ConvectiveFoam1.0: development and benchmarking of a infinite-Pr number solver

Abstract. We developed a new fluid-dynamical numerical model, which we call convectiveFoam, designed to simulate fluids with very large Prandtl number. First we implemented the high-Pr case, in which advection still acts explicitly, and then the Pr → ∞ version, where the momentum equation becomes diagnostic (that is, without time derivatives) and it is formalized as an elliptic problem. The new solver, based on a finite volume integration method, is developed on the OpenFOAM platform and it exhibits a good performance in terms of computational costs and accuracy of the results. Scaling properties show a maximum performance around 16000 cells/core, in agreement with other works developed on the same platform. A systematic validation of the solver was performed for both 2D and 3D geometries, showing that convectiveFoam is able to reproduce the main results of several iso-viscous cases. This new solver can thus simulate idealized configurations of natural geophysical convection, such as in the Earth Mantle where Pr = 10²³. This solver represents a starting point for general exploration of the behaviour and parameter dependence of several fluid systems of geological interest.