Ondřej Kreml

Grants
- Thermodynamically consistent models for fluid flows: mathematical theory and numerical solution (16-03230S)
  from 01/01/2016 to 31/12/2018 investigator
- Objectives: Mathematical and numerical analysis and numerical solution of fluid flows belong to the most often studied problems of the theory of partial differential equations and their numerical solution. During the last decades, a big progress has been achieved in these fields which enables us to study models of complex fluids including the possibility to consider their dependence on temperature. This project is focused on the study of such models of fluid thermodynamics and mechanics with the aim to extend the knowledge in the field of the theoretical analysis of the corresponding systems of partial differential equations and numerical analysis of the methods for their solution. Computational simulations using specific numerical methods will be performed to support the analytical results concerning the well-posedness of the model problems and qualitative properties of their solutions. The proposed projects assumes a tight collaboration of specialists in these fields which is an important prerequisite for further development of mathematical and computational fluid thermodynamics.
- Qualitative analysis and numerical solution of problems of flows in generally time-dependent domains with various boundary conditions (GA13-00522S)
  from 01/02/2013 to 31/12/2016 investigator
- Objectives: Mathematical and computational fluid dynamics play an important role in many areas of science and technology. The project will be concerned with the analysis of qualitative properties of the incompressible and compressible Navier-Stokes equations in fixed or time-dependent domains with various types of, in general nonstandard, boundary conditions. Let us mention, e.g., the existence, uniqueness, regularity and singular limits of their solutions. On the basis of theoretical results, in the numerical part of the project, we shall develop efficient and robust techniques for the solution and validation of theoretically analyzed flow problems and models. The developed numerical methods and their ingredients, as, e.g., adaptivity and hp-methods, will be tested on suitable problems and applied to fluid-structure interaction. With the aid of model problems, theoretical aspects of the worked out methods as stability, convergence and error estimates will be investigated.
- Transport phenomena in continuum fluid dynamics (TraFlu(SCIEX 11.152))
  from 01/07/2012 to 31/12/2013 main investigator
- Sciex Postdoctoral Fellowship for Ondřej Kreml at University of Zurich (Host institution). Objectives: Ondřej Kreml will study the results of Camillo De Lellis and László Székelyhidi about ill-posedness of bounded weak solutions for the incompressible Euler equations and bounded admissible solutions for the compressible isentropic Euler system in multiple space dimensions. The objectives of the project are to generalize the ill-posedness results for compressible isentropic Euler system and to study the Riemann problem for this system. Another objective is to modify the method of De Lellis and Székelyhidi to be applicable in other systems of partial differential equations describing inviscid fluid flows.
- Flow of fluids in domains with variable geometry (P201/11/1304)
  from 01/01/2011 to 31/12/2013 investigator
- Objectives: The goal of the project is to get new relevant results concerning flow in domains with varying geometry. From the viewpoint of theoretical analysis, we will deal with flow of fluids (incompressible and compressible) around a rotating body (existence of weak or very weak solutions, asymptotic behaviour solutions, artificial boundary conditions) in case that the axis of rotation of the body and the velocity at infinity are parallel or not parallel. We will also investigate the related hydrodynamical potential theory. Moreover, we will investigate the case of motion of rigid bodies in viscous fluid (mostrly non-Newtonian incompressible and Newtonian compressible), in several cases we include the changes of temperature. Part of the problems mentioned above will be solved numerically. Finally, we perform the numerical simulation of flow of fluids in domains with complicated geometry corresponding to the flow of blood in healthy veins as well as in cases of cardiovascular diseases.
- Nečas Center for Mathematical Modeling - part IM (LC06052)
  from 01/01/2006 to 31/12/2011 investigator
- The general goal of the Nečas Center for Mathematical Modeling is to establish a significant scientific team in the field of mathematical properties of models in continuum mechanics and thermodynamics, developed by an intensive collaboration of five important research teams at three Prague affiliations and their goal-directed collaboration with top experts from abroad. The research projects of the center include: 1) Nonlinear theoretical, numerical and computer analysis of problems of continuum physics. 2) Heat-conductive and deforming processes in compressible fluids, incompressible substances of fluid type, and in linearly elastic matters. 3) Interaction of the substances. 4) Biochemical procedures in substances. 5) Passages between models, dimensional analysis.