26 research outputs found
An efficient and effective nonlinear solver in a parallel software for large scale petroleum reservoir simulation
Abstract. We study a parallel Newton-Krylov-Schwarz (NKS) based algorithm for solving large sparse systems resulting from a fully implicit discretization of partial differential equations arising from petroleum reservoir simulations. Our NKS algorithm is designed by combining an inexact Newton method with a rank-2 updated quasi-Newton method. In order to improve the computational efficiency, both DDM and SPMD parallelism strategies are adopted. The effectiveness of the overall algorithm depends heavily on the performance of the linear preconditioner, which is made of a combination of several preconditioning components including AMG, relaxed ILU, up scaling, additive Schwarz, CRPlike(constraint residual preconditioning), Watts correction, Shur complement
A constrained pressure-temperature residual (CPTR) method for non-isothermal multiphase flow in porous media
For both isothermal and thermal petroleum reservoir simulation, the
Constrained Pressure Residual (CPR) method is the industry-standard
preconditioner. This method is a two-stage process involving the solution of a
restricted pressure system. While initially designed for the isothermal case,
CPR is also the standard for thermal cases. However, its treatment of the
energy conservation equation does not incorporate heat diffusion, which is
often dominant in thermal cases. In this paper, we present an extension of CPR:
the Constrained Pressure-Temperature Residual (CPTR) method, where a restricted
pressure-temperature system is solved in the first stage. In previous work, we
introduced a block preconditioner with an efficient Schur complement
approximation for a pressure-temperature system. Here, we extend this method
for multiphase flow as the first stage of CPTR. The algorithmic performance of
different two-stage preconditioners is evaluated for reservoir simulation test
cases.Comment: 28 pages, 2 figures. Sources/sinks description in arXiv:1902.0009
A block preconditioner for non-isothermal flow in porous media
In petroleum reservoir simulation, the industry standard preconditioner, the
constrained pressure residual method (CPR), is a two-stage process which
involves solving a restricted pressure system with Algebraic Multigrid (AMG).
Initially designed for isothermal models, this approach is often used in the
thermal case. However, it does not have a specific treatment of the additional
energy conservation equation and temperature variable. We seek to develop
preconditioners which better capture thermal effects such as heat diffusion. In
order to study the effects of both pressure and temperature on fluid and heat
flow, we consider a model of non-isothermal single phase flow through porous
media. For this model, we develop a block preconditioner with an efficient
Schur complement approximation. Both the pressure block and the approximate
Schur complement are approximately inverted using an AMG V-cycle. The resulting
solver is scalable with respect to problem size and parallelization.Comment: 35 pages, 3 figure
Algebraic Domain Decomposition Methods for Highly Heterogeneous Problems
International audienceWe consider the solving of linear systems arising from porous media flow simulations with high heterogeneities. Using a Newton algorithm to handle the non-linearity leads to the solving of a sequence of linear systems with different but similar matrices and right hand sides. The parallel solver is a Schwarz domain decomposition method. The unknowns are partitioned with a criterion based on the entries of the input matrix. This leads to substantial gains compared to a partition based only on the adjacency graph of the matrix. From the information generated during the solving of the first linear system, it is possible to build a coarse space for a two-level domain decomposition algorithm that leads to an acceleration of the convergence of the subsequent linear systems. We compare two coarse spaces: a classical approach and a new one adapted to parallel implementation
Parallel numerical modeling of hybrid-dimensional compositional non-isothermal Darcy flows in fractured porous media
This paper introduces a new discrete fracture model accounting for
non-isothermal compositional multiphase Darcy flows and complex networks of
fractures with intersecting, immersed and non immersed fractures. The so called
hybrid-dimensional model using a 2D model in the fractures coupled with a 3D
model in the matrix is first derived rigorously starting from the
equi-dimensional matrix fracture model. Then, it is dis-cretized using a fully
implicit time integration combined with the Vertex Approximate Gradient (VAG)
finite volume scheme which is adapted to polyhedral meshes and anisotropic
heterogeneous media. The fully coupled systems are assembled and solved in
parallel using the Single Program Multiple Data (SPMD) paradigm with one layer
of ghost cells. This strategy allows for a local assembly of the discrete
systems. An efficient preconditioner is implemented to solve the linear systems
at each time step and each Newton type iteration of the simulation. The
numerical efficiency of our approach is assessed on different meshes, fracture
networks, and physical settings in terms of parallel scalability, nonlinear
convergence and linear convergence