492 research outputs found
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
A numerical algorithm based on probing to find optimized transmission conditions
Optimized Schwarz Methods (OSMs) are based on optimized transmission
conditions along the interfaces between the subdomains. Optimized transmission
conditions are derived at the theoretical level, using techniques developed in
the last decades. The hypothesis behind these analyses are quite strong, so
that the applicability of OSMs is still limited. In this manuscript, we present
a numerical algorithm to obtain optimized transmission conditions for any given
problem at hand. This algorithm requires few subdomain solves to be performed
in an offline phase. This additional cost is usually negligible due to the
resulting faster convergence, even in a single-query context.Comment: 8 pages, 9 figure
Vertex centred Discretization of Two-Phase Darcy flows on General Meshes
International audienceThis paper concerns the discretization of multiphase Darcy flows, in the case of heterogeneous anisotropic porous media and general 3D meshes used in practice to represent reservoir and basin geometries. An unconditionally coercive and symmetric vertex centred approach is introduced in this paper. This scheme extends the Vertex Approximate Gradient scheme (VAG), already introduced for single phase diffusive problems in \cite{Eymard.Herbin.ea:2010}, to multiphase Darcy flows. The convergence of the VAG scheme is proved for a simplified two-phase Darcy flow model, coupling an elliptic equation for the pressure and a linear hyperbolic equation for the saturation. The ability for the VAG scheme to efficiently deal with highly heterogeneous media and complex meshes is exhibited on immiscible and miscible two phase Darcy flow models
Multi-segmented non-isothermal compositional liquid gas well model for geothermal processes
We consider a non-isothermal compositional gas liquid model for the
simulation of well operations in geothermal processes. The model accounts for
phase transitions assumed to be at thermodynamical equilibrium and is based on
an hydrodynamical Drift Flux Model (DFM) combined with a No Pressure Wave
approximation of the momentum equation. The focus of this work is on the design
of a robust discretization accounting for slanted and multibranch wells with
the ability to simulate both transient behavior such as well opening as well as
coupled simulations at the time scale of the reservoir. It is based on a
staggered finite volume scheme in space combined with a fully implicit Euler
time integration. The construction of consistent and stable numerical fluxes is
a key feature for a robust numerical method. It is achieved by combining a
monotone flux approximation for the phase superficial velocities with an upwind
approximation of the phase molar fractions, density and enthalpy. In order to
facilitate the coupling of the well and reservoir models, the Newton
linearization accounts for the elimination of the hydrodynamical unknowns
leading to Jacobian systems using the same primary unknowns than those of the
reservoir model. The efficiency of our approach is investigated on both stand
alone well test cases without and with cross flow, and on a fully coupled
well-reservoir simulation
Coupling of a two phase gas liquid compositional 3D Darcy flow with a 1D compositional free gas flow
International audienceA model coupling a three dimensional gas liquid compositional Darcy flow and a one dimensional compositional free gas flow is presented. The coupling conditions at the interface between the gallery and the porous media account for the molar normal fluxes continuity for each component, the gas liquid thermodynami-cal equilibrium, the gas pressure continuity and the gas and liquid molar fractions continuity. This model is applied to the simulation of the mass exchanges at the interface between the repository and the ventilation excavated gallery in a nuclear waste geological repository. The convergence of the Vertex Approximate Gradient discretization is analysed for a simplified model coupling the Richards approximation in the porous media and the gas pressure equation in the gallery
ComPASS: a tool for distributed parallel finite volume discretizations on general unstructured polyhedral meshes
International audienceThe objective of the ComPASS project is to develop a parallel multiphase Darcy flow simulator adapted to general unstructured polyhedral meshes (in a general sense with possibly non planar faces) and to the parallelization of advanced finite volume discretizations with various choices of the degrees of freedom such as cell centres, vertices, or face centres. The main targeted applications are the simulation of CO2 geological storage, nuclear waste repository and reservoir simulations. The CEMRACS 2012 summer school devoted to high performance computing has been an ideal framework to start this collaborative project. This paper describes what has been achieved during the four weeks of the CEMRACS project which has been focusing on the implementation of basic features of the code such as the distributed unstructured polyhedral mesh, the synchronization of the degrees of freedom, and the connection to scientific libraries including the partitioner METIS, the visualization tool PARAVIEW, and the parallel linear solver library PETSc. The parallel efficiency of this first version of the ComPASS code has been validated on a toy parabolic problem using the Vertex Approximate Gradient finite volume spacial discretization with both cell and vertex degrees of freedom, combined with an Euler implicit time integration
Convergence of a Vertex centred Discretization of Two-Phase Darcy flows on General Meshes
International audienceThis article analyses the convergence of the Vertex Approximate Gradient (VAG) scheme recently introduced for the discretization of multiphase Darcy flows on general polyhedral meshes. The convergence of the scheme to a weak solution is shown in the particular case of an incompressible immiscible two phase Darcy flow model with capillary diffusion using a global pressure formulation. A remarkable property in practice is that the convergence is proven whatever the distribution of the volumes at the cell centres and at the vertices used in the control volume discretization of the saturation equation. The numerical experiments carried out for various families of 2D and 3D meshes confirm this result on a one dimensional Buckley Leverett solution
Convergence of a Vertex centred Discretization of Two-Phase Darcy flows on General Meshes
International audienceThis article analyses the convergence of the Vertex Approximate Gradient (VAG) scheme recently introduced for the discretization of multiphase Darcy flows on general polyhedral meshes. The convergence of the scheme to a weak solution is shown in the particular case of an incompressible immiscible two phase Darcy flow model with capillary diffusion using a global pressure formulation. A remarkable property in practice is that the convergence is proven whatever the distribution of the volumes at the cell centres and at the vertices used in the control volume discretization of the saturation equation. The numerical experiments carried out for various families of 2D and 3D meshes confirm this result on a one dimensional Buckley Leverett solution
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