دانلود رایگان مقاله ارزیابی خطی و غیر خطی حل کننده برای جریان تراکم محوری

Abstract

This study investigates properties of different solvers for density driven flow problems. The focus is on both non-linear and linear solvers. For the non-linear part, we compare fully coupled method using a Newton linearization and iteratively coupled versions of Jacobi and Gauss–Seidel type. Fully coupled methods require effective preconditioners for the Jacobian. To that end we present a transformation eliminating some couplings and present a strategy for employing algebraic multigrid to the transformed system as well. The work covers theoretical aspects, and provides numerical experiments. Although the primary focus is on density driven flow, we believe that the analysis may well be extended beyond to similar equations with coupled phenomena, such as geomechanics

5. Conclusion

This study elucidated on two important aspects for solvers for density driven flow problems: First, we investigated different nonlinear solvers and compared their convergence properties in numerical experiments. Here, a fully coupled scheme proved being superior to decoupling schemes. Second, we tailored an multigrid solver for a fully coupled Newton method. The essential ingredient is a left transformation that eliminates possible negative entries arising from the self couplings for the salt mass fraction.