AFiD-Darcy: A finite difference solver for numerical simulations of convective porous media flows

Abstract

We present an efficient solver for massively-parallel simulations of convective, wall-bounded and incompressible porous media flows. The algorithm consists of a second-order finite-difference pressure-correction scheme, allowing the use of an efficient FFT-based solver in problems with different boundary conditions. The parallelization method is implemented in a two-dimensional pencil-like domain decomposition, which enables efficient parallel large-scale simulations. The original version of the code presented by van der Poel et al. (2015) [35] has been modified to solve the Darcy equation for the momentum transport, representative of porous media flows driven by buoyancy. Two schemes are implemented to treat the diffusive term of the advection-diffusion equation, namely a fully implicit and semi-implicit formulation. Despite exhibiting a higher computational cost per time step, the fully implicit scheme allows an efficient simulation of transient flows, leading to a smaller time-to-solution compared to the semi-implicit scheme. The implementation was verified against different canonical flows, and the computational performance was examined. To show the code's capabilities, the maximal driving strength explored has been doubled as compared to state-of-art simulations, corresponding to an increase of the associated computational effort of about 8 to 16 times. Excellent strong scaling performance is demonstrated for both schemes developed and for domains with more than 10¹⁰ spatial degrees of freedom.