We propose a novel finite volume method for anisotropic linear elasticity problem. The derivation of the flux approximation method for elasticity problem closely follows our previous work [1] on the nonlinear finite volume methods for diffusion equation featuring positivity and discrete maximum principles. It is based on the extensions of the harmonic point idea of [2] from the scalar to...
We develop higher order multipoint flux mixed finite element (MFMFE) methods for solving elliptic problems on quadrilateral and hexahedral grids that reduce to cell-based pressure systems. The methods are based on a new family of mixed finite elements, which are enhanced Raviart-Thomas spaces with bubbles that are curls of specially chosen polynomials. The velocity degrees of freedom of the...
In this work a general model of multiphase flow and multicomponent transport in porous media to simulate, analyze and interpret hydrocarbon recovery processes by injecting low salinity water using open source software is presented. The flow model is multiphase considering capillary pressure and relative permeabilities depending on salinity, while the transport model is multicomponent and...
CO$_2$ capture and storage is an important technology for mitigating climate change. Design of efficient strategies for safe, long-term storage requires the capability to efficiently simulate processes taking place on very different temporal and spatial scales. The physical laws describing CO$_2$ storage are the same as for hydrocarbon recovery, but the characteristic spatial and temporal...
