Multidimensional mixed–hybrid finite element method for compositional two-phase flow in heterogeneous porous media and its parallel implementation on GPU

Fučík, Radek; Klinkovský, Jakub; Solovský, Jakub; Oberhuber, Tomáš; Mikyška, Jiří

doi:10.1016/j.cpc.2018.12.004

Cited by 14 publications

(29 citation statements)

References 20 publications

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“…The resulting data from the experiments were compared against a numerical model of two-phase flow in porous media, which extends upon that of [9]. A major addition to the model is its capability to account for non-equilibrium CO 2 mass transfer between aqueous and gas phases.…”

Section: Methodsmentioning

confidence: 99%

“…The governing equations are solved using a general numerical solver based on the mixed-hybrid finite element method described in [9]. The mixed-hybrid finite element method combines velocity discretizations in the lowest order Raviart-Thomas-Nédélec space with piecewise constant approximations for the scalar variables.…”

Section: Numerical Methods and Implementationmentioning

confidence: 99%

“…is further supplemented with Dirichlet or Neumann boundary conditions, or its combination on different parts of the boundary [9]. Here we restrict ourselves only the case d = 2 which is relevant for the problems presented in the paper.…”

Section: Methodsmentioning

confidence: 99%

“…Our approach is to expand the numerical model developed in [9] to include kinetic mass transfer, and then to compare the results of the simulations performed by the model to the laboratory data from experiments that build upon methods developed in [10]. This methodology forms the basis for another article [11] that investigates multiphase CO 2 plume dynamics in relatively large-scale synthetic aquifer systems.…”

Section: Introductionmentioning

confidence: 99%

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Computational Methodology to Analyze the Effect of Mass Transfer Rate on Attenuation of Leaked Carbon Dioxide in Shallow Aquifers

Fučík¹,

Solovský²,

Plampin³

et al. 2021

Acta Polytech

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Exsolution and re-dissolution of CO2 gas within heterogeneous porous media are investigated using experimental data and mathematical modeling. In a set of bench-scale experiments, water saturated with CO2 under a given pressure is injected into a 2-D water-saturated porous media system, causing CO2 gas to exsolve and migrate upwards. A layer of fine sand mimicking a heterogeneity within a shallow aquifer is present in the tank to study accumulation and trapping of exsolved CO2. Then, clean water is injected into the system and the accumulated CO2 dissolves back into the flowing water. Simulated exsolution and dissolution mass transfer processes are studied using both nearequilibrium and kinetic approaches and compared to experimental data under conditions that do and do not include lateral background water flow. The mathematical model is based on the mixed hybrid finite element method that allows for accurate simulation of both advection- and diffusion- dominated processes.

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Section: Methodsmentioning

confidence: 99%

Section: Numerical Methods and Implementationmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Computational Methodology to Analyze the Effect of Mass Transfer Rate on Attenuation of Leaked Carbon Dioxide in Shallow Aquifers

Fučík¹,

Solovský²,

Plampin³

et al. 2021

Acta Polytech

Self Cite

View full text Add to dashboard Cite

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“…Many researches concentrate on employing some portions of finite element program on GPUs. For instance, matrix assembly and numerical integration [27][28], global finite element matrices and the solution of large sparse systems of equation solved by using GPU [29][30][31]. Some previous studies speed up the assembly of large sparse finite element matrix [32], extensive memory of GPU is needed for such approaches.…”

Section: Introductionmentioning

confidence: 99%

Parallel Performance Analysis and Numerical Simulation of Magnetic Nanoparticles Transportation and Blood Flow Pattern in Capillaries

et al. 2020

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A hybrid CPU-GPU approach is used to investigate the patterns of blood flow and magnetic particles numerically in a capillary under the existence of constant magnetic field. However, the blood flow is considered to be Newtonian, laminar and incompressible in the capillary and magnetic Nanoparticles are assumed as potential agent carrier being used therapeutically for the magnetic targeted drug transport in the fight against diseased cells. The magnetic field is embedded in the muscular volume and is produced by a permanent magnet. The flow field and particles transport dynamics are formulated by a mathematical model and is solved numerically. Finite element discretization gives a big sparse system of equations which needs a higher computation. Therefore, the hybrid approach deals the extensive computations in parallel, as this is a good platform which can decrease the times of solution significantly, if compared to the CPU application. This serves for highly effective search for distinctive mathematical model, along with their distinctive parameters. The impact of pressure P , the capillary radius R; the magnetic nanoparticle radius R M , the magnetic field intensity H on the blood flow along with magnetic particles is studied with regard to the inputs and model of magnetic field. The mathematical results for both the velocity of particles and blood are calculated. It is observed that magnetic field is directly proportional to the flow pattern as an increase in the former upsurge the latter. Moreover, the distance between magnet and capillary wall exerts a direct influence on velocity and is helpful to pull magnetic nanoparticles to the capillary wall. Thus, it is concluded by simulation that the magnetic parameters govern the velocity profile.

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A block preconditioner for two‐phase flow in porous media by mixed hybrid finite elements

Nardean

Ferronato

Abushaikha

2021

Comp and Math Methods

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In this work, we present an original block preconditioner to improve the convergence of Krylov solvers for the simulation of two-phase flow in porous media. In our modeling approach, the set of coupled governing equations is addressed in a fully implicit fashion, where Darcy's law and mass conservation are discretized in an original way by combining the mixed hybrid finite element (MHFE) and the finite volume (FV) methods. The solution to the sequence of large-size nonsymmetric linearized systems of equations that stem during a full-transient simulation represents the most time and resource consuming task, thus motivating the need for efficient preconditioned Krylov solvers. The proposed preconditioner exploits the block structure of the Jacobian matrix while coping with the nonsymmetric nature of the individual blocks. Both academic and realistic applications have been used to challenge the preconditioner, allowing to point out its robustness, stability and overall computational efficiency.

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Multidimensional mixed–hybrid finite element method for compositional two-phase flow in heterogeneous porous media and its parallel implementation on GPU

Cited by 14 publications

References 20 publications

Computational Methodology to Analyze the Effect of Mass Transfer Rate on Attenuation of Leaked Carbon Dioxide in Shallow Aquifers

Computational Methodology to Analyze the Effect of Mass Transfer Rate on Attenuation of Leaked Carbon Dioxide in Shallow Aquifers

Parallel Performance Analysis and Numerical Simulation of Magnetic Nanoparticles Transportation and Blood Flow Pattern in Capillaries

A block preconditioner for two‐phase flow in porous media by mixed hybrid finite elements

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