Let us consider equation (25.1) once again. is zero along the solid boundary and If we want to increase the accuracy, we have to retain the fourth term on the right hand side of equation (25.1). Now we shall try to evaluate the fourth term. We know from the definition of vorticity:

or,

or,

(25.16)

invoking (25.16) and substituting the values for and in equation (25.1), we get

(25.17)

Instead of we shall write to mean normal direction from the wall. We shall also substitute by a forward difference quotient as

or,

or,

(25.18)

Equation (25.18) is second order accurate boundary condition but it does not lead to stable computation for high Reynolds number flows.

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