1st Edition

Numerical Modeling of Coupled Phenomena in Science and Engineering Practical Use and Examples

    Mathematics is a universal language. Differential equations, mathematical modeling, numerical methods and computation form the underlying infrastructure of engineering and the sciences. In this context mathematical modeling is a very powerful tool for studying engineering problems, natural systems and human society. This interdisciplinary book contains a comprehensive overview, including practical examples, of the progress achieved to date in the modeling of coupled phenomena, computational mathematics and mechanics, heat transfer, fluid-structure interactions, biomechanics, and the flow of mass and energy in porous media. Numerical subjects such as grid generation, optimization, finite elements, finite differences, spectral methods, boundary elements, finite volumes and meshless methods are also discussed in detail using real examples.

    The book provides a thorough presentation of the existing numerical techniques with specific applications to concrete, practical topics. The models and solutions presented here describe various systems: mechanical, biological, geophysical, technical, ecological, etc. The book is organized in thirty six chapters, each written by distinguished experts in their respective fields. The topics presented cover the current state of knowledge in numerical engineering practice including recent and ongoing developments and the presentation of new ideas for future research on applied computational engineering mathematics.

    The book will be of interest to scientists working in engineering (structural, civil, mechanical), geology, geophysics, aquifer research, petroleum engineering, applied mathematics, and physics, as well as students in any of these areas.

    Table of Contents

    Authors’ CVs by Chapter XIX

    Part 1: Computational mathematics, modeling and numerical methods

    1 Mathematical and computational modeling in Mexico; I. Herrera-Revilla

    2 Numerical solution of boundary inverse problems for orthotropic solids; I. Brilla

    3 Reliable numerical solutions for random differential systems; L. Jódar Sánchez, J.C. Cortés & L. Villafuerte

    4 Area functionals for high quality grid generation; P. Barrera-Sánchez, G. González Flores, F. Domínguez-Mota, J.L. Castellanos Noda & A. Pérez Domínguez

    5 Multi-objective topological optimization of structures; S.I. Valdez Peña, S. Botello Rionda & A. Hernández Aguirre

    6 Some patterns in primes and their possible applications as quasi-Monte Carlo methods in multivariable integration; A. Ortiz-Tapia

    7 Comparison between discrete and continuous Schrödinger operators with a small potential well; J.A. Rodriguez-Ceballos & P. Zhevandrov

    8 Enhanced finite elements: A unified approach; I. Herrera-Revilla

    Part 2: Coupled problems in fluid-structure interactions and in heat transfer

    9 Simulation of structural response to violent-free surface flows, R. Löhner, C. Yang & E. Oñate

    10 Fluid structure interaction and proper orthogonal decomposition (POD) method, M. Benaouicha, E. Liberge & A. Hamdouni

    11 Numerical models for simulation of the seismic behavior of RC structures—A case study, H. Varum, A. Costa & H. Rodrigues

    12 Numerical modeling of wave phenomena (refraction-diffraction) applied to breakwaters of the cooling water intake of Laguna Verde nuclear power plant in Veracruz, Mexico, I.E. Herrera D., H. Ramírez, L., C. Couder C. & I. Campos P.

    13 Computer simulations of open-cell foams thermo-conductivity properties, O. Tkachenko & S. Kanaoun

    14 Numerical simulation of a basic steelmaking furnace, D.Y. Medina & M.A. Barrón

    15 Unsteady natural convection in interconnected systems, C.I. Rivera-Solorio, A.J. García-Cuéllar, J.J. González Villafaña & R. Ramírez Tijerina

    16 Dynamic-thermal-structural analysis of a gas turbine blade with internal cooling, A. Campos-Amezcua, Z. Mazur, G.M. García-Gómez, A. Gallegos-Muñoz, J.M. Riesco-Ávila, J.A. Alfaro-Ayala, V. Pérez-García & J.J. Pacheco-Ibarra

    17 Transient analysis of a geothermal snow-melting system on a typical bridge, S. Porkhial, O. Asghari & M.R. Shirzadi

    Part 3: Computational mechanics of fluids and solids, multiphysics, biomechanics

    18 Fast calculation of electro- and thermo-static fields in 3D-medium with an isolated heterogeneous inclusion using Gaussian approximating functions and application of FFT, S. Babaii K. & S. Kanaoun

    19 Analytic-numerical approach of the equations to simulate wave amplitude attenuation in silencers of exhaust systems of internal combustion engines, J.M. Arnau, J.V. Romero, M.D. Roselló & J.A. Torregrosa

    20 Adaptive FE limit analysis bounds approach to the computation of the limit load in plane stress, R. Cordero & J. Bonet

    21 Probability density functions from patterns in primes’ indices—Perspectives of usage as a quasi-Monte Carlo method, A. Ortiz-Tapia

    22 An arterial element for modeling vascular flow, S. Gallegos, J. Cortés, L. Florez & A. Robles

    Part 4: Flow of mass and energy in porous media

    23 3D analytical solutions for transport in a double porosity media, R. González-Herrera

    24 Systematic formulation of continuum systems: Theoretical modelling of combustion fronts in porous media, D. López-Falcón, M. Díaz-Viera, I. Herrera-Revilla & E. Rodríguez-Jáuregui

    25 Trefftz-Herrera collocation method: Numerical modelling of combustion fronts in porous media, M. Díaz-Viera, D. López-Falcón & I. Herrera-Revilla

    26 The integrated finite difference method (IFD), applied to simulate groundwater flow in the aquifer of Morelia, Michoacán, Mexico, J.A. Rodríguez Castro

    27 Numerical modeling of the coupled flow of brine and oil in hydrocarbon reservoirs, M.C. Suárez Arriaga, F. Samaniego & J. Bundschuh

    Part 5: Boundary elements, spectral and meshless methods, numerical optimization

    28 A novel boundary element multiscale method for damage modelling, G. Sfantos & M.H. Aliabadi

    29 A formulation based on the localized Lagrange multipliers for solving 3D frictional contact problems using the BEM, L. Rodríguez-Tembleque, J.Á. González & R. Abascal

    30 Spectral methods in third-order differential operators, C. Gómez de la Garza & G. López Mariscal

    31 Wave propagation in a biphasic fluid-solid media, with a pseudo-spectral FD scheme, J.J. Pérez Gavilán, E. Flores & F.J. Sánchez-Sesma

    32 A numerical particle method for the simulation of mass flows in volcanoes, M.X. Rodríguez Paz & D.R. Sol Martínez

    33 The car traffic problem to evacuate people in the Popocatépetl volcano, D.R. Sol Martínez, M.X. Rodríguez Paz & C. Zepeda

    34 Numeric optimization of the hydrodynamic model YAXUM/3D, C. Couder C., H. Ramírez L. & I.E. Herrera D.

    35 Calculating the outline of a petal tool for polishing optical surfaces using linear programming, C. Castañeda, L.J. Manzano, J. González & A. Cordero


    Mario César Suárez Arriaga, Jochen Bundschuh, Francisco Javier Dominguez-Mota