Boundary Layer Flow

Abstract

A tridiagonal system of equations to implement (15.98) can be derived as follows. Substituting for $u_j^\lambda ,v_j^\lambda ,L_y u_j$ and L _yy ^u _j in (15.98), we have $\begin{gathered} \left( {\lambda u_j^{n + 1} + \left( {1 - \lambda } \right)u_j^n } \right)\left( {\frac{{u_j^{n + 1} - u_j^n }} {{\Delta x}}} \right) + \hfill \\ \left( {\lambda v_j^{n + 1} + \left( {1 - \lambda } \right)v_j^n } \right)\left( {\lambda L_y u_j^{n + 1} + \left( {1 - \lambda } \right)L_y u_j^n } \right) \hfill \\ {\text{ = }}\lambda \left( {u_e u_{ex} } \right)^{n + 1} + \left( {1 - \lambda } \right)\left( {u_e u_{ex} } \right)^n + v\left( {\lambda L_{yy} u_j^{n + 1} + \left( {1 - \lambda } \right)L_{yy} u_j^n } \right). \hfill \\ \end{gathered}$