/* -*- mode: maxima -*- */

/* The discretization of the first SSA equation (without the drag term): */
lhs1: '(- 2 * w[i+1/2,j] * N[i+1/2,j]/dx * (2 * d_px(u[i,j])/dx + (D_y(v[i,j]) + D_y(v[i+1,j]))/(4*dy))
        + 2 * w[i-1/2,j] * N[i-1/2,j]/dx * (2 * d_mx(u[i,j])/dx + (D_y(v[i,j]) + D_y(v[i-1,j]))/(4*dy))
            - w[i,j+1/2] * N[i,j+1/2]/dy * (1 * d_py(u[i,j])/dy + (D_x(v[i,j]) + D_x(v[i,j+1]))/(4*dx))
            + w[i,j-1/2] * N[i,j-1/2]/dy * (1 * d_my(u[i,j])/dy + (D_x(v[i,j]) + D_x(v[i,j-1]))/(4*dx)))$

rhs1: '(-rho * g * H[i,j] * D_x(h[i,j]) / (2*dx) + tau[b,1][i,j])$

eq1: lhs1 = rhs1$

/* The discretization of the second SSA equation (without the drag term): */
lhs2: '(- 2 * w[i,j+1/2] * N[i,j+1/2]/dy * (2 * d_py(v[i,j])/dy + (D_x(u[i,j]) + D_x(u[i,j+1]))/(4*dx))
        + 2 * w[i,j-1/2] * N[i,j-1/2]/dy * (2 * d_my(v[i,j])/dy + (D_x(u[i,j]) + D_x(u[i,j-1]))/(4*dx))
            - w[i+1/2,j] * N[i+1/2,j]/dx * (1 * d_px(v[i,j])/dx + (D_y(u[i,j]) + D_y(u[i+1,j]))/(4*dy))
            + w[i-1/2,j] * N[i-1/2,j]/dx * (1 * d_mx(v[i,j])/dx + (D_y(u[i,j]) + D_y(u[i-1,j]))/(4*dy)))$

rhs2: '(-rho * g * H[i,j] * D_y(h[i,j]) / (2*dy) + taub[b,2][i,j])$

eq2: lhs2 = rhs2$