Step-by-Step Algorithm

The iterative solution method can be broken down into a number of distinct steps: i) define initial grid using blending functions in equation 29; ii) compute functions $g_{11}(\mathbf{s^0_{ij}})$, $g_{12}(\mathbf{s^0_{ij}})$,$g_{22}(\mathbf{s^0_{ij}})$, $g(\mathbf{s^0_{ij}})$, L_ij(u⁰), L_ij(v⁰), M_ij(u⁰), M_ij(v⁰), $P_{ij}(\mathbf{s}^0)$,$Q_{ij}(\mathbf{s}^0)$, and $b^l_{ij}(\mathbf{s}^0)$; iii) compute u_ij^0+1/2 by solving equation 31; iv) compute v_ij^0+1/2 by solving equation 32; v) compute u_ij⁰⁺¹ by solving equation 33; vi) compute v_ij⁰⁺¹ by solving equation 34; vii) perform tolerance test in equation 51; and viii) repeat steps 2-7 until tolerance is reached.