Question $1[20$ marks$]$

Briefly explain, using equations where you deem necessary, the following

concepts:

$($a$)$ Finite volume method $[3$ marks$]$

$($b$)$ Divergence theorem $[3$ marks$]$

$($c$)$ The main difference between the process of using a direct method $($e$.$g$.$

the Gauss elimination method$)$ to solve the governing equations and the

process of using an iterative method to solve the governing equations in

CFD$.[3$ marks$]$

$($d$)$ P$$clet number of a CFD problem in the respective of physics of a steady

diffusion$-$convection problem. $[3$ marks$]$

$($e$)$ Why the second$-$order central difference scheme and the first$-$order

upwind difference scheme may have different influences on the stability of

the CFD solve for a steady diffusion$-$convection problem. $[3$ marks$]$

$($f$)$ The benefit of and problem with using either hexahedral cells or

tetrahedral cells to create computational grids of CFD $[3$ marks$]$

$($g$)$ Residual of solutions to a governing equation $[2$ marks$]$

PTO