## Topic outline

- General
- Topic 1
### Topic 1

# Course Description

Introduction. Conservation laws of fluid motion and boundary conditions. The finite volume method for diffusion problems. The finite volume method for convection-diffusion problems. Solution algorithms for pressure-velocity coupling in steady flows. The finite volume method for unsteady flows. Turbulence and its modeling. Methods for dealing with complex geometries on structured or unstructured grids.

- Topic 2
- Topic 3
### Topic 3

## Conservation laws of fluid motion and boundary conditions

Governing equations of fluid flow and heat transfer: Conservation of mass momentum and energy. Equations of state. Navier–Stokes equations for a Newtonian fluid. Conservative form of the governing equations of fluid flow. Differential and integral forms of the general transport equations. Classification of fluid flow equations.

- Topic 4
### Topic 4

# The finite volume method for diffusion problems

The finite volume method for one-dimensional steady state diffusion. The tri-diagonal matrix algorithm. The finite volume method for two and three-dimensional steady state diffusion. Application of TDMA method to two and three-dimensional problems.

- Topic 5
### Topic 5

## The finite volume method for convection-diffusion problems

Steady one dimensional convection and diffusion. The central difference, upwind, hybrid, power law, QUICK and other higher order schemes. Properties of discretisation schemes: Conservativeness, boundedness, transportiveness. Stability problems of the schemes. TVD schemes; flux limiter functions

- Topic 6
### Topic 6

# Solution algorithms for pressure-velocity coupling in steady flows

The staggered and non-staggered grids. The momentum equations. The SIMPLE, SIMPLER, SIMPLEC and PISO algorithms

- Topic 7
### Topic 7

## The finite volume method for unsteady flows

One-dimensional unsteady heat conduction. Explicit, implicit and Crank-Nicholson schemes. Implicit methods for two-and three-dimensional convection-diffusion problems. Transient SIMPLE and PISO algorithms.

- Topic 8
### Topic 8

## Turbulence and its modeling

Transition from laminar to turbulent flow. Effect of turbulence on time averaged Navier-Stokes equations. Characteristics of simple turbulent flows. Free turbulent flows. Flat plate boundary layer and pipe flow. Turbulence models. Mixing length model The k-e model. Reynolds stress equation models. Algebraic stress equation models. Some recent advances.

- Topic 9
- Topic 10
### Topic 10

## Finite volume method on unstructured grids

Body-fitted co-ordinate grids for complex geometries. Cartesian vs. curvilinear grids. Curvilinear grids-difficulties. Block structured grids. Unstructured grids. Discritesation in unstructured grids. Discretisation of the diffusion, convection and source terms. Calculation of surface areas, volumes and gradients. Assembly of discretised equations. MIM method. TVD schemes in unstructured grids. High order convection schemes in unstructured grids.