8 ME4.2-COMPUTATIONAL FLUID FLOW AND HEAT TRANSFER
Units: I
Review of basic fluid mechanics and the governing (Navier-Stokes) equations.
Types of partial differential equations- hyperbolic, parabolic and elliptic.
Traditional solution methods- method of characteristics, separation of variables, Greens
function
method.
Units: II
Preliminary computational techniques: Discretisation, converting derivatives to discrete
algebric expressions, spatial derivatives, time derivatives. Approximation of derivatives,
Taylor series expansion, general techniques. Accuracy of discretisation process-higher order
vs lower order formulae.
Units: III
Finite difference method: conceptual implementation, application to transient heat conduction
problem.
Convergence, consistency and stability of FD equation.
Units: IV
Weighted residual methods: General formulation, Introduction to Finite Volume method.
Finite Volume method: Equations with first derivatives and second derivatives. FV
method applied to Laplace’s equation.
Units: V
Finite Element method: Linear interpolation, quadratic interpolation, two
dimensional interpolation. Application to heat transfer problems.