Oct 15, 2019   1:15 p.m. Terézia
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doc. RNDr. Peter Frolkovič, PhD.
Identification number: 3011
University e-mail: peter.frolkovic [at] stuba.sk
 
Docent CSc.,PhD. - Department of Mathematics and Constructive Geometry (FCE)

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Basic information

Basic information about a final thesis

Type of thesis: Habilitation thesis
Thesis title:Numerical methods of some advection dominated problems
Written by (author): doc. RNDr. Peter Frolkovič, PhD.
Department: Faculty of Civil Engineering
Opponent 1:prof. RNDr. Igor Bock, PhD.
Opponent 2:prof. RNDr. Daniel Ševčovič, DrSc.
Opponent 3:doc. Ing. Gabriel Okša, PhD.
Final thesis progress:Final thesis was successfully defended.


Additional information

Additional information about the final thesis follows. Click on the language link to display the information in the desired language.

Language of final thesis:English

Slovak        English

Title of the thesis:Numerical methods of some advection dominated problems
Summary:The habilitation theses deals mainly with the numerical solution of advection dominated problems. In introductory chapters the most important facts and properties of such methods are discussed. A representative advection equation is introduced together with the description of characteristic curves that characterizes the behavior of solution of this problem. Afterwards, the advection equation is reformulated into an equivalent form describing the balance or conservation laws for the integral of solution. Such formulation is then used to apply a flux-based finite volume discretization to find the numerical solution of advection equation. Several original results are used in the presented numerical methods. They are related, among others, to an unconditional stability with respect to the choice of time step and a high-resolution form that produces satisfactory accuracy of numerical solutions without exhibiting unphysical oscillations. The engineering applications of such discretization methods that are discussed in this habilitation theses, can be divided into two large groups. The first one deals with the numerical solution of contaminant transport in groundwater, and the second one with the numerical capturing of moving interfaces in several engineering applications using so called level set methods.
Key words:advection, finite volume method, flux

Parts of thesis with postponed release:

Final thesis (final thesis appendices) unlimited
Reviews for final thesis unlimited