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Module 1

Python Programming Fundamentals

• Installation of Anaconda Environment, working with Jupyter notebook

• Basics of Python Language; Python objects with details of shell/numbers/variables etc.

• Introduction to NumPy Library.

• Arithmetic and Numerical operations using NumPy

• Data Visualization and plotting using Matplotlib.

Module 2

Numerical Schemes and Solvers

• Forward, backward and central schemes, order of accuracy.

• Assessment of various schemes through python coding.

• Introduction to Iterative Solvers

• Implementation of Jacobi, Gauss-Seidel and SOR solvers using Python and study on their convergence behavior.

Module 3

Finite Element Method Fundamentals

• Governing equations, Strong vs weak form

• Galerkin formulation; Boundary conditions (Dirichlet and Neumann)

• Element types: 1D linear & quadratic

• Shape functions and interpolation error, Isoparametric mapping, Gaussian quadrature and integration                      accuracy

• Python implementation: Axial bar under static load, 1D Heat conduction

Module 4

Finite Element Methods for two-dimensional problems

• 2D triangular elements

• Poisson equation formulation

• Stress and flux computation; post-processing and visualization

• Python implementation: Plane stress plate with hole, 2D heat conduction (welding: moving heat source)

Module 5

Error Analysis & Convergence in FEM

• Sources of FEM error, error norms

• Mesh convergence studies (h-convergence)

• Patch test & consistency check       

• Python implementation in the Stress convergence in bar problem

Module 6

Finite Volume Methods Fundamentals

• Introduction to FVM, its formulation and basic theoretical concepts.

• 1D steady and unsteady heat conduction, stability conditions

• Developing python implementations of 1D steady & unsteady heat conduction equations.

• 1D Advection- Diffusion: Stability, upwinding & concepts of Numerical Diffusion.

• Developing python implementations of 1D Advection-diffusion Equations.

Module 7

Finite volume Methods for two-dimensional problems

• 2D diffusion equation

• Python implementation on 2D Diffusion equation and insights

• Fluid flow in 2D- Stream Function-Vorticity Approach.

• Implementing Lid driven cavity flow problem using Python.

• Visualization & Insights.