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Curso internacional de curta duração: NUMERICAL SOLUTIONS IN WATER RESOURCES AND ENVIRONMENTAL APPLICATIONS



NUMERICAL SOLUTIONS IN WATER RESOURCES AND  ENVIRONMENTAL APPLICATIONS

Professor: José Goes Vasconcelos (Universidade de Auburn – AL – EUA)

                    https://www.researchgate.net/profile/Jose_Vasconcelos4

VAGAS LIMITADAS! – Pré-inscrição: g.ecotecno@gmail.com até 10 de junho de 2019.

CARGA-HORÁRIA: 30 horas – Período do curso 17 e 27/06/2019 – (dias e horário a combinar), podendo contabilizar 2 créditos correspondentes nos Cursos de pós-graduação.

Local: Centro de Tecnologia da UFSM

Público alvo: Alunos de Mestrado e Doutorado de Cursos de Engenharia

O curso será ministrado em português, com material em inglês.

Pré-requisitos: Conhecimentos de inglês, ofimática e disciplinas de hidráulica. Recomendável possuir conhecimentos de programação em qualquer linguagem.

EMENTA: 

Course Introduction

  • Background and history of numerical modeling
  • Fundamental concepts of numerical solutions
  • Parts of a numerical solution
  • Physical processes and mathematical models
  • Numerical methods vs. numerical schemes
  • Errors: types and sources. Accuracy
  • Theoretical and practical Stability concepts
  • Assignment 1 – Essay theme “My research interests and current available numerical solutions”

Introduction to Numerical solutions for Ordinary Differential Equations (ODEs)

  • ODE definition and components: initial conditions, boundary conditions
  • The example of a terminal velocity calculation – analytical solution
  • Contrasting analytical and numerical solutions
  • Numerical schemes for ODE solution
  • Introducing Finite-Difference, Explicit schemes for ODEs
  • Euler scheme / Runge-Kutta schemes

Numerical solutions for Ordinary Differential Equations (ODEs)

  • Revisiting Terminal Velocity Problem – numerical vs. analytical solution
  • Applications of ODEs in water and environmental engineering
  • Assignment 2 – Select one problem to solve:
  • River backwater profile calculation
  • Numerical solution of Streeter-Phelps equation
  • Stormwater Detention emptying solution
  • Hydrological routing using Muskingum-Cunge method
  • Transmission main startup calculation

Introduction to Numerical solutions for Partial Differential Equations (PDEs)

  • Classification of PDEs
  • Finite-Difference, Explicit schemes for PDEs
  • A solver for a 2-D Laplace Equation using Excel
  • Water Resources and Environmental Applications of PDEs
  • Fischer’s Initial Period Mixing of Contaminants in Rivers
  • One-dimensional turbulent diffusion processes for contaminant spread
  • Stream routing using the Kinematic Wave approach
  • Simple dam break solver
  • Assignment 3 – Select one PDE problem to solve

Wrapping up – more complex applications

  • St. Venant Equations with non-linear schemes
  • Shallow water equations/ Navier-Stokes equations

 


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