Method SPH for numerical solution of filtering problems: including capillary forces in fluid flow simulation

Abstract

This paper explores the theory of filtration within porous media, focusing on multicomponent mixtures’ dynamics and their numerical modeling. Key equations governing filtration, including Darcy’s law and mass conservation, are introduced. The concept of smoothed particle hydrodynamics (SPH) is presented as a powerful numerical technique for approximating these equations. SPH’s integral interpolation approach accommodates complex fluid-solid interactions and is applied to one-dimensional and two-dimensional test cases. Results demonstrate SPH’s effectiveness in capturing intricate dynamics and aligning with traditional methodologies. This study contributes to understanding fluid dynamics in porous media and underscores SPH’s potential for accurate simulations in diverse applications, from hydrocarbon reservoirs to environmental systems. The first section in your paper.