Models and simulations of variable-density flow in fractured porous media

Reiter, Sebastian; Logashenko, D.; Stichel, S.; Wittum, Gabriel; Grillo, Alfio

doi:10.1504/ijcse.2014.064527

Cited by 6 publications

(9 citation statements)

References 33 publications

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“…The sPDE ( 8 ) computations were performed with UG4 [ 49 , 50 , 51 ] based on Finite Volumes discretisations [ 52 , 53 , 54 ] and massively parallel multigrid solvers [ 55 , 56 ]. (UG has been used successfully within various areas of computational physics [ 57 , 58 ] and biophysics, namely computational neuroscience [ 59 , 60 , 61 , 62 ] and computational pharmacology [ 63 , 64 ]). For technical details concerning the discretization methods and the massively parallel multigrid solvers, we refer to our former paper [ 27 ].…”

Section: Methodsmentioning

confidence: 99%

Quantitative Analysis of Hepatitis C NS5A Viral Protein Dynamics on the ER Surface

Knodel

Nägel

Reiter

et al. 2018

Viruses

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Exploring biophysical properties of virus-encoded components and their requirement for virus replication is an exciting new area of interdisciplinary virological research. To date, spatial resolution has only rarely been analyzed in computational/biophysical descriptions of virus replication dynamics. However, it is widely acknowledged that intracellular spatial dependence is a crucial component of virus life cycles. The hepatitis C virus-encoded NS5A protein is an endoplasmatic reticulum (ER)-anchored viral protein and an essential component of the virus replication machinery. Therefore, we simulate NS5A dynamics on realistic reconstructed, curved ER surfaces by means of surface partial differential equations (sPDE) upon unstructured grids. We match the in silico NS5A diffusion constant such that the NS5A sPDE simulation data reproduce experimental NS5A fluorescence recovery after photobleaching (FRAP) time series data. This parameter estimation yields the NS5A diffusion constant. Such parameters are needed for spatial models of HCV dynamics, which we are developing in parallel but remain qualitative at this stage. Thus, our present study likely provides the first quantitative biophysical description of the movement of a viral component. Our spatio-temporal resolved ansatz paves new ways for understanding intricate spatial-defined processes central to specfic aspects of virus life cycles.

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Section: Methodsmentioning

confidence: 99%

Quantitative Analysis of Hepatitis C NS5A Viral Protein Dynamics on the ER Surface

Knodel

Nägel

Reiter

et al. 2018

Viruses

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“…In this section, we briefly describe the PDEs and refer to [36,38] for details. From the modeling point of view, we consider the porous medium M ⊂ D surrounding the fracture with the porosity ϕ m : M → (0, 1) and the permeability K m : M → R d×d .…”

Section: Governing Equations For the Flowmentioning

confidence: 99%

“…In particular, we assume the validity of the Darcy's law inside the fracture. Without loss of generality, we consider in this work only one fracture, see [36,38] for the generalization. The fracture is represented by a surface S ⊂ D, M ∪ S = D, M ∩ S = ∅.…”

Section: Governing Equations For the Flowmentioning

confidence: 99%

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Estimation of uncertainties in the density driven flow in fractured porous media using MLMC

Logashenko,

Litvinenko,

Tempone

et al. 2024

Preprint

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We use the Multi Level Monte Carlo method to estimate uncertainties in a Henry-like salt water intrusion problem with a fracture. The flow is induced by the variation of the density of the fluid phase, which depends on the mass fraction of salt. We assume that the fracture has a known fixed location but an uncertain aperture. Other input uncertainties are the porosity and permeability fields and the recharge. In our setting, porosity and permeability vary spatially and recharge is time-dependent. For each realisation of these uncertain parameters, the evolution of the mass fraction and pressure fields is modelled by a system of non-linear and time-dependent PDEs with a jump of the solution at the fracture. The uncertainties propagate into the distribution of the salt concentration, which is an important characteristic of the quality of water resources. We show that the multilevel Monte Carlo (MLMC) method is able to reduce the overall computational cost compared to classical Monte Carlo methods. This is achieved by balancing discretisation and statistical errors. Multiple scenarios are evaluated at different spatial and temporal mesh levels. The deterministic solver ug4 is run in parallel to calculate all stochastic scenarios.

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“…There is a variety of models for flow and transport in the fractures, cf. e.g., Angot et al 2009;Reiter et al 2014;Bastian et al 2000; 2012Fumagalli and Scotti 2012). For the solvers, the following aspects are important: Numerical treatment of the fractures as full-dimensional subdomains is possible only in special cases as it results in very ill-conditioned discretized systems.…”

Section: Fracturesmentioning

confidence: 99%

Aspects of Solvers for Large-Scale Coupled Problems in Porous Media

et al. 2019

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This work summarizes solution strategies for discrete systems occurring in the simulation of processes in the subsurface. The focus is on scalable solvers for large and coupled systems. The goal of this work is to enable researchers to select suitable algorithms and parameter settings to efficiently solve their problems. The work provides an overview of existing methods, highlighting their features, potential, and also frequent pitfalls. Numerical examples are provided for single phase flow, density driven flow and poroelasticity.Aspects of multiphase flow are discussed briefly; a detailed discussion of reactive transport is beyond the scope of the article. Future trends are discussed. Keywords Multigrid • Scalable solvers • Coupled problems • High performance computing • Porous media U.M. Yang: Portions of this work were performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

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Models and simulations of variable-density flow in fractured porous media

Cited by 6 publications

References 33 publications

Quantitative Analysis of Hepatitis C NS5A Viral Protein Dynamics on the ER Surface

Quantitative Analysis of Hepatitis C NS5A Viral Protein Dynamics on the ER Surface

Estimation of uncertainties in the density driven flow in fractured porous media using MLMC

Aspects of Solvers for Large-Scale Coupled Problems in Porous Media

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