Modified Method of Characteristics for Generating EOR Oil Recovery Curves

The paper describes a fast and approximate 1D simulation algorithm for calculating the percent recovery that can be obtained from an oil reservoir if gas injection is carried out at a pressure lower than the minimum miscibility pressure. The algorithm is based on the Method of Characteristics. While a conventional 1D reservoir simulation of a gas injection scenario may take minutes or even hours, the proposed algorithm allows a full evaluation of the recovery to be completed within seconds. To make the method numerically robust, a number of approximations were needed. The result is an extremely fast algorithm that not only provides a good estimate of the recovery obtained by gas injection, but also gives a good visualization of how the gas displaces the oil.

A Numerical Method for Compressible Model of Contamination from Nuclear Waste in Porous Media

This paper studies and analyzes a model describing the flow of contaminated brines through the porous media under severe thermal conditions caused by the radioactive contaminants. The problem is approximated based on combining the mixed finite element method with the modified method of characteristics. In order to solve the resulting algebraic nonlinear equations efficiently, a two-grid method is presented and discussed in this paper. This approach includes a small nonlinear system on a coarse grid with size H and a linear system on a fine grid with size h . It follows from error estimates that asymptotically optimal accuracy can be obtained as long as the mesh sizes satisfy H = O h 1 / 3 .

A Three-Dimensional Monotonicity-Preserving Modified Method of Characteristics on Unstructured Tetrahedral Meshes

Slope limiters have been widely used to eliminate nonphysical oscillations near discontinuities generated by finite volume methods for hyperbolic systems of conservation laws. In this study, we investigate the performance of these limiters as applied to three-dimensional modified method of characteristics on unstructured tetrahedral meshes. The focus is on the construction of monotonicity-preserving modified method of characteristics for three-dimensional transport problems with discontinuities and steep gradients in their solutions. The proposed method is based on combining the modified method of characteristics with a finite element discretization of the convection equations using unstructured grids. Slope limiters are incorporated in the method to reconstruct a monotone and essentially nonoscillatory solver for three-dimensional problems at minor additional cost. The main idea consists in combining linear and quadratic interpolation procedures using nodes of the element where departure points are localized. We examine the performance of the proposed method for a class of three-dimensional transport equations with known analytical solutions. We also present numerical results for a transport problem in three-dimensional pipeline flows. In considered test problems, the proposed method demonstrates its ability to accurately capture the three-dimensional transport features without nonphysical oscillations.

A stabilized well-balanced RBF-FD meshless method for shallow-water equations

In this work, we are concerned with the study and computing of stabilized radial basis function-generated finite difference (RBF-FD) approximations for shallow-water equations. In order to obtain both stable and highly accurate numerical approximations of convection-dominated shallow-water equations, we use stabilized flat Gaussians (RBFSGA-FD) and polyharmonic splines with supplementary polynomials (RBFPHS-FD) as basis functions, combined with modified method of characteristics. These techniques are combined with careful design for the spatial derivative operators in the momentum flux equation, according to a general criterion for the exact preservation of the “lake at rest” solution in general mesh-based and meshless numerical schemes for the strong form of the shallow-water equations with bottom topography. Both structured and unsructured point clouds are employed for evaluating the influence of cloud refinement, size of local supports and maximal permissible degree of the polynomials in RBFPHS-FD.