Showing papers by "Mary F. Wheeler published in 1999"

Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. Part I

Abstract: Three Galerkin methods using discontinuous approximation spaces are introduced to solve elliptic problems. The underlying bilinear form for all three methods is the same and is nonsymmetric. In one case, a penalty is added to the form and in another, a constraint on jumps on each face of the triangulation. All three methods are locally conservative and the third one is not restricted. Optimal a priori hp error estimates are derived for all three procedures.

A Parallel Multiblock/Multidomain Approach for Reservoir Simulation

Abstract: Our approach for parallel multiphysics and multiscale simulation uses two levels of domain decomposition: physical and computational. First, the physical domain is decomposed into subdomains or blocks according to the geometry, geology, and physics/chemistry/biology. Each subdomain represents a single physical system, on a reasonable range of scales, such as a black oil region, a compositional region, a region to one side of a fault, or a near-wellbore region. Second, the computations are decomposed on a parallel machine for efficiency. That is, we use a multiblock or macro-hybrid approach, in which we describe a domain as a union of regions or blocks, and employ an appropriate hierarchical model on each block. This approach allows one to define grids and computations independently on each block. This local grid structure has many advantages. It allows the most efficient and accurate discretization techniques to be employed in each block. The multiblock structure of the algebraic systems allows for the design and use of efficient domain decomposition solvers and preconditioners. Decomposition into independent blocks offers great flexibility in accommodating the shape of the external boundary, the presence of internal features such as faults and wells, and the need to refine a region of the domain in space or time (by treating it as a distinct block); interfacing structured and unstructured grids; and accommodating various models of multiscale and multiphysical phenomena. The resulting grid is not suited to direct application of discretization methods. We use mortar space techniques to impose physically meaningful, mass conservative, fluxmatching conditions on the interfaces between blocks. We present numerical simulations to illustrate several of these decomposition strategies, including the coupling of IMPES and fully implicit models and upscaling by varying the number of degrees of freedom on the block interfaces.

Staggered In Time Coupling of Reservoir Flow Simulation and Geomechanical Deformation: Step 1 - One-Way Coupling

Abstract: An isothermal, implicit, mixed finite element black oil reservoir simulator from the University of Texas is coupled to an explicit, quasistatic, nonlinear finite element solid mechanics code from Sandia National Laboratories. Both codes are 3d and parallel. The former models (in a locally conservative manner) the flow of oil, gas, and water fluid phases in the reservoir while the latter has been specialized to solve large-scale geomechanics problems involving significant inelastic deformations. In this paper we illustrate a uni-directional coupling of the two codes in which flow simulation output (pore pressures) from a 10-year test case based on the Belridge Field in California drives the geomechanics simulation for the same time period. The highporosity, low-permeability Belridge diatomite undergoes significant compaction including 6 feet of vertical displacement at the top of the reservoir.