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Description
Hermes-3 uses the pressure-diffusion model to represent the cross-field transport of fluid neutrals. This enables neutral advection, conduction and viscosity in the perpendicular direction according to diffusion coefficients which are each subject to flux limitation.
Hermes-3 has a fully implicit solver. Due to the inherent nonlinearity in the neutral equations and high neutral speeds through small cells, achieving good performance requires preconditioning.
While algebraic preconditioners such as LU are highly effective in 2D systems, they do not scale well to the large domains present in 3D turbulence or FCI applications of the code.
In this work, we consider an approach for physical preconditioning the neutral equations. Through an approximate block factorisation based on the physical blocks of neutral density, momentum and pressure, we derive a preconditioning approach that aims to preserve the underlying physics as much as possible while requiring an efficient approximation of the Schur complement that arises. Nonetheless, many questions and challenges still remain from the extreme scales and desire for overall computational efficiency in realistic simulations.