Iterative schemes for coupled flow and transport in porous media -- Convergence and truncation errors

Abstract

Nonlinearities of coupled flow and transport problems for partially saturated porous media are solved with explicit iterative L-schemes. Their behavior is analyzed with the aid of the computational orders of convergence. This approach allows highlighting the influence of the truncation errors in the numerical schemes on the convergence of the iterations. Further, by using manufactured exact solutions, error-based orders of convergence of the iterative schemes are assessed and the convergence of the numerical solutions is demonstrated numerically through grid-convergence tests.

Keywords

• Richards' equation
• Coupled flow and transport
• Finite differences
• Global random walk
• Iterative schemes
• Convergence order