Ilya D. Mishev

On the coupling of finite volume and discontinuous Galerkin method for elliptic problems

The coupling of cell-centered finite volume method with primal discontinuous Galerkin method is introduced in this paper for elliptic problems. Convergence of the method with respect to the mesh size is proved. Numerical examples confirm the theoretical rates of convergence. Advantages of the coupled scheme are shown for problems with discontinuous coefficients or anisotropic diffusion matrix.

Nonconforming Finite Volume Methods

We extend and generalize recently proposed finite volume methods using the framework of mixed finite element methods. Proposed discretizations are defined for tensor permeabilities and naturally produce a generalization of harmonic averaging, and are therefore well suited for heterogeneous and anisotropic media. They are locally mass conservative and work on extremely flexible distorted meshes. Flux variables can be excluded locally and the resulting discretizations for the pressures has the same stencils for Voronoi/PEBI grids as 2-point finite volume discretizations currently used in many simulators.

Adaptive Parallel Reservoir Simulation

This paper was selected for presentation by an IPTC Programme Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the International Petroleum Technology Conference and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the International Petroleum Technology Conference, its officers, or members. Papers presented at IPTC are subject to publication review by Sponsor Society Committees of IPTC. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the International Petroleum Technology Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Abstract The availability of multi-core CPUs for personal computers makes desktop parallel computing a reality. Parallel computing for reservoir simulation creates the opportunity for significant run time reduction but also introduces additional technical challenges, particularly in the areas of load balancing and general algorithmic robustness. In this paper we will discuss the development and application of ExxonMobils numerical reservoir simulator, EM powerTM , to parallel desktop systems, focusing on the following areas: • A flexible, hierarchical, object-oriented design that supports fast development, functionality encapsulation, and ease of maintenance • A fully unstructured grid for modeling large and complex reservoirs with fewer gridblocks, yet retaining accurate physics • A highly efficient and robust parallel partition of the fully unstructured grids for modeling large and complex reservoirs • Built-in intelligence for the solver suite and parallel execution to fulfill specific algorithmic needs • Adaptive Implicit Method (AIM) for a high-level of numerical stability with significant run-time speed-up and memory footprint reduction • Dynamic load balancing for seamless integration between shared-memory based parallel computing and adaptive implicit methods We will also describe experiences with real models and briefly discuss mechanisms for addressing problems encountered. We will demonstrate that we can achieve a 3~4 time speedup over serial runs without AIM on real field cases using quad-core machines.