-
-
Grants
-
-
-
-
-
Advanced methods for flow-field analysis (P101-14-02067S)
from 01/01/2014
to 31/12/2016 investigator
-
The investigation aims at developing advanced methods for flow-field analysis particularly for transitional and turbulent flows. The work deals
with decomposition techniques, mainly with decomposition of motion and vorticity. The vortex-identification criterion under development at
present is associated with the corotation of line segments near a point and with the so-called residual vorticity obtained after the 'removal' of
local shearing motion. The new quantity - the average corotation - is a vector, thus it provides a good starting point for developing both regionand
line-type vortex-identification methods, especially predictor-corrector type schemes. Further, the project aims to analyze the strain-rate
skeleton so as to draw a more complete picture of the flow. For testing purposes, large-scale numerical experiments based on the solution of
the Navier-Stokes equations (NSE) will be performed for selected 3D flow problems using finite element method on parallel supercomputers.
Some qualitative properties of the solutions to the NSE will be studied and described in detail.
-
-
-
Stochastic and deterministic modelling of biological and biochemical phenomena with applications to circadian rhythms and pattern formation (StochDetBioModel (328008))
from 01/03/2013
to 31/08/2014 main investigator
-
Marie Curie Intra European Fellowship for T. Vejchodsky at the University of Oxford. Grant Agreement Number: PIEF-GA-2012-328008.
-
-
-
Advanced algorithms for solution of coupled problems in electromagnetism (102/07/0496)
from 01/01/2007
to 31/12/2009 investigator
-
The project resulted in internationally recognized results in the development and implementation of advanced algorithms for numerical modeling of coupled problems in the field of heavy current electrical engineering and electrotechnics. These tasks are characterized by an interaction of several physical fields. Characterization of such interactions is essential for reliable and economical design. Members of the research team focused primarily on advanced finite element method of higher order accuracy (hp-FEM) and the selected method of integral and integro-differential equations. The obtained were published in Dolezel, I., Karban, P. Solin, P.: Integral Methods in Low-Frequency Electromagnetics. Wiley, Hoboken, NJ, UA (2009), 388 pages.
-
-
-
Methods of higher order of accuracy for solution of multi-physics coupled problems (IAA100760702)
from 01/01/2007
to 31/12/2011 investigator
-
The design of efficient numerical methods for computer simulations of large nonlinear and associated transient problems belongs among the most recent topics in the sphere of technical and scientific computing. Examples include processing solid and liquid metals by electromagnetic field,
problems of thermoelasticity and termoplasticity, fluid interaction with solid structures and others. The difficulty of coupled problems stems from the fact that various components of solutions exhibit specific characters, such as boundary layers in fluids or singularities in electromagnetic fields. Efficient and accurate solution of these problems requires the representation of various components by geometrically different meshes. From the mathematical point of view, various solution components belong to different Hilbert spaces and, therefore, their approximations require various types of finite elements. For each solution component we use the modern hp-adaptive version of the finite element method (hp-FEM), which is known for its exponential convergence.
-
-
-
Mesh adaptivity for numerical solution of parabolic partial differential equations (201/04/P021)
from 01/01/2003
to 31/12/2006 main investigator
-
Mesh adaptivity for numerical solution of parabolic partial differential equations
-
grants
