Shape sensitivity analysis of time-dependent flows of incompressible non-Newtonian fluids

We study the shape differentiability of a cost function for the flow of an incompressible viscous fluid of power-law type. The fluid is confined to a bounded planar domain surrounding an obstacle. For smooth perturbations of the shape of the obstacle we express the shape gradient of the cost function which can be subsequently used to improve the initial design

Tvarová optimalizace pro Navierovy-Stokesovy rovnice s viskozitou

We study the shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to the optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by the generalised Navier-Stokes system with nontrivial boundary conditions. The objective is to analyze theoretically this problem (proof of the existence of a solution), its discretization and the numerical realization.V práci se řeší problém optimalizace tvaru vstupní komory, která je součástí strojů na výrobu papíru a která přivádi směs "voda+dřevní hmota" do výrobního procesu. Cílem je navrhnout takový tvar, který zajišťuje a priori daný průběh rychlosti směsi na výtokové části. Z matematického hlediska se jedná o úlohu optimálního řízení, kdy řídící proměnnou je tvar oblasti, která představuje vstupní komoru, stavovou úlohou je zobecnění Navier-Stokesův systém s netriviálními okrajovými podmínkami. Cílem je teoretické studium této úlohy (důkaz existence řešení), její diskretizace a numerická realizace.Katedra numerické matematikyDepartment of Numerical MathematicsFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Shape optimization for Stokes problem with threshold slip

summary:We study the Stokes problems in a bounded planar domain $\Omega$ with a friction type boundary condition that switches between a slip and no-slip stage. Our main goal is to determine under which conditions concerning the smoothness of $\Omega$ solutions to the Stokes system with the slip boundary conditions depend continuously on variations of $\Omega$. Having this result at our disposal, we easily prove the existence of a solution to optimal shape design problems for a large class of cost functionals. In order to release the impermeability condition, whose numerical treatment could be troublesome, we use a penalty approach. We introduce a family of shape optimization problems with the penalized state relations. Finally we establish convergence properties between solutions to the original and modified shape optimization problems when the penalty parameter tends to zero

On topological derivative for contact problem in elasticity

In the paper the general method for shape-topology sensitivity analysis of contact problems is proposed. The method uses the domain decomposition method combined with the specific properties of minimizers for the energy functional. The method is applied to the static problem of an elastic body in frictionless contact with an rigid foundation. The contact model allows a finite interpenetration of the bodies on the contact region. This interpenetration is modeled by means of a scalar function that depends on the normal component of the displacement field on the potential contact zone. We present the asymptotic behavior of the energy shape functional when a spheroidal void is introduced in an arbitrary point of the elastic body. For the asymptotic analysis, we use the domain decomposition technique and the associated Steklov-Poincaré pseudodifferential operator. The differentiability of the energy with respect to the non-smooth perturbation is established. A closed form for the topological derivative is also presented

Stability with respect to domain of the low Mach number limit of compressible viscous fluids

We study the asymptotic limit of solutions to the barotropic Navier-Stokes system, when the Mach number is proportional to a small parameter \ep \to 0 and the fluid is confined to an exterior spatial domain \Omega_\ep that may vary with \ep. As $\epsilon \rightarrow 0$, it is shown that the fluid density becomes constant while the velocity converges to a solenoidal vector field satisfying the incompressible Navier-Stokes equations on a limit domain. The velocities approach the limit strongly (a.a.) on any compact set, uniformly with respect to a certain class of domains. The proof is based on spectral analysis of the associated wave propagator (Neumann Laplacian) governing the motion of acoustic waves.Comment: 32 page

Weak solutions to the barotropic Navier-Stokes system with slip boundary conditions in time dependent domains

We consider the compressible (barotropic) Navier-Stokes system on time-dependent domains, supplemented with slip boundary conditions. Our approach is based on penalization of the boundary behaviour, viscosity, and the pressure in the weak formulation. Global-in-time weak solutions are obtained

SPRINGS WITH CALCAREOUS TUFA IN THE VALLEY OF THE JAMNE CREEK IN GORCE

The study gives a detail characteristic of a hard water springs habitat with the communities of Cratoneurion commutati (habitat code of Nature 2000: 7220), localized within Nature 2000 protected area Ostoja Gorczańska PLH120018, in an upper part of the valley of Jamne creek. The plants are described along with the main habitat parameters, namely: altitude, exposition, slope gradient, insolation, type of bedrock, water flow regime and the spring outflow efficiency. The temperature, pH, electrical conductivity were measured in the field, the concentrations of Ca and Mg in spring water were measured by Atomic Absorption Spectroscopy (AAS). The investigated headwater areas are small (0.7–80 m2) and highly differentiated by the intensity of calcareous tufa precipitation and the degree of plant cover development

Development, Production and Evaluation of Aerosol Climate Data Records from European Satellite Observations (Aerosol_cci)

Producing a global and comprehensive description of atmospheric aerosols requires integration of ground-based, airborne, satellite and model datasets. Due to its complexity, aerosol monitoring requires the use of several data records with complementary information content. This paper describes the lessons learned while developing and qualifying algorithms to generate aerosol Climate Data Records (CDR) within the European Space Agency (ESA) Aerosol_cci project. An iterative algorithm development and evaluation cycle involving core users is applied. It begins with the application-specific refinement of user requirements, leading to algorithm development, dataset processing and independent validation followed by user evaluation. This cycle is demonstrated for a CDR of total Aerosol Optical Depth (AOD) from two subsequent dual-view radiometers. Specific aspects of its applicability to other aerosol algorithms are illustrated with four complementary aerosol datasets. An important element in the development of aerosol CDRs is the inclusion of several algorithms evaluating the same data to benefit from various solutions to the ill-determined retrieval problem. The iterative approach has produced a 17-year AOD CDR, a 10-year stratospheric extinction profile CDR and a 35-year Absorbing Aerosol Index record. Further evolution cycles have been initiated for complementary datasets to provide insight into aerosol properties (i.e., dust aerosol, aerosol absorption).Peer reviewe

Shape Optimization for Navier-Stokes Equations with Viscosity

We study the shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to the optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by the generalised Navier-Stokes system with nontrivial boundary conditions. The objective is to analyze theoretically this problem (proof of the existence of a solution), its discretization and the numerical realization