A Collocated Finite Volume Scheme for High-Performance Simulation of Induced Seismicity in Geo-Energy Applications

2021 ◽  
Author(s):  
A. Novikov ◽  
D. V. Voskov ◽  
M. Khait ◽  
H. Hajibeygi ◽  
J. D. Jansen
Keyword(s):  
Finite Volume ◽  
Induced Seismicity ◽  
High Performance ◽  
General Procedure ◽  
Pressure Fluctuations ◽  
Finite Volume Scheme ◽  
Parallel Solution ◽  
Energy Applications ◽  
Fully Implicit ◽  
Flux Approximation

Abstract We develop a collocated Finite Volume Method (FVM) to study induced seismicity as a result of pore pressure fluctuations. A discrete system is obtained based on a fully-implicit coupled description of flow, elastic deformation, and contact mechanics at fault surfaces on a fully unstructured mesh. The cell-centered collocated scheme leads to convenient integration of the different physical equations, as the unknowns share the same discrete locations on the mesh. Additionally, a multi-point flux approximation is formulated in a general procedure to treat heterogeneity, anisotropy, and cross-derivative terms for both flow and mechanics equations. The resulting system, though flexible and accurate, can lead to excessive computational costs for field-relevant applications. To resolve this limitation, a scalable parallel solution algorithm is developed and presented. Several proof-of-concept numerical tests, including benchmark studies with analytical solutions, are investigated. It is found that the presented method is indeed accurate, stable and efficient; and as such promising for accurate and efficient simulation of induced seismicity.

scholarly journals A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal Aquifers

Water ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1639
Author(s):  
Abdelkrim Aharmouch ◽  
Brahim Amaziane ◽  
Mustapha El Ossmani ◽  
Khadija Talali
Keyword(s):  
Finite Volume ◽  
Coastal Aquifers ◽  
Nonlinear Partial Differential Equations ◽  
Time Integration ◽  
Mass Conservation ◽  
Coupled System ◽  
Finite Volume Scheme ◽  
Time Step ◽  
Volume Scheme ◽  
Fully Implicit

We present a numerical framework for efficiently simulating seawater flow in coastal aquifers using a finite volume method. The mathematical model consists of coupled and nonlinear partial differential equations. Difficulties arise from the nonlinear structure of the system and the complexity of natural fields, which results in complex aquifer geometries and heterogeneity in the hydraulic parameters. When numerically solving such a model, due to the mentioned feature, attempts to explicitly perform the time integration result in an excessively restricted stability condition on time step. An implicit method, which calculates the flow dynamics at each time step, is needed to overcome the stability problem of the time integration and mass conservation. A fully implicit finite volume scheme is developed to discretize the coupled system that allows the use of much longer time steps than explicit schemes. We have developed and implemented this scheme in a new module in the context of the open source platform DuMu X . The accuracy and effectiveness of this new module are demonstrated through numerical investigation for simulating the displacement of the sharp interface between saltwater and freshwater in groundwater flow. Lastly, numerical results of a realistic test case are presented to prove the efficiency and the performance of the method.

scholarly journals Convergence of a finite-volume scheme for a degenerate-singular cross-diffusion system for biofilms

2020 ◽  
Author(s):  
Esther S Daus ◽  
Ansgar Jüngel ◽  
Antoine Zurek
Keyword(s):  
Finite Volume ◽  
System Modeling ◽  
Gradient Flow ◽  
Continuous Model ◽  
Diffusion System ◽  
Finite Volume Scheme ◽  
Biofilm Growth ◽  
Volume Scheme ◽  
Cross Diffusion ◽  
Flux Approximation

Abstract An implicit Euler finite-volume scheme for a cross-diffusion system modeling biofilm growth is analyzed by exploiting its formal gradient-flow structure. The numerical scheme is based on a two-point flux approximation that preserves the entropy structure of the continuous model. Assuming equal diffusivities the existence of non-negative and bounded solutions to the scheme and its convergence are proved. Finally, we supplement the study by numerical experiments in one and two space dimensions.

Numerical Analysis of a Stable Finite Volume Scheme for a Generalized Thermistor Model

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mustapha Ghilani ◽  
El Houssaine Quenjel ◽  
Mohamed Rhoudaf
Keyword(s):  
Weak Solution ◽  
Finite Volume ◽  
Electric Potential ◽  
Discrete Maximum Principle ◽  
Finite Volume Scheme ◽  
Volume Scheme ◽  
Stiffness Coefficients ◽  
Fully Implicit ◽  
The Stability ◽  
Stability Issues

AbstractA generalized thermistor model is discretized thanks to a fully implicit vertex-centered finite volume scheme on simplicial meshes. An assumption on the stiffness coefficients is mandatory to prove a discrete maximum principle on the electric potential. This property is fundamental to handle the stability issues related to the Joule heating term. Then the convergence to a weak solution is established. Finally, numerical results are presented to show the efficiency of the methodology and to illustrate the behavior of the temperature together with the electric potential within the medium.

scholarly journals Development of high-performance hybrid ANN-finite volume scheme (ANN-FVS) for simulation of pharmaceutical continuous granulation

2020 ◽  
Vol 163 ◽  
pp. 320-326 ◽  
Author(s):  
Hamza Y. Ismail ◽  
Mehakpreet Singh ◽  
Saeed Shirazian ◽  
Ahmad B. Albadarin ◽  
Gavin M. Walker
Keyword(s):  
Finite Volume ◽  
High Performance ◽  
Finite Volume Scheme ◽  
Volume Scheme

scholarly journals Improvement of numerical approximation of coupled multiphase multicomponent flow with reactive geochemical transport in porous media

2018 ◽  
Vol 73 ◽  
pp. 73 ◽  
Author(s):  
Etienne Ahusborde ◽  
Brahim Amaziane ◽  
Mustapha El Ossmani
Keyword(s):  
Porous Media ◽  
Differential Equations ◽  
Finite Volume ◽  
Reactive Transport ◽  
Numerical Results ◽  
Nuclear Waste Repository ◽  
Finite Volume Scheme ◽  
Multicomponent Flow ◽  
Fully Implicit ◽  
Highly Nonlinear

In this paper, we consider a parallel finite volume algorithm for modeling complex processes in porous media that include multiphase flow and geochemical interactions. Coupled flow and reactive transport phenomena often occur in a wide range of subsurface systems such as hydrocarbon reservoir production, groundwater management, carbon dioxide sequestration, nuclear waste repository or geothermal energy production. This work aims to develop and implement a parallel code coupling approach for non-isothermal multiphase multicomponent flow and reactive transport simulation in the framework of the parallel open-source platform DuMuX. Modeling such problems leads to a highly nonlinear coupled system of degenerate partial differential equations to algebraic or ordinary differential equations requiring special numerical treatment. We propose a sequential fully implicit scheme solving firstly a multiphase compositional flow problem and then a Direct Substitution Approach (DSA) is used to solve the reactive transport problem. Both subsystems are discretized by a fully implicit cell-centred finite volume scheme and then an efficient sequential coupling has been implemented in DuMuX. We focus on the stability and robustness of the coupling process and the numerical benefits of the DSA approach. Parallelization is carried out using the DUNE parallel library package based on MPI providing high parallel efficiency and allowing simulations with several tens of millions of degrees of freedom to be carried out, ideal for large-scale field applications involving multicomponent chemistry. As we deal with complex codes, we have tested and demonstrated the correctness of the implemented software by benchmarking, including the MoMaS reactive transport benchmark, and comparison to existing simulations in the literature. The accuracy and effectiveness of the approach is demonstrated through 2D and 3D numerical simulations. Parallel scalability is investigated for 3D simulations with different grid resolutions. Numerical results for long-term fate of injected CO2 for geological storage are presented. The numerical results have demonstrated that this approach yields physically realistic flow fields in highly heterogeneous media and showed that this approach performs significantly better than the Sequential Iterative Approach (SIA).

scholarly journals Total velocity-based finite volume discretization of two-phase Darcy flow in highly heterogeneous media with discontinuous capillary pressure

2021 ◽  
Author(s):  
K Brenner ◽  
R Masson ◽  
E H Quenjel ◽  
J Droniou
Keyword(s):  
Capillary Pressure ◽  
Finite Volume ◽  
Heterogeneous Media ◽  
Rock Type ◽  
Heterogeneous Porous Media ◽  
Darcy Flow ◽  
Stability And Convergence ◽  
Finite Volume Scheme ◽  
Two Phase ◽  
Flux Approximation

Abstract This work proposes a finite volume scheme for two-phase Darcy flow in heterogeneous porous media with different rock types. The fully implicit discretization is based on cell-centered, as well as face-centered degrees of freedom in order to capture accurately the nonlinear transmission conditions at different rock type interfaces. These conditions play a major role in the flow dynamics. The scheme is formulated with natural physical unknowns, and the notion of global pressure is only introduced to analyze its stability and convergence. It combines a two-point flux approximation of the gradient normal fluxes with a Hybrid Upwinding approximation of the transport terms. The convergence of the scheme to a weak solution is established taking into account the discontinuous capillary pressure at different rock type interfaces and the degeneracy of the phase mobilities. Numerical experiments show the additional robustness of the proposed discretization compared with the classical Phase Potential Upwinding approach.

Computation of Sub-Micron Thermal Transport Using an Unstructured Finite Volume Method

2002 ◽  
Vol 124 (6) ◽  
pp. 1176-1181 ◽  
Author(s):  
J. Y. Murthy ◽  
S. R. Mathur
Keyword(s):  
Finite Volume ◽  
Isotropic Scattering ◽  
Finite Volume Scheme ◽  
Boltzmann Transport ◽  
Linear Set ◽  
Volume Scheme ◽  
Relaxation Time Approximation ◽  
Fully Implicit ◽  
Volume Method ◽  
Unstructured Finite Volume Method

An unstructured finite volume scheme is applied to the solution of sub-micron heat conduction problems. The phonon Boltzmann transport equation (BTE) in the relaxation time approximation is considered. The similarity between the radiative transfer equation (RTE) and the BTE is exploited in developing a finite volume scheme for the BTE. The spatial domain is divided into arbitrary unstructured polyhedra, the angular domain into control angles, and the frequency domain into frequency bands, and conservation equations for phonon energy are written. The unsteady wave propagation term, not usually present in thermal radiation problems, is differentiated using a fully implicit scheme. A sequential multigrid scheme is applied to solve the nominally linear set. Isotropic scattering due to a variety of mechanisms such as impurity and Umklapp scattering is considered. The numerical scheme is applied to a variety of sub-micron conduction problems, both unsteady and steady. Favorable comparison is found with the published literature and with exact solutions.

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