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Programs and Algorithms of Numerical Mathematics 13 International Conference Programs and Algorithms of Numerical Mathematics 13 in honor of Ivo Babu·ska's 80th birthday under the auspices of Prof. V¶aclavPa·ces, the President of the Academy of Sciences of the Czech Republic Mathematical Institute, Academy of Sciences, Zitn¶a25,· Prague, Czech Republic May 28{31, 2006 Photo courtesy of C. Fonville PROCEEDINGS Edited by J. Chleboun, K. Segeth, T. Vejchodsk¶y Mathematical Institute Academy of Sciences of the Czech Republic Prague 2006 ISBN 80-85823-54-3 Matematick¶y¶ustav AV CR· Praha 2006 Contents Preface .........................................................................7 Lud·ekBene·s,Karel Kozel, Ivo Sl¶adek Numerical modeling of flow and pollution dispersion over real topography . 9 Michal Bene·s,Petr Mayer Numerical analysis of mathematical model of heat and moisture transport in concrete at high temperatures . .16 Radim Blaheta Hierarchical FEM: strengthened CBS inequalities, error estimates and iterative solvers .........................................................................24 Pavel Burda, Jaroslav Novotn¶y,Jakub S¶³stek· Accuracy investigation of a stabilized FEM for solving flows of incompressible fluid ...........................................................................30 Lubor Bu·ri·c,Vladim¶³rJanovsk¶y On a tra±c problem . 37 Claudio Canuto, Tom¶a·sKozubek A ¯ctitious domain approach to the numerical solution of elliptic boundary value problems de¯ned in stochastic domains . 46 Jan Chleboun On a Sandia structural mechanics challenge problem . 53 Ji·r¶³Dobe·s,Herman Deconinck A second order unconditionally positive space-time residual distribution method for solving compressible flows on moving meshes . 60 Ji·r¶³Dobi¶a·s,Svatopluk Pt¶ak,Zden·ekDost¶al,V¶³tVondr¶ak Scalable algorithms for contact problems with geometrical and material non-linearities . .67 V¶³tDolej·s¶³ An e±cient implementation of the semi-implicit discontinuous Galerkin method for compressible flow simulation . 74 Lenka Dubcov¶a,Miloslav Feistauer, Petr Sv¶a·cek Numerical simulation of interaction of fluids and solid bodies . 80 Ji·r¶³FÄurst Finite volume WLSQR scheme and its applications to transonic flows . 86 3 Antti Hannukainen, Sergey Korotov Two-sided a posteriori estimates of global and local errors for linear elliptic type boundary value problems . 92 Milan Hokr Benchmark calculations of the variable-density flow in porous media . .104 D¶a·saJanovsk¶a,Vladim¶³rJanovsk¶y Remark on computing the analytic SVD . 111 Volker John, Petr Knobloch A computational comparison of methods diminishing spurious oscillations in ¯nite element solutions of convection{di®usion equations . 122 R. Keslerov¶a,K. Kozel, V. Prokop Numerical solution of Newtonian flow in bypass and non-Newtonian flow in branching channels . 137 Martin Kocurek The use of basic iterative methods for bounding a solution of a system of linear equations with an M-matrix and positive right-hand side . .143 Ale·sKrop¶a·c,Michal K·r¶³·zek On the longest-edge bisection algorithm . 149 Michal K·r¶³·zek,Alena Solcov¶a,Lawrence· Somer Sindel· sequences and the Prague horologe . 156 Radek Ku·cera, Tom¶a·sKozubek, Jaroslav Haslinger On solving non-symmetric saddle-point systems arising from ¯ctitious domain approaches . .165 V¶aclavKu·cera The discontinuous Galerkin method for low-Mach flows . 172 Milan Kucha·r¶³k,Richard Liska, Pavel V¶achal,Mikhail Shashkov Arbitrary Lagrangian-Eulerian (ALE) methods in compressible fluid dynamics 178 Pavel Kºus,V¶³tDolej·s¶³ Solution of time-dependent convection-di®usion equations with the aid of higher order adaptive methods with respect to space and time . .184 Ladislav Luk·san,Ctirad Matonoha, Jan Vl·cek Interior-point method for large-scale l1 optimization . .190 Jaroslav Ml¶ynek The application of the thermal balance method for computation of warming in elect- ric machines . 196 4 Vratislava Mo·sov¶a Why are the meshless methods used? . 202 Jan Posp¶³·sil Numerical approaches to parameter estimates in stochastic di®erential equations driven by fractional Brownian motion . 208 Ale·sPracha·r,Karel Najzar Numerical integration in the discontinuous Galerkin method for elliptic problems . .214 Petra Pun·coch¶a·rov¶a,Karel Kozel, Ji·r¶³FÄurst,Jarom¶³rHor¶a·cek An unsteady numerical solution of viscous compressible flows in a channel . .220 Karel Segeth, Pavel Sol¶³n· On some a posteriori error estimation results for the method of lines . 229 Petr Sv¶a·cek On a ¯nite element method application in aeroelasticity . 235 J. Vala, S. St·'astn¶³k,H. Km¶³nov¶a Uncertainties in measurement of thermal technical characteristics of building insulations . 240 Tom¶a·sVejchodsk¶y,Pavel Sol¶³n· Discrete Green's function and maximum principle . 247 List of Participants . 253 5 6 Preface This book contains most papers presented at the international conference Programs and Algorithms of Numerical Mathematics (PANM) held in Prague, Czech Republic, May 28{31, 2006, in honor of Ivo Babu·ska's 80th birthday. It is the thirteenth volume in the series of the PANM proceedings. The conference was organized by the Mathematical Institute of the Academy of Sciences of the Czech Republic (ASCR) and continued the previous PANM seminars (conferences) held in Al·sovice, Brat·r¶³kov, Janov nad Nisou, Ko·renov, L¶azn·eLibverda, and Doln¶³Maxov in the period 1983{2004. The objective of this series of seminars has been to provide a forum for presentation and discussion of advanced topics, new approaches, and applications of computational methods; moreover, the participation of PhD students and young scientists has been encouraged. The conference was honored by the presence of Ivo Babu·ska, who spent three days and four nights in Prague during his 2006 Europe Tour focused on conferences organized in Prague, Zurich, and London to celebrate his birthday, and who used to be a leading scientist in the Institute in the 1960s. This year, the conference left its traditional Jizera Mountains locations, and was held on the Prague premises of the Institute, to make the participation of distin- guished foreign guests easier or even possible. To further emphasize the signi¯cance of the conference, it was organized under the auspices of Professor V¶aclav Pa·ces, president of the ASCR, who, moreover, presented the Honorary Medal \De scientia et humanitate optime meritis" (the ASCR highest distinction) to Ivo Babu·ska during a closed meeting in the course of the conference. It would not have been possible to organize the conference without the ¯nancial support of the Czech Science Foundation, the Grant Agency of the ASCR, and the ASCR (project no. 201/04/1503, project no. A1019201, and Institutional Research Plan no. AV0Z10190503, respectively). The Organizing Committee included Jan Chleboun, Michal K·r¶³·zek,Petr P·rikryl,Karel Segeth, Alena Solcov¶a,and· Tom¶a·s Vejchodsk¶y. More than 80 participants from the ¯eld took part in the conference. Although most of them came from Czech universities and the institutes of the ASCR, for- eign scholars were also present (Canada, China, Finland, Germany, the Netherlands, United Kingdom, and the U.S.A.). They witnessed the presentation of the Honorary Medal of the Ministry of Education, Youth, and Sports to Ivo Babu·ska on the third day of the conference. As regards the technical aspects of this book of proceedings, all the papers have been reproduced directly from materials submitted by the authors, but an attempt has been made to use a uni¯ed layout for each paper. We are indebted to Mrs. Hana B¶³lkov¶afor her e®ort in preparing the manuscripts for print and to Dr. Karel Hor¶ak and Mr. Ladislav Capanda for their technical help with printing the book. 7 The editors and organizers also wish to thank all scientists who peer reviewed the submitted manuscripts. In many cases, their comments and recommendations led to substantial improvements of the manuscripts. Besides this PANM volume, a special issue of Applications of Mathematics (no. 3, 2007) consisting of selected papers presented at the conference will be published. J. Chleboun, K. Segeth, T. Vejchodsk¶y 8 NUMERICAL MODELING OF FLOW AND POLLUTION DISPERSION OVER REAL TOPOGRAPHY¤ Lud·ekBene·s,Karel Kozel, Ivo Sl¶adek 1. Introduction The Atmospheric Boundary Layer (ABL) is the lowest part of the atmosphere. Its thickness usually ranges from several hundred meters to approximately two kilo- meters. The air pollution resulting from rapid industrialization has become a serious environmental problem mainly in the North Bohemia region. In this contribution, the influence of several types of obstacles on dustiness of coal depot in open coal mine was numerically modeled. 2. Mathematical models In our computations, the flow in ABL is assumed to be viscous, steady, incom- pressible, turbulent and indi®erently strati¯ed. Two di®erent mathematical and numerical methods have been used for numerical simulations. ² The full RANS model The ¯rst model is based on Reynolds Averaged Navier{Stokes equations. The gov- erning equations are considered in the conservative, non-dimensional, and vector form: Wt + Fx + Gy + Hz = (KR)x + (KS)y + (KT )z + fv; (1) where F = (u; u2+p; uv; uw; uC )T , G = (v; vu; v2+p; vw; vC )T , H = (w; wu; wv; 2 T T T w + p; wC ) , R = (0; ux; vx; wx;Cx/σC ) , S = (0; uy; vy; wy;Cy/σC ) , T = T 2 T (0; uz; vz; wz;Cz/σC ) . W = (p=¯ ; u; v; w; C) stands for the vector of unknown variables the pressure, three velocity components V = (u; v; w)T , and the concentra- tion of passive pollutant, respectively. Further fv denotes the volume force, σC is the turbulent Prandtl's number, ¯ arti¯cial compressibility coe±cient and ¯nally K represents the turbulent di®usion coe±cient, see equation (5). The arti¯cial com- pressibility method is used for the numerical solution of this model. ² Boussinesq equations The NS equations are simpli¯ed by the so called Boussinesq approximation. The instantenous values of the density, pressure and potential temperature can be de- composed into two parts: the large synoptic scale part denoted by subscript 0 and ¤The ¯nancial support for the presented project is partly provided by the Research Plan MSM No.
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