Pivoting Strategies in the Solution of the Saint-Venant Equations

Abstract

Pivoting was incorporated in the process of solving the linear system of equations that results after discretizing the Saint- Venant equations using the four-point implicit scheme, and applying the Newton–Raphson algorithm to the resulting set of nonlinear equations. Both exchange of rows only (partial pivoting) and exchange of rows and columns (full pivoting) were investigated using the CanalMan hydraulic model. Partial pivoting was used with the LU (lower and upper) decomposition linear equation solver, whereas full pivoting was used with the Gauss–Jordan elimination algorithm. It was demonstrated that the application of partial and full pivoting to the solution of the linear set of equations during Newton–Raphson iterations can make the difference between convergence and divergence of the solution, and should be applied as needed. However, full pivoting should be used only when needed because it slows the simulation considerably.