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AuthorAlkhalifah, Tariq Ali (63)Sun, Shuyu (36)Salama, Amgad (27)Hoteit, Ibrahim (26)Calo, Victor M. (24)View MoreDepartment

Earth Science and Engineering Program (168)

Environmental Science and Engineering Program (168)Physical Sciences and Engineering (PSE) Division (166)Applied Mathematics and Computational Science Program (35)Computational Transport Phenomena Lab (35)View MoreJournalGeophysical Prospecting (17)74th EAGE Conference and Exhibition incorporating EUROPEC 2012 (11)Geophysics (11)SEG Technical Program Expanded Abstracts 2011 (11)London 2013, 75th eage conference en exhibition incorporating SPE Europec (10)View MorePublisherEAGE Publications (39)Elsevier BV (34)Society of Exploration Geophysicists (27)Wiley-Blackwell (20)Society of Petroleum Engineers (SPE) (15)View MoreSubjectAnisotropy (7)Migration (7)Traveltime (7)Subsurface flow models (5)Finite element method (4)View MoreTypeArticle (107)Conference Paper (61)Year (Issue Date)2017 (2)2016 (1)2015 (7)2014 (52)2013 (46)View MoreItem AvailabilityMetadata Only (158)Open Access (10)

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Downscaling the 2D Bénard convection equations using continuous data assimilation

Altaf, Muhammad; Titi, E. S.; Gebrael, T.; Knio, Omar; Zhao, L.; McCabe, Matthew; Hoteit, Ibrahim (Computational Geosciences, Springer Nature, 2017-02-27) [Article]

We consider a recently introduced continuous data assimilation (CDA) approach for downscaling a coarse resolution configuration of the 2D Bénard convection equations into a finer grid. In this CDA, a nudging term, estimated as the misfit between some interpolants of the assimilated coarse-grid measurements and the fine-grid model solution, is added to the model equations to constrain the model. The main contribution of this study is a performance analysis of CDA for downscaling measurements of temperature and velocity. These measurements are assimilated either separately or simultaneously, and the results are compared against those resulting from the standard point-to-point nudging approach (NA). Our numerical results suggest that the CDA solution outperforms that of NA, always converging to the true solution when the velocity is assimilated as has been theoretically proven. Assimilation of temperature measurements only may not always recover the true state as demonstrated in the case study. Various runs are conducted to evaluate the sensitivity of CDA to noise in the measurements, the size, and the time frequency of the measured grid, suggesting a more robust behavior of CDA compared to that of NA.

Computing and Comparing Effective Properties for Flow and Transport in Computer-Generated Porous Media

Allen, Rebecca; Sun, Shuyu (Geofluids, Hindawi Publishing Corporation, 2017-02-13) [Article]

We compute effective properties (i.e., permeability, hydraulic tortuosity, and diffusive tortuosity) of three different digital porous media samples, including in-line array of uniform shapes, staggered-array of squares, and randomly distributed squares. The permeability and hydraulic tortuosity are computed by solving a set of rescaled Stokes equations obtained by homogenization, and the diffusive tortuosity is computed by solving a homogenization problem given for the effective diffusion coefficient that is inversely related to diffusive tortuosity. We find that hydraulic and diffusive tortuosity can be quantitatively different by up to a factor of ten in the same pore geometry, which indicates that these tortuosity terms cannot be used interchangeably. We also find that when a pore geometry is characterized by an anisotropic permeability, the diffusive tortuosity (and correspondingly the effective diffusion coefficient) can also be anisotropic. This finding has important implications for reservoir-scale modeling of flow and transport, as it is more realistic to account for the anisotropy of both the permeability and the effective diffusion coefficient.

Continuous data assimilation for downscaling large-footprint soil moisture retrievals

Altaf, Muhammad; Jana, Raghavendra Belur; Hoteit, Ibrahim; McCabe, Matthew (Remote Sensing for Agriculture, Ecosystems, and Hydrology XVIII, SPIE-Intl Soc Optical Eng, 2016) [Conference Paper]

Soil moisture is a key component of the hydrologic cycle, influencing processes leading to runoff generation, infiltration and groundwater recharge, evaporation and transpiration. Generally, the measurement scale for soil moisture is found to be different from the modeling scales for these processes. Reducing this mismatch between observation and model scales in necessary for improved hydrological modeling. An innovative approach to downscaling coarse resolution soil moisture data by combining continuous data assimilation and physically based modeling is presented. In this approach, we exploit the features of Continuous Data Assimilation (CDA) which was initially designed for general dissipative dynamical systems and later tested numerically on the incompressible Navier-Stokes equation, and the Benard equation. A nudging term, estimated as the misfit between interpolants of the assimilated coarse grid measurements and the fine grid model solution, is added to the model equations to constrain the model's large scale variability by available measurements. Soil moisture fields generated at a fine resolution by a physically-based vadose zone model (HYDRUS) are subjected to data assimilation conditioned upon coarse resolution observations. This enables nudging of the model outputs towards values that honor the coarse resolution dynamics while still being generated at the fine scale. Results show that the approach is feasible to generate fine scale soil moisture fields across large extents, based on coarse scale observations. Application of this approach is likely in generating fine and intermediate resolution soil moisture fields conditioned on the radiometerbased, coarse resolution products from remote sensing satellites.

Parallel simulation of wormhole propagation with the Darcy-Brinkman-Forchheimer framework

Wu, Yuanqing; Salama, Amgad; Sun, Shuyu (Computers and Geotechnics, Elsevier BV, 2015-07-09) [Article]

The acid treatment of carbonate reservoirs is a widely practiced oil and gas well stimulation technique. The injected acid dissolves the material near the wellbore and creates flow channels that establish a good connectivity between the reservoir and the well. Such flow channels are called wormholes. Different from the traditional simulation technology relying on Darcy framework, the new Darcy-Brinkman-Forchheimer (DBF) framework is introduced to simulate the wormhole forming procedure. The DBF framework considers both large and small porosity conditions and should output better simulation results than the Darcy framework. To process the huge quantity of cells in the simulation grid and shorten the long simulation time of the traditional serial code, a parallel code with FORTRAN 90 and MPI was developed. The experimenting field approach to set coefficients in the model equations was also introduced. Moreover, a procedure to fill in the coefficient matrix in the linear system in the solver was described. After this, 2D dissolution experiments were carried out. In the experiments, different configurations of wormholes and a series of properties simulated by both frameworks were compared. We conclude that the numerical results of the DBF framework are more like wormholes and more stable than the Darcy framework, which is a demonstration of the advantages of the DBF framework. Finally, the scalability of the parallel code was evaluated, and we conclude that superlinear scalability can be achieved. © 2015 Elsevier Ltd.

Consistent model reduction of polymer chains in solution in dissipative particle dynamics: Model description

Moreno Chaparro, Nicolas; Nunes, Suzana Pereira; Calo, Victor M. (Computer Physics Communications, Elsevier BV, 2015-06-30) [Article]

We introduce a framework for model reduction of polymer chain models for dissipative particle dynamics (DPD) simulations, where the properties governing the phase equilibria such as the characteristic size of the chain, compressibility, density, and temperature are preserved. The proposed methodology reduces the number of degrees of freedom required in traditional DPD representations to model equilibrium properties of systems with complex molecules (e.g., linear polymers). Based on geometrical considerations we explicitly account for the correlation between beads in fine-grained DPD models and consistently represent the effect of these correlations in a reduced model, in a practical and simple fashion via power laws and the consistent scaling of the simulation parameters. In order to satisfy the geometrical constraints in the reduced model we introduce bond-angle potentials that account for the changes in the chain free energy after the model reduction. Following this coarse-graining process we represent high molecular weight DPD chains (i.e., ≥200≥200 beads per chain) with a significant reduction in the number of particles required (i.e., ≥20≥20 times the original system). We show that our methodology has potential applications modeling systems of high molecular weight molecules at large scales, such as diblock copolymer and DNA.

Speeding up the flash calculations in two-phase compositional flow simulations - The application of sparse grids

Wu, Yuanqing; Kowitz, Christoph; Sun, Shuyu; Salama, Amgad (Journal of Computational Physics, Elsevier BV, 2015-03) [Article]

Flash calculations have become a performance bottleneck in the simulation of compositional flow in subsurface reservoirs. We apply a sparse grid surrogate model to substitute the flash calculation and thus try to remove the bottleneck from the reservoir simulation. So instead of doing a flash calculation in each time step of the simulation, we just generate a sparse grid approximation of all possible results of the flash calculation before the reservoir simulation. Then we evaluate the constructed surrogate model to approximate the values of the flash calculation results from this surrogate during the simulations. The execution of the true flash calculation has been shifted from the online phase during the simulation to the offline phase before the simulation. Sparse grids are known to require only few unknowns in order to obtain good approximation qualities. In conjunction with local adaptivity, sparse grids ensure that the accuracy of the surrogate is acceptable while keeping the memory usage small by only storing a minimal amount of values for the surrogate. The accuracy of the sparse grid surrogate during the reservoir simulation is compared to the accuracy of using a surrogate based on regular Cartesian grids and the original flash calculation. The surrogate model improves the speed of the flash calculations and the simulation of the whole reservoir. In an experiment, it is shown that the speed of the online flash calculations is increased by about 2000 times and as a result the speed of the reservoir simulations has been enhanced by 21 times in the best conditions.

Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machines

Woźniak, Maciej; Paszyński, Maciej R.; Pardo, D.; Dalcin, Lisandro; Calo, Victor M. (Computer Methods in Applied Mechanics and Engineering, Elsevier BV, 2015-02) [Article]

This paper derives theoretical estimates of the computational cost for isogeometric multi-frontal direct solver executed on parallel distributed memory machines. We show theoretically that for the Cp-1 global continuity of the isogeometric solution, both the computational cost and the communication cost of a direct solver are of order O(log(N)p2) for the one dimensional (1D) case, O(Np2) for the two dimensional (2D) case, and O(N4/3p2) for the three dimensional (3D) case, where N is the number of degrees of freedom and p is the polynomial order of the B-spline basis functions. The theoretical estimates are verified by numerical experiments performed with three parallel multi-frontal direct solvers: MUMPS, PaStiX and SuperLU, available through PETIGA toolkit built on top of PETSc. Numerical results confirm these theoretical estimates both in terms of p and N. For a given problem size, the strong efficiency rapidly decreases as the number of processors increases, becoming about 20% for 256 processors for a 3D example with 1283 unknowns and linear B-splines with C0 global continuity, and 15% for a 3D example with 643 unknowns and quartic B-splines with C3 global continuity. At the same time, one cannot arbitrarily increase the problem size, since the memory required by higher order continuity spaces is large, quickly consuming all the available memory resources even in the parallel distributed memory version. Numerical results also suggest that the use of distributed parallel machines is highly beneficial when solving higher order continuity spaces, although the number of processors that one can efficiently employ is somehow limited.

Investigation of thermal energy transport from an anisotropic central heating element to the adjacent channels: A multipoint flux approximation

Salama, Amgad; Sun, Shuyu; El-Amin, Mohamed (Annals of Nuclear Energy, Elsevier BV, 2015-02) [Article]

The problem of heat transfer from a central heating element pressed between two clad plates to cooling channels adjacent and outboard of the plates is investigated numerically. The aim of this work is to highlight the role of thermal conductivity anisotropy of the heating element and/or the encompassing plates on thermal energy transport to the fluid passing through the two channels. When the medium is anisotropic with respect to thermal conductivity; energy transport to the neighboring channels is no longer symmetric. This asymmetry in energy fluxes influence heat transfer to the coolant resulting in different patterns of temperature fields. In particular, it is found that the temperature fields are skewed towards the principal direction of anisotropy. In addition, the heat flux distributions along the edges of the heating element are also different as a manifestation of thermal conductivity anisotropy. Furthermore, the peak temperature at the channel walls change location and magnitude depending on the principal direction of anisotropy. Based on scaling arguments, it is found that, the ratio of width to the height of the heating system is a key parameter which can suggest when one may ignore the effect of the cross-diagonal terms of the full conductivity tensor. To account for anisotropy in thermal conductivity, the method of multipoint flux approximation (MPFA) is employed. Using this technique, it is possible to find a finite difference stencil which can handle full thermal conductivity tensor and in the same time enjoys the simplicity of finite difference approximation. Although the finite difference stencil based on MPFA is quite complex, in this work we apply the recently introduced experimenting field approach which construct the global problem automatically.

Efficient traveltime solutions of the acoustic TI eikonal equation

Waheed, Umair bin; Alkhalifah, Tariq Ali; Wang, Hui (Journal of Computational Physics, Elsevier BV, 2015-02) [Article]

Numerical solutions of the eikonal (Hamilton-Jacobi) equation for transversely isotropic (TI) media are essential for imaging and traveltime tomography applications. Such solutions, however, suffer from the inherent higher-order nonlinearity of the TI eikonal equation, which requires solving a quartic polynomial for every grid point. Analytical solutions of the quartic polynomial yield numerically unstable formulations. Thus, it requires a numerical root finding algorithm, adding significantly to the computational load. Using perturbation theory we approximate, in a first order discretized form, the TI eikonal equation with a series of simpler equations for the coefficients of a polynomial expansion of the eikonal solution, in terms of the anellipticity anisotropy parameter. Such perturbation, applied to the discretized form of the eikonal equation, does not impose any restrictions on the complexity of the perturbed parameter field. Therefore, it provides accurate traveltime solutions even for models with complex distribution of velocity and anisotropic anellipticity parameter, such as that for the complicated Marmousi model. The formulation allows for large cost reduction compared to using the direct TI eikonal solver. Furthermore, comparative tests with previously developed approximations illustrate remarkable gain in accuracy in the proposed algorithm, without any addition to the computational cost.

Regional Ocean Data Assimilation

Edwards, Christopher A.; Moore, Andrew M.; Hoteit, Ibrahim; Cornuelle, Bruce D. (Annual Review of Marine Science, Annual Reviews, 2015-01-03) [Article]

This article reviews the past 15 years of developments in regional ocean data assimilation. A variety of scientific, management, and safety-related objectives motivate marine scientists to characterize many ocean environments, including coastal regions. As in weather prediction, the accurate representation of physical, chemical, and/or biological properties in the ocean is challenging. Models and observations alone provide imperfect representations of the ocean state, but together they can offer improved estimates. Variational and sequential methods are among the most widely used in regional ocean systems, and there have been exciting recent advances in ensemble and four-dimensional variational approaches. These techniques are increasingly being tested and adapted for biogeochemical applications.

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