Tuesday, August 25. 2020
Numerical approximations of the Keyfitz-Kranzer type models by using entropy stable schemes
Carlos A. Vega1 Departmento de Matem´aticas y Estadıstica, Universidad del Norte, Km 5 Via Puerto Colombia Barranquilla, Colombia.
Sonia Valbuena Grupo GIHEM, Universidad del Atl´antico, Km 7 Via Puerto Colombia Barranquilla, Colombia.
Abstract: Numerical simulations for the Keyfitz-Kranzer system of equations are developed by using high-order entropy stable schemes proposed by Fjordholm et. al. [Arbitrary high-order essentially non-oscillatory entropy stable schemes for systems of conservation laws, SIAM J. Numer. Anal., 50, 544-573 (2012)]. Since existence of entropy pairs is an important ingredient to this approach, they are described in details. Numerical experiments include errors and convergence rates to illustrate the performance of the schemes.
c 2020 European Society of Computational Methods in Sciences and Engineering
Keywords: Conservation laws, Keyfitz-Kranzer system, entropy conservative flux, entropy stable scheme. Mathematics Subject Classification: 35L65, 35L45, 35L67, 58J45, 65M06
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Wednesday, May 6. 2020
Finite Integration Method Using Chebyshev Expansion for Solving Nonlinear Poisson Equations on Irregular Domains
A. Duangpan1 and R. Boonklurb2
1,2Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand
Received 27 March, 2019; accepted in revised form 28 April, 2020
Abstract: Several boundary value problems are dened on complex shaped domains, such as pentagonal, circular, L-shaped, butter y, peanut-shaped and elliptic domains. These irregular domains give diculty in term of solving both analytically and numerically. This paper devises the nite integration method via Chebyshev polynomials (FIM-CBS) to deduce the ecient numerical scheme for solving two-dimensional nonlinear Poisson equations over these irregular domains with the discretization through Chebyshev nodes. The demonstrative numerical examples are provided. The numerical solutions by the FIM-CBS are compared with the analytical solutions. The results show that the proposed method is very eective and accurate with a small number of computational nodes.
c 2020 European Society of Computational Methods in Sciences and Engineering
Keywords: nite integration method, Chebyshev polynomial, nonlinear Poisson equation, irregular domain Mathematics Subject Classication: 65D30, 65M50, 65N30
Thursday, March 26. 2020
SEMI-EMPIRICAL COMPUTATIONAL METHOD FOR STUDYING THE DIFFUSION OF MOISTURE AND GENERATOR GASES IN THE CAPILLARY-POROUS SPACE OF REPRESENTATIVE BIOFUELS
T.V. Karpukhina1, V.N. Kovalnogov1,2, M.S. Boyarkin1
1Department of Heat-and-Power Engineering, Faculty of Power Engineering, Ulyanovsk State Technical University, SevernyVenets Street 32, 432027 Ulyanovsk, Russian Federation 2Scientific and Educational Center "Digital Industry", South Ural State University, 76 Lenin Ave., 454080 Chelyabinsk, Russian Federation
Received 10 March, 2020; Accepted in revised form 23 March, 2020
Abstract The complex of issues related to the mathematical modeling of heat-and-mass transfer of moisture and gas in the capillary-porous space of solid biofuel cells is discussed. This is the theoretical basis for developing of biofuel enrichment technologies which include heating with simultaneous saturation of the capillary-porous space by the synthesis gas and the combustible components of the recycle gas that in complex contributes the most complete combustion of cells and improve the fuel efficiency and environmental friendliness of the boiler plant. The mathematical model defining the kinetics of heat and humidity conditions and saturation of biofuel cellsis given and discussed. Keywords: diffusion, capillary-porous space, heat-and-humidity state, modeling,enrichment technology.
c 2020 European Society of Computational Methods in Sciences and Engineering
Tuesday, January 28. 2020
Structure preserving algorithms for simulation of linearly damped acoustic systems
Vasileios Chatziioannou1
1Department of Music Acoustics, University of Music and Performing Arts Vienna, Austria Received: 22 August 2017 ; Accepted in revised form: 22 January 2020
Abstract: Energy methods for constructing time-stepping algorithms are of increased in- terest in application to nonlinear problems, since numerical stability can be inferred from the conservation of the system energy. Alternatively, symplectic integrators may be constructed that preserve the symplectic form of the system. This methodology has been established for Hamiltonian systems, with numerous applications in engineering problems. In this paper an extension of such methods to non-conservative acoustic systems is presented. Discrete conservation laws, equivalent to that of energy-conserving schemes, are derived for systems with linear damping, incorporating the action of external forces. Furthermore the evolution of the symplectic structure is analysed in the continuous and the discrete case. Existing methods are examined and novel methods are designed using a lumped oscillator as an elemental model. The proposed methodology is extended to the case of distributed systems and exemplified through a case study of a vibrating string bouncing against a rigid obstacle.
c 2019 European Society of Computational Methods in Sciences and Engineering Keywords: Energy conservation, symplectic form, mechanical integrator, linear damping Mathematics Subject Classification: 65M06, 65P10, 65Z05
Monday, December 2. 2019
Radiation-Resistant Robotic Complex: Hardware, Software And Mathematical Concepts
E.M. Chavkin1, A.N. Fomin1, V.V. Prikhodko1, A.A. Sobolev1, A.V.Zhukov1, P.E. Kapustin1, V.E. Kiryukhin1, D.S. Lavygin1, V.V. Levshchanov1, S.V. Pavlov2, V.P. Smirnov2, V.V. Svetukhin3
1S.P. Kapitsa Technological Research Institute of Ulyanovsk State University, Ulyanovsk, Russia, vp@kapitsa.tech 2 Sosny Research and Development Company, Dimitrovgrad, Ulyanovsk region, Russia 3 SMC «Technological Center», Zelenograd, Moscow, Russia.
Received: 12 November 2019; Accepted in revised form: 29 November 2019
Abstract. The results of developing a radiation-hardened robotic complex to work in hot cells at nuclear industry facilities are presented. For each constituting element of the complex – arobotic manipulator, a control device with force feedback, control software – a detailed description is given.Special attention is paid to the mathematical basis of the manual control mode implemented by means of an original 6-DoF joystick.Further development of the control software made it possible to create a training simulator, the software part of which is identical to that used for the robotic arm control. The simulator hardware consists of VR equipment and the 6-DoF joystick.
Keywords: robotic complex, manipulator, control device, force feedback, joystick, control algorithms, mathematical basis, radiation-protected chamber, hot cell, training simulator, virtual reality, VR, control software.
Sunday, July 28. 2019
Numerical Analysis of Bearing Capacity of Soil S. Harabinova, E. Panulinova, E. Kormanikova Institute of Structural Engineering, Faculty of Civil Engineering, Technical University of Kosice, 042 00 Kosice, Slovakia
Received 31 January, 2018; accepted in revised form 23 July, 2019
Abstract: The strength of soil and the bearing capacity are a keys design parameters in designing foundations and other earth structures. Proper interpretation of shear strength parameters and the application to bearing capacity problems are presented and evaluated in this paper. Theory of bearing capacity is developed, on the basis of plastic theory, by changing the shear strength parameters for cohesive soil. In foundation design, the capacity of the foundation to support footing load is given by the soil´s bearing capacity, which is a function of its strength parameters. The maximum pressure, that the soil can support at foundation level without failure depends on the bearing capacity of soil. The bearing capacity of soil in purely cohesive material changes linear with cohesion resistance. However, the bearing capacity changes exponential with the angle of internal friction of soil. By comparing obtained results it was founded, that change the angle of internal friction in cohesive soils have more effect on increasing bearing capacity.
© European Society of Computational Methods in Sciences and Engineering Keywords: bearing capacity, foundation, failure, strength of soil, cohesive soil, numerical analysis Mathematics SubjectClassification: 00A69, 49Mxx
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Friday, July 19. 2019
Evaluation of Turbulence Models for Flow Over a Thermally Loaded Hill
Ivan Kološ1, a), Lenka Lausová1, b) and Vladimíra Michalcová1, c)
1VŠB - Technical University of Ostrava, Faculty of Civil Engineering, L. Podéště 1875/17, 708 33 Ostrava-Poruba, Czech Republic
a)Corresponding author: ivan.kolos@vsb.cz, b)lenka.lausova@vsb.cz, c)vladimira.michalcova@vsb.cz
Abstract. CFD models are widely used for modelling of flow over objects, as they provide very good results of the turbulence characteristics of the flow. The aim of the paper is to analyse suitability of selected numerical models of flow in an unstable temperature-stratified boundary layer over the temperature-loaded object. A numerical analysis has been carried out using four turbulence models: Transition SST κ-ω model, LES model, SAS model and DES model. The velocity and temperature fields of a single temperature loaded hill are evaluated in horizontal profiles at four levels of the hill on both, the windward and leeward sides. © European Society of Computational Methods in Sciences and Engineering
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Wednesday, July 17. 2019
Fundamentals of Mathematical Modeling of Cognitive Digital Automata
V.V. Kozhevnikov
Technological Research Institute of Ulyanovsk State University, 1/4 Universitetskaya Naberezhnaya, Ulyanovsk, 432017, Russia
Received: 31 May 2019; accepted in revised form: 18 June 2019
Abstract An approach to the mathematical modeling of cognitive digital automata (CDA) is proposed. This approach represents a further development of the theory of digital automata and is based on the methods of mathematical modeling of conventional digital automata. At the same time, the task of formalizing the concept of cognitivity of the mathematical model of CDA comes to the fore. Cognitivity of the mathematical model, respectively, is determined by the possibility of training and generating solutions that are not provided for in the process of learning. A specific feature of the mathematical model of CDA consists in the fact that the description of the neural network (NN) structure serves as the structure diagram of digital automata, and the logical function “NOT-AND-OR” is used as the model of the neuron. In the case of the formation of feedbacks from the output to the inputs of the neurons, the model of the neuron is a binary trigger with a logical function “NOT-AND-OR” at the input. The mathematical apparatus of Petri nets (PNs) is proposed as a tool for constructing the mathematical model of CDA: marked graphs, inhibitory PNs and PNs with programmable logic. The mathematical model is constructed on the basis of the representation of CDA in the form of the state equation of PNs from the class of Murata equations (matrix equations) or a system of linear algebraic equations. The task of formalizing the concept of cognitivity is solved as a result of the synthesis of the logic of the initial CDA structure diagram or the formation of the formula of CDA. At the same time, the possibility of forming the formula of CDA depends on the critical mass of training sets and training algorithms. Hence, the task of generating the minimum training sets for a given function or experimentally determined function of CDA bears particular importance. Prediction or generation of solutions, in its turn, is performed on the basis of the mathematical model of CDA obtained in the training process. Keywords: intelligent control system, cognitive digital automata, artificial intelligence, neural networks, machine learning, cognition, Petri nets, equation of states, mathematical modeling, synthesis, generation, analysis, logic.
c 2019 European Society of Computational Methods in Sciences and Engineering
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Friday, June 21. 2019
Effect of Fluid in the Moving Container
K. Kotrasova and E. Kormanikova Department of Structural Mechanics, Institute of Structural Engineering, Civil Engineering Faculty, Technical University of Košice, 04200 Kosice, Slovakia
Received 31 January, 2019; accepted in revised form 18 March, 2019
Abstract: When a rectangular tank contained liquid vibrates, the liquid exerts hydrodynamic pressure acting onto tank walls and tank bottom. This paper describes theoretical background of effect of fluid in moving rectangular container. The rectangular concrete container excited by the movement of the earth surface was analyzed on the example. The analysis was performed of the fluid effect on solid of container and ground motion effect on liquid filled tank.
© European Society of Computational Methods in Sciences and Engineering Keywords: Fluid, container, moving Mathematics Subject Classification: 00A69, 49Mxx
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Friday, February 15. 2019
DEVELOPMENT OF THE THEORY FOR MODELING AND RESEARCH OF ADVANCED TECHNOLOGIES FOR ENRICHING BIOFUEL CELLS WITH GENERATOR GASES
V.N. Kovalnogov1,2, T.V. Karpukhina2, M.S. Boyarkin2
1Group of Numerical and Applied Mathematics on Urgent Problems of Energy and Power Engineering, Faculty of Power Engineering, Ulyanovsk State Technical University, Severny Venets Street 32, 432027 Ulyanovsk, Russian Federation 2Department of Heat-and-Power Engineering, Faculty of Power Engineering, Ulyanovsk State Technical University, Severny Venets Street 32, 432027 Ulyanovsk, Russian Federation
Received: 10 December 2018; accepted in revised form: 12 February 2019
Abstract The complex of issues related to the mathematical modeling of heat-and-mass transfer of moisture and gas in the capillary-porous space of solid biofuel cells is discussed. This is the theoretical basis for developing of biofuel enrichment technologies which include heating with simultaneous saturation of the capillary-porous space by the synthesis gas and the combustible components of the recycle gas that in complex contributes the most complete combustion of cells and improve the fuel efficiency and environmental friendliness of the boiler plant. The mathematical model defining the kinetics of heat and humidity conditions and saturation of biofuel cells, as well as some numerical results of parameters of cell condition in the process of enrichment of recycled exhaust gases are given and discussed. Keywords: biofuels, enrichment technology, capillary-porous space, heat-and-humidity state, modeling
c 2019 European Society of Computational Methods in Sciences and Engineering
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Friday, February 15. 2019
SOFTWARE AND INFORMATION COMPLEX FOR THE COUPLED NUMERICAL SOLUTION OF THE EQUATIONS OF HEAT-AND-MOISTURE TRANSFER AND THE STUDYING OF HEAT-AND-HUMIDITY KINETICS OF BIOFUEL CELLS
V.N. Kovalnogov1,2, T.V. Karpukhina2, M.S. Boyarkin2
1Group of Numerical and Applied Mathematics on Urgent Problems of Energy and Power Engineering, Faculty of Power Engineering, Ulyanovsk State Technical University, Severny Venets Street 32, 432027 Ulyanovsk, Russian Federation 2Department of Heat-and-Power Engineering, Faculty of Power Engineering, Ulyanovsk State Technical University, Severny Venets Street 32, 432027 Ulyanovsk, Russian Federation
Received: 10 December 2018; accepted in revised form: 12 February 2019
Abstract The complex of issues related to the mathematical modeling of heat-and-mass transfer of moisture and gas in the capillary-porous space of solid biofuel cells is discussed. The mathematical model, a difference approximation of differential equations defining the kinetics of heat-and-humidity conditions and saturation of biofuel cells, as well as the calculation algorithm are given and discussed. Keywords: heat-and-humidity state, coupled solution, modeling, capillary-porous space.
c 2019 European Society of Computational Methods in Sciences and Engineering
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Friday, December 7. 2018
THE CONCEPT OF DESIGNING AN INTELLECTUAL ROBOT CONTROL SYSTEM BASED ON THE MATHEMATICAL MODEL OF COGNITIVE DIGITAL AUTOMATA
V.V.Kozhevnikov1, B.M.Kostishko1, M.Yu.Leontev1, E.R.Mingachev1, S.V.Pavlov2, V.V.Prikhodko1
1S.P. Kapitsa Technological Research Institute of Ulyanovsk State University, Ulyanovsk, Russia 2Sosny Research and Development Company, Dimitrovgrad, Ulyanovsk region, Russia
Received: 10 November 2018; accepted in revised form: 04 December 2018
Abstract. An intellectual control system (ICS) to control robots can be built (designed) on the basis of the mathematical model of cognitive digital automata (CDA). The intellectual control system in this case is a software and hardware complex, where the mathematical model of the CDA determines the control system as an intellectual one. The cognitive ability of the mathematical model is determined by the possibility of forming new knowledge based on the knowledge gained at the training stage. The creativity of a mathematical model is determined by the ability to construct sequences (logical chains) of generating new knowledge. A specific feature of the mathematical model of the CDA consists in the fact that the description of the neural network (NN) structure serves as the initial structural scheme of automata, and the logical function "NOT-AND-OR" is used as the neuron model. The mathematical apparatus of Petri nets (PN) is proposed as a tool to construct the mathematical model of the CDA. The structure, composition and algorithm of functioning of the robot’s intellectual control system based on the mathematical model of the CDA is discussed in the paper. In accordance with the algorithm, the ICS operates in three modes: training, manual and automatic control. Training a mathematical model of the CDA can be performed both in the manual mode and in the automatic control mode. The possibility of learning in the automatic control mode, in its turn, provides the possibility of regenerating knowledge and, accordingly, the possibility of cognitive control.
Keywords: intellectual control system, robots, cognitive automata, artificial intelligence, neural networks, machine learning, cognition, thinking, Petri nets, equation of states, mathematical modeling, synthesis, generation, analysis, logic.
c 2018 European Society of Computational
Methods in Sciences and Engineering
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Monday, November 12. 2018
NICOLETA E. TARFULEA DEPARTMENT OF MATHEMATICS, PURDUE UNIVERSITY NORTHWEST, USA
Abstract. HIV can infect cells via cell-to-cell and virus-to-cell transmissions. These two types of transmission may occur in a combined way and enable viral spread. In this paper, we investigate analytically and numerically the influence of these two transmission modes, as well as the viral loss due to infection of T-cells. We introduce, analyze, and compare three mathematical models and show that viral loss due to infection of cells has little effect on the dynamics of HIV. Moreover, we show that additional conditions for the steady state stability are needed when virus-to-cell-transmission is included and a critical value for this parameter is provided. Numerical simulations illustrate the theoretical results and further investigate the differences between these systems.
c 2018 European Society of Computational
Methods in Sciences and Engineering
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Monday, October 15. 2018
N. Chaabane1,a, B. Rivierea, Mikhail Sekachevb and Henri Calandrab aCAAM department, Rice University bTotal E&P Research & Technology USA, LLC 1E-mail: nc33@rice.edu
Abstract: In [7], a sequential approach was
introduced to solve the Biot system where the pressure and displacement
variables are decoupled. A stabilization term was added and the discontinuous
Galerkin method was used to discretize the equations in space and the backward
Euler method was used to discretize the equations in time. The convergence of
the method was established both theoretically and numerically. In this work, we
run several numerical experiments to further validate this approach. Cases with
more complex boundary conditions and realistic input parameters are solved. We
also carry out a strong scalability analysis to show the efficiency of this
method on supercomputers.
c 2018 European Society of Computational
Methods in Sciences and Engineering
Keywords: Poroelasticity; Biot system;
Discontinuous Galerkin; Barry-Mercer; sequential method; parallel
implementation
Mathematics Subject Classiffication: 65M60
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Monday, September 3. 2018
R. Boonklurb1, A. Duangpan2 and T. Treeyaprasert3 1,2Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand 3Department of Mathematics and Statistics, Thammasat University, Rangsit Center, Pathumthani 12120, Thailand
Received 10 January 2018; accepted in revised form 27 August 2018
Abstract: We propose a modified finite integration method (FIM) by using the Chebyshev polynomial, to construct the first order integral matrix for solving linear differential equations in one and two dimensions. The grid points for the computation are generated by the zeros of the Chebyshev polynomial of a certain degree. We implement our method with several examples arose from real-world applications. In comparison with the finite difference method and the traditional FIMs (trapezoidal and Simpson's rules), numerical computations show that our modified FIM using Chebyshev nodes require the less computational cost to achieve significant improvement in accuracy.
c 2018 European Society of Computational Methods in Sciences and Engineering Keywords: Finite integration method, Linear differential equations, Chebyshev polynomial. Mathematics Subject Classication: 65L05, 65L10, 65N30
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