Derive expressions for ( i=1, 2, 3 and j=1, 2, 3) for a 3D curvilinear grid.

Using Equations 6.24 and 6.27, express dA _i and dV for a 3D curvilinear grid.

Starting with the p ? equation in Cartesian coordinates (see Chapter 5), derive Equation 6.39. Identify the neglected terms in Equation 6.39 and explain how the effect of these terms can be recovered in a predictor-corrector fashion.

Analogous to Equation 6.42, derive an expression for , _P.

Derive Equations 6.91, 6.92, and 6.93.

Derive Equation 6.113.

Using Equations 6.121 and 6.122, derive explicit symmetry boundary conditions for u _1,B and u _2,B.

Using Equations 6.125 and 6.126, derive explicit exit boundary conditions for u _1,B and u _2,B.

A boundary receives radiant influx . Derive expressions for Su and Sp for the node adjacent to this boundary and evaluate T _B .

Derive an exact expression for by control-volume discretisation over cell-face control volume c ₁ c ₂ c ₃ c ₄ shown in Figure 6.13.

Show that .

Verify Equations 6.139 and 6.140 in the evaluation of .

Starting with Equation 6.62, derive an expression for total convective-diffusive transport at the cell face of a tetrahedral element.

In Exercise 13, if the cell face were a boundary face, how would you determine the tangent vector if is along PP ₂?

Carry out discretisation of convection terms using a TVD...