Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
A SINGULAR CONSTITUTIVE RELATION FOR SATURATED/UNSATURATED FLOWS THROUGH POROUS MEDIA
Submission Author:
Maria Laura Martins-Costa , RJ , Brazil
Co-Authors:
Lucas Neves de Almeida, Maria Laura Martins-Costa, ROGERIO GAMA
Presenter: Lucas Neves de Almeida
doi://10.26678/ABCM.COBEM2023.COB2023-1316
Abstract
This work uses a mixture theory framework to describe a porous medium filling up or emptying process by a fluid, able to describe the saturated-unsaturated transition and vice-versa and to use the same mathematical tool for treating unsaturated and saturated flows. The mixture consists of three overlapping continuous constituents: a solid (rigid porous matrix), a liquid (incompressible fluid), and a gas with very low mass density, accounting for the mixture's compressibility. This paper proposes a new constitutive relation for pressure as a function of saturation, ensuring the system remains hyperbolic even when the flow becomes saturated and allowing a closed solution to the Riemann problem associated with the flow. The complete solution to the associated Riemann problem is presented in detail, allowing an explicit function relationship involving the saturation, the eigenvalues, and Riemann invariants, independent of velocity. Some graphs for saturation and velocity for selected time instants highlight the proposed constitutive relation advantages, especially when the states are connected by two shocks.
Keywords
Nonlinear Hyperbolic System, Constitutive Relation for Pressure, Flow through Unsaturated Porous Media, Shock Waves
