National Repository of Grey Literature 6 records found  Search took 0.00 seconds. 
Mathematical modelling of liver perfusion
Kociánová, Barbora ; Rohan, Eduard (advisor) ; Bulíček, Miroslav (referee)
Liver perfusion can be modelled by Darcy's flow in multiple connected com- partments. The first part of the present thesis shows in detail the existence of a solution to the multi-compartmental model. The flow in each compartment in this model is characterized by a permeability tensor, which is obtained from the geometry of liver vasculature. It turns out that this tensor might be singular, which potentially causes solvability problems. The second part deals with this abnormality in one compartment. By using the theory of degenerate Sobolev spaces, an appropriate weak formulation is defined. Analogues of Poincar'e and traces inequalities in this degenerate setting are proved, which also imply the existence of the weak solutions. In addition, this part justifies another possibil- ity how to deal with degenerate permeability, which is regularizing the tensor by adding a small isotropic permeability to it. In the third part, the aim is to find subdomains of autonomous perfusion with respect to the source positions. This is formulated as a minimization problem and several numerical results are presented. 1
Numerical modelling of unstable fluid flow past heated bodies
Pech, Jan ; Maršík, František (advisor) ; Feistauer, Miloslav (referee) ; Rohan, Eduard (referee)
Title: Numerical modeling of unstable fluid flow past heated bodies Author: Jan Pech Department: Mathematical Institute of Charles University Supervisor: prof. Ing. František Maršík, DrSc., Mathematical Institute of Charles University Abstract: Presented work brings new results to numerical computations of flow influenced by temperature changes. Constructed numerical algorithm takes into account variable coefficients of the differential operators in the system of in- compressible Navier-Stokes equations coupled with thermal heat equation. The spatial discretisation of the problem targets to application of high order method, the spectral element method. Phenomenons connected with high order approxi- mations are discussed on a number of examples and comparisons with methods of lower order, which are more common. Results were achieved for two fluids with opposite response to heating, air and water. The observed quantity is par- ticularly a frequency of vortex shedding, the Strouhal number, as dependent on temperature and Reynolds number. The calculated values were compared with experimental results and exhibit a good coincidence. Numerical analysis of sep- aration angle in flow around heated circular cylinder may give a new impulse to verification of accuracy and reliability of the developed method. Keywords:...
Modeling of phase transformations in shape memory materials
Frost, Miroslav ; Maršík, František (advisor) ; Rohan, Eduard (referee) ; Seiner, Hanuš (referee)
Title: Modeling of phase transformations in shape memory materials Author: Miroslav Frost Department: Mathematical Institute of Charles University Supervisor: Prof. Ing. František Maršík, DrSc., Mathematical Institute of Charles University Abstract: This thesis presents a new thermomechanical three-dimensional con- stitutive model of NiTi-based shape memory alloys. The model was formulated within the framework of generalised standard models and it features a novel form of the dissipation function, which combines contributions stemming from the phase transformation between austenite and martensite and from the reorienta- tion of martensite. The change in the material response associated with the phase transformation between austenite and R-phase as well as material anisotropy and tension-compression asymmetry are also covered. The time-evolutionary problem of a quasistatic mechanical loading of a NiTi body with prescribed temperature evolution was formulated and analyzed within the framework of energetic so- lutions. The corresponding time-incremental minimization problem provided a conceptual algorithm utilized in the numerical treatment. The constitutive mod- el was implemented into the finite element package Abaqus. Several numerical simulations were performed and compared with experiments. Keywords:...
Approximation, numerical realization and qualitative analysis of contact problems with friction
Ligurský, Tomáš ; Haslinger, Jaroslav (advisor) ; Segeth, Karel (referee) ; Rohan, Eduard (referee)
Title: Approximation, numerical realization and qualitative analysis of contact problems with friction Author: Tomáš Ligurský Department: Department of Numerical Mathematics Supervisor: prof. RNDr. Jaroslav Haslinger, DrSc., Department of Numerical Mathe- matics Abstract: This thesis deals with theoretical analysis and numerical realization of dis- cretized contact problems with Coulomb friction. First, discretized 3D static contact prob- lems with isotropic and orthotropic Coulomb friction and solution-dependent coefficients of friction are analyzed by means of the fixed-point approach. Existence of at least one solution is established for coefficients of friction represented by positive, bounded and con- tinuous functions. If these functions are in addition Lipschitz continuous and upper bounds of their values together with their Lipschitz moduli are sufficiently small, uniqueness of the solution is guaranteed. Second, properties of solutions parametrized by the coefficient of friction or the load vector are studied in the case of discrete 2D static contact problems with isotropic Coulomb friction and coefficient independent of the solution. Conditions under which there exists a local Lipschitz continuous branch of solutions around a given reference point are established due to two variants of the...
Shape optimization of channels for incompressible flows
Záhorová, Zuzana ; Rohan, Eduard (advisor) ; Feistauer, Miloslav (referee)
Název práce: Optimalizace tvaru kanálu v úlohách nestlačitelného proudění Autor: Zuzana Záhorová Katedra: Katedra numerické matematiky Vedoucí diplomové práce: Doc. Dr. Ing. Eduard Rohan e-mail vedoucího: Abstrakt: V předložené práci studujeme problém tvarové optimalizace pro úlohy vnitřního proudění ve 3D. Uvažováno je laminární, nestlačitelné, stacionární proudění popsané Navier- Stokesovými rovnicemi. Jsou popsány stabilizace Navier-Stokesových rovnic potřebné pro řešení úloh s nízkou viskozitou. Předloženy jsou teoretické poznatky týkající se problému tvarové optimalizace včetně důkazu existence řešení. Je popsána adjungovaná metoda pro řešení optimalizační úlohy. Odvozena je analytická analýza citlivosti. Představujeme postupy využité při výpočtech a numerický software pro řešení optimalizačních úloh. Jsou prezentovány výsledky pro stabilizované i nestabilizované řešení Navier-Stokesových rovnic. Představíme výsledky zahrnující lineární omezení geometrie oblasti. Klíčová slova: Nestlačitelné Navier-Stokesovy rovnice, SUPG/PSPG stabilizace, Adjun- govaná metoda, Analýza citlivosti Title: Shape optimization of channels for incompressible flows Author: Zuzana Záhorová Department:...
Homogenization in Perforated Domains
Rozehnalová, Petra ; Bock, Igor (referee) ; Rohan, Eduard (referee) ; Franců, Jan (advisor)
Numerické řešení matematických modelů popisujících chování materiálů s jemnou strukturou (kompozitní materiály, jemně perforované materiály, atp.) obvykle vyžaduje velký výpočetní výkon. Proto se při numerickém modelování původní materiál nahrazuje ekvivalentním materiálem homogenním. V této práci je k nalezení homogenizovaného materiálu použita dvojškálová konvergence založena na tzv. rozvinovacím operátoru (anglicky unfolding operator). Tento operátor poprvé použil J. Casado-Díaz. V disertační práci je operátor definován jiným způsobem, než jak uvádí původní autor. To dovoluje pro něj dokázat některé nové vlastnosti. Analogicky je definován operátor pro funkce definované na perforovaných oblastech a jsou dokázány jeho vlastnosti. Na závěr je rozvinovací operátor použit k nalezení homogenizovaného řešení speciální skupiny diferenciálních problémů s integrální okrajovou podmínkou. Odvozené homogenizované řešení je ilustrováno na numerických experimentech.

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