Numerical Simulation in Engineering.

Objectives

  • Analyse engineering problems;
  • Analyse engineering problems and their modelling;
  • Clarify the main concepts in solving differential equations;
  • Introduce the most common methods for solving equations with partial derivatives
  • Implement numerical algorithms;
  • Evaluate numerical results;
  • Use of numerical computing tools

Program

  • Basic concepts of numerical integration and differentiation; Ordinary differential equations. Partial derivative equations (PDE).
  • 2D boundary conditions problems: elliptic equations. Finite difference method and formulation of the Finite Volume Method. Study of meshes. Mesh generation. Unstructured meshes. Resolution of algebraic discretization systems.
  • Non-stationary problems: 1D and 2D parabolic equations. Pre and post processing problems.
  • Formulation of the Finite Element Method. Interpolation and shape functions.
  • Application examples in various engineering domains. Test Problems/Application Examples in commercial software: Matlab and Ansys (Fluent).

Bibliography

  • S.C. Chapra e R.P. Canale, Numerical Methods for Engineers (7th edition), McGraw-Hill, 2015.
  • S.C. Chapra, Applied Numerical Methods W/MATLAB: for Engineers & Scientists (3rd Edition), McGraw-Hill, 2012.
  • Ferziger, J H ; Peric, M (1998). Computational Methods for fluids Dynamics, Springer Verlag, 1998.
  • Pozrikidis, C., Numerical computation in Science and Engineering, Oxford University Press, 1998.
  • Versteeg H.K. and Malalasekera W., “An introduction to Computational Fluid Dynamics: The finite volume method”, Longman Scientific & Technical, 1995.

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