Internal Research Project I-02

Iterative solvers for ill-conditioned nonsymmetric monolithic systems

Research

Coupling porous media and free-flow is a common denominator of CFD research within SFB 1313, with a multitude of application domains. To address these problems computationally, the ‘coupled until proven uncoupled’ paradigm has been established. One way to achieve full coupling also in a numerical scheme is the monolithic approach, which is particularly attractive if the porous medium is described by some averaged formulation such as Darcy’s Law in the most simple case: All underlying physics, such as variants of the Navier-Stokes equations in the free-flow domain, and Darcy-like equations for the porous medium, are assembled into one nonlinear system. However, it turns out that this system, and linearised variants thereof, are notoriously hard to solve with classical iterative schemes for linear(ised) systems. This is due to the extreme difference in the rate in which the flow in the two domains is evolving, and in the scale difference of the domains of interest. In this auxiliary project, we will primarily examine novel and specifically tailored preconditioning techniques to solve monolithic systems with iterative schemes. In addition, we examine variants of monolithic Newton-like approaches for the nonlinear loop.

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