ИСТИНА

Mathematical modelling of magma formation and transport into the Earth's crust requires consideration of physical processes on multiple spatial and temporal scales. In particular, the equations describing the coupled filtration flow of magmatic melt and deformation of permeable porous rocks, require formulation of closure relations, usually obtained by averaging the properties of an idealized media \cite{yarushina2020}. Such constitutive models can be validated using direct numerical simulation of coupled deformation, chemical reactions, and multicomponent diffusion processes on a pore scale. In this work, we present an example of a pore-scale numerical modelling of nonlinear diffusion with phase separation in melting rocks, based on the solution of equations of the Cahn-Hilliard type. Also, we develop a coupled model of the filtration flow of melt through deformable permeable rocks and a thermodynamic model of plagioclase melting based on Gibbs energy minimization approach. The formation of regions with a high melt concentration due to spontaneous focusing of filtration flow being the result of viscoplastic (de)compaction of the pore space is shown.