Unsteady Flux-Vector-Based Green Element Method

Abstract

This article extends the mathematical formulation and solution procedure of the modified 'q-based' GEM to unsteady situations, namely to the modified unsteady 'q-based' GEM. Solutions that provide information on the evolution of the pressure and the flux over long time intervals are available by incorporating the additional dimension of time into steady problems. This approach is first tested by solving an example for which an analytical solution is available. The numerical results for this example is found to be in excellent agreement with the analytical solution. Several problems involving geological features, such as wells and faults, are then investigated, with different properties applying to the faults. A strong influence of the low permeability faults is in evidence in these problems.

An Element-Driven Boundary Integral Treatment for Nonlinearity: A Coupled Nonlinear Two-Dimensional Burger’s Equation Test Case

“…Details of this procedure have previously been dealt with elsewhere (Onyejekwe [54][55][56], Lorinczi [27,28], Archer [30], Ramsuroop [53], Onyejekwe [54][55][56]); so only the most relevant will be mentioned. By Applying the Green's theorem, the integral analogs of equations (1a) and (1b) are given as:…”

“…The compelling need to make BEM a purely boundary-driven numerical technique motivates this trend. Unfortunately this is often accompanied by some numerical challenges some of which have been mentioned above and in some previous papers (Percher et al [26], Lorinczi [27], Lorinczi et al [28], Archer et al [29], Archer [30], Onyejekwe [31,32], Onyejekwe and Onyejekwe [33] Archer and Horne [34]). Numerical experience shows that direct application of BEM theory performs poorly in the absence of a strong link between the problem domain and the boundary as is found in the Laplace equation.…”

A Coupled Novel Green Element and Embedded Discrete Fracture Model for Simulation of Fluid Flow in Fractured Reservoir

“…Archer (1999Archer ( , 2006 et al [15,16] pointed out the error of original GEM can be reduced by adopting the overhauser interpolation functions. Pecher et al (2001) [17] and Lorinczi et al (2006Lorinczi et al ( , 2008Lorinczi et al ( , 2010 [18][19][20][21] presented a modified GEM, in which they used the continuity of flux vector component to approximate the flux term and increased the number of degrees of freedom of each internal node. Lorinczi et al do not use the traditional way of coupling the equations at the same source point into one equation.…”