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On mathematical modelling of gust response using the finite element method

Sváček, Petr, Horáček, Jaromír (2013)

Applications of Mathematics 2013

In this paper the numerical approximation of aeroelastic response to sudden gust is presented. The fully coupled formulation of two dimensional incompressible viscous fluid flow over a flexibly supported structure is used. The flow is modelled with the system of Navier-Stokes equations written in Arbitrary Lagrangian-Eulerian form and coupled with system of ordinary differential equations describing the airfoil vibrations with two degrees of freedom. The Navier-Stokes equations are spatially discretized...

On simplicial red refinement in three and higher dimensions

Korotov, Sergey, Křížek, Michal (2013)

Applications of Mathematics 2013

We show that in dimensions higher than two, the popular "red refinement" technique, commonly used for simplicial mesh refinements and adaptivity in the finite element analysis and practice, never yields subsimplices which are all acute even for an acute father element as opposed to the two-dimensional case. In the three-dimensional case we prove that there exists only one tetrahedron that can be partitioned by red refinement into eight congruent subtetrahedra that are all similar to the original...

On the computation of moments of the partial non-central χ -square distribution function

Gil, Amparo, Segura, Javier, Temme, Nico C. (2013)

Applications of Mathematics 2013

Properties satisfied by the moments of the partial non-central χ -square distribution function, also known as Nuttall Q-functions, and methods for computing these moments are discussed in this paper. The Nuttall Q-function is involved in the study of a variety of problems in different fields, as for example digital communications.

On the computational identification of temperature-variable characteristics of heat transfer

Vala, Jiří (2013)

Applications of Mathematics 2013

The mathematical analysis of a heat equation and its solutions is a standard part of most textbook of applied mathematics and computational mechanics. However, serious problems from engineering practice do not respect formal simplifications of such analysis, namely at high temperatures, for phase-change materials, etc. This paper, motivated by the material design and testing of a high-temperature thermal accumulator, as a substantial part of the Czech-Swedish project of an original equipment for...

On the interpolation constants over triangular elements

Kobayashi, Kenta (2015)

Application of Mathematics 2015

We propose a simple method to obtain sharp upper bounds for the interpolation error constants over the given triangular elements. These constants are important for analysis of interpolation error and especially for the error analysis in the Finite Element Method. In our method, interpolation constants are bounded by the product of the solution of corresponding finite dimensional eigenvalue problems and constant which is slightly larger than one. Guaranteed upper bounds for these constants are obtained...

On the number of stationary patterns in reaction-diffusion systems

Rybář, Vojtěch, Vejchodský, Tomáš (2015)

Application of Mathematics 2015

We study systems of two nonlinear reaction-diffusion partial differential equations undergoing diffusion driven instability. Such systems may have spatially inhomogeneous stationary solutions called Turing patterns. These solutions are typically non-unique and it is not clear how many of them exists. Since there are no analytical results available, we look for the number of distinct stationary solutions numerically. As a typical example, we investigate the reaction-diffusion system designed to model...

On the quality of local flux reconstructions for guaranteed error bounds

Vejchodský, Tomáš (2015)

Application of Mathematics 2015

In this contribution we consider elliptic problems of a reaction-diffusion type discretized by the finite element method and study the quality of guaranteed upper bounds of the error. In particular, we concentrate on complementary error bounds whose values are determined by suitable flux reconstructions. We present numerical experiments comparing the performance of the local flux reconstruction of Ainsworth and Vejchodsky [2] and the reconstruction of Braess and Schöberl [5]. We evaluate the efficiency...

On using artificial compressibility method for solving turbulent flows

Louda, Petr, Kozel, Karel, Příhoda, Jaromír (2012)

Applications of Mathematics 2012

In this work, artificial compressibility method is used to solve steady and unsteady flows of viscous incompressible fluid. The method is based on implicit higher order upwind discretization of Navier-Stokes equations. The extension for unsteady simulation is considered by increasing artificial compressibility parameter or by using dual time stepping. The methods are tested on laminar flow around circular cylinder and used to simulate turbulent unsteady flows by URANS approach. The simulated cases...

Parallel programming and optimization of heat radiation intensity

Mlýnek, Jaroslav, Srb, Radek (2013)

Applications of Mathematics 2013

This article focuses on the practical possibilities of a suitable use of parallel programming during the computational processing of heat radiation intensity optimization across the surface of an aluminium or nickel mould. In practice, an aluminium or nickel mould is first preheated by infrared heaters located above the outer mould surface. Then the inner mould surface is sprinkled with a special PVC powder and the outer mould surface is continually warmed by infrared heaters. This is an energy-efficient...

Path-following the static contact problem with Coulomb friction

Haslinger, Jaroslav, Janovský, Vladimír, Kučera, Radek (2013)

Applications of Mathematics 2013

Consider contact problem with Coulomb friction on two planar domains. In order to find non-unique solutions we propose a new path following algorithm: Given a linear loading path we approximate the corresponding solution path. It consists of oriented piecewise linear branches connected by transition points. We developed a) predictor-corrector algorithm to follow oriented linear branches, b) branching and orientation indicators to detect transition points. The techniques incorporate semi-smooth Newton...

Preface

Segeth, K. (2015)

Application of Mathematics 2015

Preface

Segeth, Karel (2012)

Applications of Mathematics 2012

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