A high order method is formulated for solving the miscible displacement problem and modeling viscous fingering. Viscous fingering in porous media may occur when a fluid with low viscosity is used to displace a fluid with high viscosity. For this type of flow instability, a tiny perturbation can be amplified exponentially, which triggers a finger-like pattern in the fluid concentration profile...
In this presentation, we discuss enriched Galerkin (EG) algorithms for modeling Darcy flow, reactive transport, and elastic wave propagation. This approach involves enriching the continuous Galerkin finite element method with discontinuous elements. For transport EG is coupled with entropy residual stabilization for transport. The method provides locally and globally conservative fluxes,...
The accurate high-order approximation in space and time is of fundamental importance for the simulation of dynamic poroelastic models which include coupled fluid flow, deformation and wave propagation.
Dynamic poroelastic models appear for example Lithium-ion battery fast-charge simulations and include sharp concentration and pressure gradients, high mechanical stresses, elastic wave...
Newly developed weak Galerkin (WG) finite element methods will be introduced for solving partial differential equations on polygonal mesh.
The weak Galerkin method is a natural extension of the standard Galerkin finite element method for the function with discontinuity where classical derivatives are substituted by weakly defined derivatives. Therefore, the weak Galerkin methods have the...
Standard models for flows in porous media assume that quantities like saturation, phase pressure differences, or relative permeability are related by monotone, algebraic relationships. These relationships are determined experimentally, assuming that the involved quantities have reached a local equilibrium. Under such assumptions, the solutions of the resulting mathematical models have...
We present a general implicit weighted essentially non-oscillatory (iWENO) method for solving advection-diffusion equations that is locally conservative and third order accurate, simple to implement, and allows general computational meshes. The scheme is quite robust, since it is unconditionally stable for smooth solutions to linear problems in 1D. The scheme requires only two unknowns per...
One of the most challenging issues in computational poromechanics is the development of numerical schemes capable of capturing in an accurate fashion the effects of spatial variability in the formation properties by handling highly heterogeneous coefficients with complex spatial distributions while preserving local conservation properties. In this work we present a new higher order...
The ISECG aims to realize the Mars manned space exploration mission in the 2030s. Since the duration of the Mars mission is assumed to be three years, a big concern is how to supply food for astronauts during the mission. The realization of space agriculture may be a solution for food supply problems in space. Understanding a moisture behavior in porous media under various small gravity...
Recently, a new theoretical framework to describe 2-phase flow in porous media has been put forward by our research group. Within this theory, a transport equation for the wetting phase saturation can be derived. In order to utilize this new theory a constitutive relation is needed that characterizes the “mixing” of the two fluids. Here mixing is understood not as mixing on a molecular level,...
There are two main roles for the fractures in the gas reservoir development. On the one hand, fractures will improve the permeability of the reservoir, and the gas recovery of the high permeability reservoir will be higher than that of the low permeability under the same abandonment gas production rate. On the other hand, the water will rush along the fractures and the gas-water two phases...
Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, New York, United States
An instability analysis of Poiseuille flow of concentrated suspensions in a channel is studied. The Poiseuille flow with two layers where both dilute and concentrated suspensions flow is overlaid by a soft porous media is considered for the analysis. The Brinkmann equation together...
This paper introduces an original application of the hypercomplex numbers known as Quaternions to model non-isothermal processes in porous rocks. The general thermoporoelastic linear theory is introduced in four dimensions and reformulated as a set of quaternions. The need of the fourth dimension appears naturally because of the pores presence. It is shown that a minimum set of four...
Enriched Galerkin (EG) methods were defined in 2009. The idea is to use a variational form arising from a discontinuous Galerkin (DG) method, but instead of using discontinuous approximating spaces, one uses a continuous space enriched with piecewise discontinuous constants. EG has fewer degrees of freedom than DG, and so is easier to solve, but it maintains the local conservation property of...
Weighted essentially non-oscillatory (WENO) schemes can be used to solve the equations governing transport in porous media. They are also useful in defining slope limiters for discontinuous Galerkin and other finite volume or finite difference methods. WENO reconstructions are a weighted average of polynomial approximations defined on various grid stencils. They are designed to produce high...
