Week 1: Governing conservations equations of fluid flow and classification of system of partial differential equations (PDEs)
Week 2: Methods for approximate solution of PDEs: brief overview of finite difference, finite volume and finite element approaches
Week 3: Taylor table approach for constructing finite difference schemes of arbitrary orders of accuracy, implementation of schemes near boundaries
Week 4: Numerical solution of steady state heat conduction (Elliptic PDE) using various explicit and implicit schemes, implementation of boundary conditions, mesh dependence and convergence of solution
Week 5: Numerical solution of unsteady heat conduction (Parabolic PDE) using various schemes, implementing initial and boundary conditions, stability analysis, multi-dimensional implementation
Week 6: Numerical solution of linear wave equation (Hyperbolic PDE) using various schemes, artificial viscosity, diffusion and dispersion error, stability analysis
Week 7: Numerical solution of one dimensional convection-diffusion equation
Week 8: Numerical solution of two dimensional incompressible Navier Stokes equations
Week 9: Numerical solution of one dimensional Euler equation for shock tube problem
Week 10:Basics of interface capturing methods for application in multiphase flow
Week 11:Basics of turbulence modeling
Week 12:Structured and unstructured grid generation
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