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