Characteristics Collocation Method of Compressible Miscible Displacement with Dispersion

Abstract

The compressible miscible displacement in a porous media is considered in this paper. The problem is a nonlinear system with dispersion in non-periodic space. The concentration is treated by a characteristics collocation method, and the pressure is treated by an orthogonal collocation method. Optimal order estimates are derived.

Bound-Preserving Discontinuous Galerkin Method for Compressible Miscible Displacement in Porous Media

“…Subsequently, many new methods were introduced to solve the compressible miscible displacements, such as finite difference method [43,44,45], characteristics collocation method [21], splitting positive definite mixed element method [35] and H 1 -Galerkin mixed method [3]. Besides the above, in [30], an accurate and efficient simulator is developed for problems with wells.…”

High Order Bound-Preserving Discontinuous Galerkin Methods and Their Applications in Petroleum Engineering

“…Later, the compressible problem was studied in [17] and the optimal order estimates in L 2 -norm and almost optimal order estimates in L ∞ -norm were given in [11]. Subsequently, many new numerical methods were introduced, such as the finite difference method [47,48,49], characteristic finite element method [27], splitting positive definite mixed element method [40] and H1-Galerkin mixed method [9]. Besides the above, in [35], an accurate and efficient simulator was developed for problems with wells.…”

Discontinuous Galerkin methods for convection-diffusion equations and applications in petroleum engineering

“…Subsequently, many new numerical methods were introduced, such as the finite difference method[81,82,83], characteristic finite element method[48], splitting positive definite mixed element method[70] and H1-Galerkin mixed method[7]. Besides the above, in[59], an accurate and efficient simulator was developed for problems with wells.…”