equilibrium Steady States in Open Systems. Entropy 2019, 21, 704 .

AMA Style

Miroslav Bulíček, Josef Málek, Vít Průša. Thermodynamics and Stability of Non-Equilibrium Steady States in Open Systems. Entropy. 2019; 21 (7):704.

Chicago/Turabian Style

Miroslav Bulíček; Josef Málek; Vít Průša. 2019. "Thermodynamics and Stability of Non-Equilibrium Steady States in Open Systems." Entropy 21, no. 7: 704.

Journal article
Published: 09 May 2019 in Nonlinear Analysis: Real World Applications
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Kolmogorov seems to have been the first to recognize that a two-equation model of turbulence might be used as the basis of turbulent flow prediction. Nowadays, a whole hierarchy of phenomenological two-equation models of turbulence is in place. The structure of their governing equations is similar to the Navier–Stokes equations for incompressible fluids, the difference is that the viscosity is not constant but depends on two scalar quantities that measure the effect of turbulence: the average of the kinetic energy of velocity fluctuations (i.e. the turbulent energy) and the measure related to the length scales of turbulence. For these two scalar quantities two additional evolutionary convection–diffusion equations are added to the generalized Navier–Stokes system. Although Kolmogorov’s model has so far been almost unnoticed, it exhibits interesting features. First of all, in contrast to other two-equation models of turbulence, there is no source term in the equation for the frequency. Consequently, nonhomogeneous Dirichlet boundary conditions for the quantities measuring the effect of turbulence are assigned to a part of the boundary. Second, the structure of the governing equations is such that one can find an “equivalent” reformulation of the equation for turbulent energy that eliminates the presence of the energy dissipation acting as the source in the original equation for turbulent energy and which is merely an L1 quantity. Third, the material coefficients such as the viscosity and turbulent diffusivities may degenerate, and thus the a priori control of the derivatives of the quantities involved is unclear. We establish long-time and large-data existence of a suitable weak solution to three-dimensional internal unsteady flows described by Kolmogorov’s two-equation model of turbulence. The governing system of equations is completed by initial and boundary conditions; concerning the velocity we consider generalized stick–slip boundary conditions. The fact that the admissible class of boundary conditions includes various types of slipping mechanisms on the boundary makes the result robust from the point of view of possible applications.

ACS Style

Miroslav Bulíček; Josef Málek. Large data analysis for Kolmogorov’s two-equation model of turbulence. Nonlinear Analysis: Real World Applications 2019, 50, 104 -143.

AMA Style

Miroslav Bulíček, Josef Málek. Large data analysis for Kolmogorov’s two-equation model of turbulence. Nonlinear Analysis: Real World Applications. 2019; 50 ():104-143.

Chicago/Turabian Style

Miroslav Bulíček; Josef Málek. 2019. "Large data analysis for Kolmogorov’s two-equation model of turbulence." Nonlinear Analysis: Real World Applications 50, no. : 104-143.

Journal article
Published: 19 March 2019 in International Journal of Engineering Science
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We derive a thermodynamically consistent model of heterogeneous catalysis for chemically reacting fluid mixtures formulated in the framework of continuum thermodynamics. The model takes into account standard transport phenomena in the bulk domain and involves mass transfer of the species between the bulk and the catalytic (active) part of the boundary where the surface counterparts to the bulk transport processes take place. Concerning the balance laws on the catalytic surface, the model benefits from description of the active part of the boundary as an interface between the bulk domain and its exterior which allows to employ the framework of continuum mechanics with interfacial transport phenomena. The constitutive relations involving vectorial and tensorial quantities such as the Cauchy stress, energy and entropy fluxes and diffusive fluxes relevant to individual constituents are constructed in a systematic manner ensuring compatibility with the second law of thermodynamics. The constitutive procedure follows from the specification of constitutive equations for suitable thermodynamic potentials (free energies) of the mixture in the bulk and on the active part of the boundary and from the identification of the bulk and surface entropy productions. The active part of the boundary is described by means of statistical physics and this description then serves as a building block for the derivation of surface continuum thermodynamic potentials. The derived model is suitable for further mathematical, numerical and computational analysis of relevant initial and boundary value problems. While the model employs a relatively simple description of the active part of the boundary as a monolayer lattice with single-site Langmuir-type adsorption, its detailed derivation presented here provides clear guidelines for the incorporation of other sorption models.

ACS Style

Ondřej Souček; Vít Orava; Josef Málek; Dieter Bothe. A continuum model of heterogeneous catalysis: Thermodynamic framework for multicomponent bulk and surface phenomena coupled by sorption. International Journal of Engineering Science 2019, 138, 82 -117.

AMA Style

Ondřej Souček, Vít Orava, Josef Málek, Dieter Bothe. A continuum model of heterogeneous catalysis: Thermodynamic framework for multicomponent bulk and surface phenomena coupled by sorption. International Journal of Engineering Science. 2019; 138 ():82-117.

Chicago/Turabian Style

Ondřej Souček; Vít Orava; Josef Málek; Dieter Bothe. 2019. "A continuum model of heterogeneous catalysis: Thermodynamic framework for multicomponent bulk and surface phenomena coupled by sorption." International Journal of Engineering Science 138, no. : 82-117.

Article
Published: 26 February 2019 in Journal of Elasticity
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In this paper we study the deformation of a body with a notch subject to an anti-plane state of stress within the context of a new class of elastic models. These models stem as approximations of constitutive response functions for an elastic body that is defined within the context of an implicit constitutive relation between the stress and the deformation gradient. Gum metal and many metallic alloys are described well by such constitutive relations. We consider the state of anti-plane stress of a body with a smoothened V-notch within the context of constitutive relations for the linearized strain in terms of a power-law for the stretch. The problem is solved numerically and the convergence and the stability of the solution is studied.

ACS Style

Vojtěch Kulvait; Josef Málek; K. R. Rajagopal. The State of Stress and Strain Adjacent to Notches in a New Class of Nonlinear Elastic Bodies. Journal of Elasticity 2019, 135, 375 -397.

AMA Style

Vojtěch Kulvait, Josef Málek, K. R. Rajagopal. The State of Stress and Strain Adjacent to Notches in a New Class of Nonlinear Elastic Bodies. Journal of Elasticity. 2019; 135 (1-2):375-397.

Chicago/Turabian Style

Vojtěch Kulvait; Josef Málek; K. R. Rajagopal. 2019. "The State of Stress and Strain Adjacent to Notches in a New Class of Nonlinear Elastic Bodies." Journal of Elasticity 135, no. 1-2: 375-397.

Original paper
Published: 16 February 2019 in Acta Mechanica
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We propose a numerical scheme for simulation of transient flows of incompressible non-Newtonian fluids characterised by a non-monotone relation between the symmetric part of the velocity gradient (shear rate) and the Cauchy stress tensor (shear stress). The main difficulty in dealing with the governing equations for flows of such fluids is that the non-monotone constitutive relation allows several values of the stress to be associated with the same value of the symmetric part of the velocity gradient. This issue is handled via a reformulation of the governing equations. The equations are reformulated as a system for the triple pressure–velocity–apparent viscosity, where the apparent viscosity is given by a scalar implicit equation. We prove that the proposed numerical scheme has—on the discrete level—a solution, and using the proposed scheme, we numerically solve several flow problems.

ACS Style

Adam Janečka; Josef Malek; Vít Průša; Giordano Tierra. Numerical scheme for simulation of transient flows of non-Newtonian fluids characterised by a non-monotone relation between the symmetric part of the velocity gradient and the Cauchy stress tensor. Acta Mechanica 2019, 230, 729 -747.

AMA Style

Adam Janečka, Josef Malek, Vít Průša, Giordano Tierra. Numerical scheme for simulation of transient flows of non-Newtonian fluids characterised by a non-monotone relation between the symmetric part of the velocity gradient and the Cauchy stress tensor. Acta Mechanica. 2019; 230 (3):729-747.

Chicago/Turabian Style

Adam Janečka; Josef Malek; Vít Průša; Giordano Tierra. 2019. "Numerical scheme for simulation of transient flows of non-Newtonian fluids characterised by a non-monotone relation between the symmetric part of the velocity gradient and the Cauchy stress tensor." Acta Mechanica 230, no. 3: 729-747.

Journal article
Published: 26 September 2018 in Fluids
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Viscoelastic rate-type fluid models involving the stress and frame-indifferent time derivatives of second order, like those in Burgers’ model, are used to describe the complicated response of fluid like materials that are endowed with a complex microstructure that allows them to possess two different relaxation mechanisms as well as other non-Newtonian characteristics. Such models are used in geomechanics, biomechanics, chemical engineering and material sciences. We show how to develop such rate-type fluid models that include the classical Burgers’ model as well as variants of Burgers’ model, using a thermodynamic approach based on constitutive assumptions for two scalar quantities (namely, how the material stores energy and how the energy is dissipated) and appealing to the concept of natural configuration associated with the placement of the body that evolves as the body deforms.

ACS Style

Josef Málek; Kumbakonam R. Rajagopal; Karel Tůma. Derivation of the Variants of the Burgers Model Using a Thermodynamic Approach and Appealing to the Concept of Evolving Natural Configurations. Fluids 2018, 3, 69 .

AMA Style

Josef Málek, Kumbakonam R. Rajagopal, Karel Tůma. Derivation of the Variants of the Burgers Model Using a Thermodynamic Approach and Appealing to the Concept of Evolving Natural Configurations. Fluids. 2018; 3 (4):69.

Chicago/Turabian Style

Josef Málek; Kumbakonam R. Rajagopal; Karel Tůma. 2018. "Derivation of the Variants of the Burgers Model Using a Thermodynamic Approach and Appealing to the Concept of Evolving Natural Configurations." Fluids 3, no. 4: 69.

Preprint
Published: 14 September 2018
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ACS Style

Anna Abbatiello; Tomáš Los; Josef Málek; Ondřej Souček. On three-dimensional flows of pore pressure activated Bingham fluids. 2018, 1 .

AMA Style

Anna Abbatiello, Tomáš Los, Josef Málek, Ondřej Souček. On three-dimensional flows of pore pressure activated Bingham fluids. . 2018; ():1.

Chicago/Turabian Style

Anna Abbatiello; Tomáš Los; Josef Málek; Ondřej Souček. 2018. "On three-dimensional flows of pore pressure activated Bingham fluids." , no. : 1.

Book chapter
Published: 06 April 2018 in Handbook of Mathematical Analysis in Mechanics of Viscous Fluids
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The chapter starts with overview of the derivation of the balance equations for mass, momentum, angular momentum, and total energy, which is followed by a detailed discussion of the concept of entropy and entropy production. While the balance laws are universal for any continuous medium, the particular behavior of the material of interest must be described by an extra set of material-specific equations. These equations relating, for example, the Cauchy stress tensor and the kinematical quantities are called the constitutive relations. The core part of the chapter is devoted to the presentation of a modern thermodynamically based phenomenological theory of constitutive relations. The key feature of the theory is that the constitutive relations stem from the choice of two scalar quantities, the internal energy and the entropy production. This is tantamount to the proposition that the material behavior is fully characterized by the way it stores the energy and produces the entropy. The general theory is documented by several examples of increasing complexity. It is shown how to derive the constitutive relations for compressible and incompressible viscous heat-conducting fluids (Navier-Stokes-Fourier fluid), Korteweg fluids, and compressible and incompressible heat-conducting viscoelastic fluids (Oldroyd-B and Maxwell fluid).

ACS Style

Josef Málek; Vít Průša. Derivation of Equations for Continuum Mechanics and Thermodynamics of Fluids. Handbook of Mathematical Analysis in Mechanics of Viscous Fluids 2018, 3 -72.

AMA Style

Josef Málek, Vít Průša. Derivation of Equations for Continuum Mechanics and Thermodynamics of Fluids. Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. 2018; ():3-72.

Chicago/Turabian Style

Josef Málek; Vít Průša. 2018. "Derivation of Equations for Continuum Mechanics and Thermodynamics of Fluids." Handbook of Mathematical Analysis in Mechanics of Viscous Fluids , no. : 3-72.

Journal article
Published: 01 February 2018 in Physics of Fluids
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We propose thermodynamically consistent models for viscoelastic fluids with a stress diffusion term. In particular, we derive variants of compressible/incompressible Maxwell/Oldroyd-B models with a stress diffusion term in the evolution equation for the extra stress tensor. It is shown that the stress diffusion term can be interpreted either as a consequence of a nonlocal energy storage mechanism or as a consequence of a nonlocal entropy production mechanism, while different interpretations of the stress diffusion mechanism lead to different evolution equations for the temperature. The benefits of the knowledge of the thermodynamical background of the derived models are documented in the study of nonlinear stability of equilibrium rest states. The derived models open up the possibility to study fully coupled thermomechanical problems involving viscoelastic rate-type fluids with stress diffusion.

ACS Style

Josef Málek; Vít Průša; Tomáš Skřivan; Endre Süli. Thermodynamics of viscoelastic rate-type fluids with stress diffusion. Physics of Fluids 2018, 30, 023101 .

AMA Style

Josef Málek, Vít Průša, Tomáš Skřivan, Endre Süli. Thermodynamics of viscoelastic rate-type fluids with stress diffusion. Physics of Fluids. 2018; 30 (2):023101.

Chicago/Turabian Style

Josef Málek; Vít Průša; Tomáš Skřivan; Endre Süli. 2018. "Thermodynamics of viscoelastic rate-type fluids with stress diffusion." Physics of Fluids 30, no. 2: 023101.

Book chapter
Published: 01 January 2018 in Contemporary Mathematics
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ACS Style

Miroslav Bulíček; Josef Malek; Vít Průša; Endre Süli. PDE analysis of a class of thermodynamically compatible viscoelastic rate-type fluids with stress-diffusion. Contemporary Mathematics 2018, 710, 25 -51.

AMA Style

Miroslav Bulíček, Josef Malek, Vít Průša, Endre Süli. PDE analysis of a class of thermodynamically compatible viscoelastic rate-type fluids with stress-diffusion. Contemporary Mathematics. 2018; 710 ():25-51.

Chicago/Turabian Style

Miroslav Bulíček; Josef Malek; Vít Průša; Endre Süli. 2018. "PDE analysis of a class of thermodynamically compatible viscoelastic rate-type fluids with stress-diffusion." Contemporary Mathematics 710, no. : 25-51.

Preprint
Published: 15 September 2017
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Thermodynamical arguments are known to be useful in the construction of physically motivated Lyapunov functionals for nonlinear stability analysis of spatially homogeneous equilibrium steady states in thermodynamically isolated systems. Unfortunately, the limitation to thermodynamically isolated systems is essential, and standard arguments are not applicable even for some very simple thermodynamically open systems. On the other hand, the nonlinear stability of inhomogenous non-equilibrium states in thermodynamically open systems is usually investigated using the so-called energy method. However, when the method is used in the stability analysis of coupled thermomechanical systems, the designation "energy method" is clearly a misnomer. The reason is that one of the key quantities of interest is the volume integral of the square of temperature field, which is by no means linked to the energy in the physical sense of the word. This indicates that the mathematical method is used rather artificially without a tight link to the physics. Consequently, it would seem that thermodynamical concepts are of no use in the nonlinear stability analysis of thermodynamically open systems. We show that this is not true. In particular, we propose a construction that in the case of simple heat conduction problem leads to a physically well-motivated Lyapunov functional, which effectively replaces the artificial Lyapunov functional used in the standard energy method. The proposed construction seems to be general enough to be applied in more complex thermomechanical settings, hence it could provide a tool for nonlinear stability analysis of thermodynamically open systems that are currently beyond the reach of the standard energy method.

ACS Style

Miroslav Bulíček; Josef Málek; Vít Průša. Thermodynamics and stability of non-equilibrium steady states in open systems. 2017, 1 .

AMA Style

Miroslav Bulíček, Josef Málek, Vít Průša. Thermodynamics and stability of non-equilibrium steady states in open systems. . 2017; ():1.

Chicago/Turabian Style

Miroslav Bulíček; Josef Málek; Vít Průša. 2017. "Thermodynamics and stability of non-equilibrium steady states in open systems." , no. : 1.

Article
Published: 09 September 2017 in Meccanica
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We provide numerical simulations of an incompressible pressure-thickening and shear-thinning lubricant flowing in a plane slider bearing. We study the influence of several parameters, namely the ratio of the characteristic lengths \(\varepsilon >0\) (with \(\varepsilon \searrow 0\) representing the Reynolds lubrication approximation); the coefficient of the exponential pressure–viscosity relation \(\alpha ^*\ge 0\); the parameter \(G^*\ge 0\) related to the Carreau–Yasuda shear-thinning model and the modified Reynolds number \({\mathrm {Re}}_\varepsilon \ge 0\). The finite element approximations to the steady isothermal flows are computed without resorting to the lubrication approximation. We obtain the numerical solutions as long as the variation of the viscous stress \(\varvec{S}=2\eta (p,{{\mathrm{tr}}}\,\varvec{D}^2)\varvec{D}\) with the pressure is limited, say \(|\partial \varvec{S}/\partial p|\le 1\). We show conclusively that the existing practice of avoiding the numerical difficulties by cutting the viscosity off for large pressures leads to results that depend sorely on the artificial cut-off parameter. We observe that the piezoviscous rheology generates pressure differences across the fluid film.

ACS Style

Martin Lanzendörfer; Josef Málek; Kumbakonam R. Rajagopal. Numerical simulations of an incompressible piezoviscous fluid flowing in a plane slider bearing. Meccanica 2017, 53, 209 -228.

AMA Style

Martin Lanzendörfer, Josef Málek, Kumbakonam R. Rajagopal. Numerical simulations of an incompressible piezoviscous fluid flowing in a plane slider bearing. Meccanica. 2017; 53 (1-2):209-228.

Chicago/Turabian Style

Martin Lanzendörfer; Josef Málek; Kumbakonam R. Rajagopal. 2017. "Numerical simulations of an incompressible piezoviscous fluid flowing in a plane slider bearing." Meccanica 53, no. 1-2: 209-228.

Case report
Published: 11 August 2017 in Journal of Neurological Surgery Part A: Central European Neurosurgery
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Computational fluid dynamics (CFD) has been studied as a tool for the stratification of aneurysm rupture risk. We performed CFD analysis in a patient operated on for a ruptured anterior communicating artery aneurysm. The point of rupture was identified during surgery. The aneurysm and blood vessels were segmented from computed tomography angiography to prepare a model for simulations. We found that the streamlines showed a concentrated inflow jet directed straight at the rupture point, and high wall shear stress was found at the point of rupture in the aneurysm sac. Thus specific local hemodynamics may be indicative of the aneurysm rupture site.

ACS Style

Helena Svihlova; Alena Sejkorova; Tomáš Radovnický; Daniel Adámek; Jaroslav Hron; Dan Dragomir-Daescu; Josef Malek; Martin Sameš; Aleš Hejčl. Computational Fluid Dynamics of a Fatal Ruptured Anterior Communicating Artery Aneurysm. Journal of Neurological Surgery Part A: Central European Neurosurgery 2017, 78, 610 -616.

AMA Style

Helena Svihlova, Alena Sejkorova, Tomáš Radovnický, Daniel Adámek, Jaroslav Hron, Dan Dragomir-Daescu, Josef Malek, Martin Sameš, Aleš Hejčl. Computational Fluid Dynamics of a Fatal Ruptured Anterior Communicating Artery Aneurysm. Journal of Neurological Surgery Part A: Central European Neurosurgery. 2017; 78 (6):610-616.

Chicago/Turabian Style

Helena Svihlova; Alena Sejkorova; Tomáš Radovnický; Daniel Adámek; Jaroslav Hron; Dan Dragomir-Daescu; Josef Malek; Martin Sameš; Aleš Hejčl. 2017. "Computational Fluid Dynamics of a Fatal Ruptured Anterior Communicating Artery Aneurysm." Journal of Neurological Surgery Part A: Central European Neurosurgery 78, no. 6: 610-616.

Preprint
Published: 31 May 2017
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We propose an Eulerian thermodynamically compatible model for ideal plasticity of crystalline solids treated as a material flow through an adjustable crystal lattice space. The model is based on the additive splitting of the velocity gradient into the crystal lattice part and the plastic part. The approach extends a Gibbs-potential-based formulation developed by Rajagopal and Srinivasa for obtaining the response functions for elasto-visco-plastic crystals. The framework makes constitutive assumptions for two scalar functions: the Gibbs potential and the rate of dissipation. The constitutive equations relating the stress to kinematical quantities is then determined using the condition that the rate of dissipation is maximal providing that the relevant constraints are met. The proposed model is applied to three-dimensional micropillar compression, and its features, both on the level of modelling and computer simulations, are discussed and compared to relevant studies.

ACS Style

Jan Kratochvíl; Josef Málek; Piotr Minakowski. A Gibbs-potential-based framework for ideal plasticity of crystalline solids treated as a material flow through an adjustable crystal lattice space and its application to three-dimensional micropillar compression. 2017, 1 .

AMA Style

Jan Kratochvíl, Josef Málek, Piotr Minakowski. A Gibbs-potential-based framework for ideal plasticity of crystalline solids treated as a material flow through an adjustable crystal lattice space and its application to three-dimensional micropillar compression. . 2017; ():1.

Chicago/Turabian Style

Jan Kratochvíl; Josef Málek; Piotr Minakowski. 2017. "A Gibbs-potential-based framework for ideal plasticity of crystalline solids treated as a material flow through an adjustable crystal lattice space and its application to three-dimensional micropillar compression." , no. : 1.

Journal article
Published: 01 May 2017 in International Journal of Engineering Science
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ACS Style

H. Švihlová; Jaroslav Hron; Josef Malek; K.R. Rajagopal. Determination of pressure data from velocity data with a view towards its application in cardiovascular mechanics. Part 2. A study of aortic valve stenosis. International Journal of Engineering Science 2017, 114, 1 -15.

AMA Style

H. Švihlová, Jaroslav Hron, Josef Malek, K.R. Rajagopal. Determination of pressure data from velocity data with a view towards its application in cardiovascular mechanics. Part 2. A study of aortic valve stenosis. International Journal of Engineering Science. 2017; 114 ():1-15.

Chicago/Turabian Style

H. Švihlová; Jaroslav Hron; Josef Malek; K.R. Rajagopal. 2017. "Determination of pressure data from velocity data with a view towards its application in cardiovascular mechanics. Part 2. A study of aortic valve stenosis." International Journal of Engineering Science 114, no. : 1-15.