Adaptive stopping criterion of iterative solvers for efficient computational cost reduction: Application to Navier–Stokes with thermal coupling

In this article, a strategy for efficient computational cost reduction of numerical simulations for complex industrial applications is developed and evaluated on multiphysics problems. The approach is based on the adaptive stopping criterion for iterative linear solvers previously implemented for elliptic partial differential equations and the convection–diffusion equation. Control of the convergence of iterative linear solvers is inferred from a posteriori error estimators used for anisotropic mesh adaptation. Provided that the computed error indicator provides an equivalent control on the discretization error, it is a suitable ingredient to assess when enough accuracy has been reached so that iterations of algebraic solvers can be stopped. In practice the iterative solution is stopped when the algebraic error is lower than a percentage of the estimated discretization error. The proposed method proves to be an effective cost-free strategy to reduce the number of iterations needed without degrading the accuracy of the solution. The discretization in the current work is based on stabilized finite elements, while the Generalized Minimal Residual method (GMRES) is used as iterative linear solver. Numerical experiments are performed of increasing complexity, from manufactured solutions to industrial configurations to evaluate the efficiency and the strengths of the proposed adaptive method.