Comparison of finite-volume schemes for diffusion problems

Schneider, Martin; Gläser, Dennis; Flemisch, Bernd; Helmig, Rainer

doi:10.2516/ogst/2018064

Cited by 29 publications

(19 citation statements)

References 45 publications

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“…There can be found, for example, multi-scale mixed finite element methods [4] suitable for parallel implementation of porous media flow simulations, or the transport of multi-component multiphase mixtures coupled with reactive geochemistry, always with a view to effective parallelization [5]. In this category, there can also be considered the design of a new theoretical formalism to classify a large number of known finite volume methods [6], or at the opposite end, the very pragmatic application of MUSCL reconstructions in order to improve the accuracy of chemical tracer calculations [7].…”

mentioning

confidence: 99%

Numerical methods and HPC

Wheeler

Anciaux–Sedrakian

Tran

2019

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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The use of High-Performance Computing (HPC) by industrial companies is one of the most important pillars of digital product design. High-performance computing is at the heart of digital technology and is a critical element in the modeling and simulation of increasingly complex physical phenomena that are inaccessible on a human scale. Therefore, more and more real-time applications, such as Human Brain-behavior simulation or CO 2 storage, require highperformance computing, with ever-increasing computing power and processing of very large volumes of data.HPC offers hardware and software tools serving for strategic decision making and support processes. The current trend for hardware architectures toward heterogeneous and multi-cores systems with more and more cores by CPU to generate Exascale computing power. The exascale definition limited to machines capable of a rate of 1018 flops is of interest to only few scientific domains. Main issues arising from such systems are: i) HPC System Architecture and Components, ii) System Software and Management, iii) Programming Environments, iv) Code Optimization, v) Energy and Resiliency, vi) Balance Compute, vii) I/O and Storage Performance, viii) Mathematics and algorithms for HPC systems and finally Big Data and HPC usage Models.The use of currently proven approaches on multi-core CPUs and accelerators (e.g. GPUs, Many-core CPUs) has resulted in a significant performance for several applications. In this topical issue "Numerical methods and HPC", several of these issues are addressed, for example programming environments, I/O and storage performance, Big Data and HPC usage, and mathematics and algorithms dedicated to HPC systems.Since applications that employ high performance computing resources usually have a longer life than hardware architecture, we emphasis here programming environments that include programming models and languages. To allow portable performance of applications at extreme scales, several programming models are presented, such as PyCOMPSs [1] which supports both homogenous and

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mentioning

confidence: 99%

Numerical methods and HPC

Wheeler

Anciaux–Sedrakian

Tran

2019

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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“…For instance, in case of high levels of anisotropy (like those we observe in our case), numerical schemes produce numerical solutions with negative values and spurious oscillations [15]. Dealing with this problematic sometimes requires a compromise, depending on the studied application and its requirements [16]. In our case, we considered positivity as the most primordial property to be ensured by the upgraded scheme.…”

Section: Numerical Properties Expected From Schemes Solving a Typical Diffusion Problemmentioning

confidence: 90%

“…Besides, positivity preserving and Minimum/Maximum principle preserving FV variants exist [15] and have been tested for reservoir engineering applications [16]. This paper is organized as follows : Section 2 is devoted to the presentation of the general 3D diffusion frame in radiation belts and the numerically challenging 2D diffusion case that retain most of the numerical constraints that we were interested in.…”

Section: Introductionmentioning

confidence: 99%

On the modelling of highly anisotropic diffusion for electron radiation belt dynamic codes

Dahmen

Rogier

Maget

2020

Computer Physics Communications

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Electron radiation belts are regions surrounding Earth, filled with highly energetic electrons and overlapping the majority of satellite orbits. Their multi-scale and rapidly evolving dynamics are modelled by the mean of a diffusion equation involving a highly anisotropic and inhomogeneous diffusion tensor. Finite difference based methods have been the preferred method of discretization in physical codes, starting from ONERA's Salammbô-Electron model, the pioneering 3-dimensional code in the radiation belts community. This choice however does not prevent several numerically induced constraints impacting the reliability of the code as well as its computational cost.Thus in this paper we present the outcome of our investigation to improve Salammbô's numerical core. In particular, we present our special diffusion frame and its numerically induced limitations on our finite difference based scheme. Then we test potential alternative finite volume schemes with physically relevant properties and we finally highlight with a real case simulation the contribution of the positivity preserving scheme to evaluate the impact

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“…Consequently, we obtain a full and well-defined effective permeability tensor for each block in the model (Duquerroix et al 1993;Noetinger and Haas 1996). Schneider et al (2018) have shown very nicely how different discretisation schemes can lead to unexpected solutions that do not agree with each other. The advantage of the AFRM approaches is that the model is cell-centred, providing all implicit and explicit permeabilities for each cell.…”

Section: Anisotropymentioning

confidence: 96%

Modelling the Impact of Anisotropy on Hydrocarbon Production in Heterogeneous Reservoirs

2020

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Effective and optimal hydrocarbon production from heterogeneous and anisotropic reservoirs is a developing challenge in the hydrocarbon industry. While experience leads us to intuitive decisions for the production of these heterogeneous and anisotropic reservoirs, there is a lack of information concerning how hydrocarbon and water production rate and cumulative production as well as water cut and water breakthrough time depend on quantitative measures of heterogeneity and anisotropy. In this work, we have used Generic Advanced Fractal Reservoir Models (GAFRMs) to model reservoirs with controlled heterogeneity and vertical and/or horizontal anisotropy, following the approach of Al-Zainaldin et al. (Transp Porous Media 116(1):181-212, 2017). This Generic approach uses fractal mathematics which captures the spatial variability of real reservoirs at all scales. The results clearly show that some anisotropy in hydrocarbon production and water cut can occur in an isotropic heterogeneous reservoir and is caused by the chance placing of wells in high-quality reservoir rock or vice versa. However, when horizontal anisotropy is introduced into the porosity, cementation exponent and grain size (and hence also into the permeability, capillary pressure, water saturation) in the reservoir model, all measures of early stage and middle stage hydrocarbon and water production become anisotropic, with isotropic flow returning towards the end of the reservoir's lifetime. Specifically, hydrocarbon production rate and cumulative production are increased in the direction of anisotropy, as is water cut, while the time to water breakthrough is reduced. We found no such relationship when varying vertical anisotropy because we were using vertical wells but expect there to be an effect if horizontal wells were used.

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Comparison of finite-volume schemes for diffusion problems

Cited by 29 publications

References 45 publications

Numerical methods and HPC

Numerical methods and HPC

On the modelling of highly anisotropic diffusion for electron radiation belt dynamic codes

Modelling the Impact of Anisotropy on Hydrocarbon Production in Heterogeneous Reservoirs

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