## Search

Now showing items 1-8 of 8

JavaScript is disabled for your browser. Some features of this site may not work without it.

AuthorCalo, Victor M. (3)Efendiev, Yalchin R. (3)Ghommem, Mehdi (3)Elsheikh, Ahmed H. (2)Hoteit, Ibrahim (2)View MoreDepartment

Earth Science and Engineering Program (8)

Environmental Science and Engineering Program (8)Physical Sciences and Engineering (PSE) Division (8)Applied Mathematics and Computational Science Program (4)Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division (3)View MoreJournal
Journal of Computational Physics (8)

PublisherElsevier BV (8)SubjectModel reduction (3)Dynamic mode decomposition (2)Proper orthogonal decomposition (2)Subsurface flow models (2)Anisotropy (1)View MoreTypeArticle (8)Year (Issue Date)2015 (2)2014 (4)2013 (2)Item AvailabilityMetadata Only (8)

Now showing items 1-8 of 8

- List view
- Grid view
- Sort Options:
- Relevance
- Title Asc
- Title Desc
- Issue Date Asc
- Issue Date Desc
- Submit Date Asc
- Submit Date Desc
- Results Per Page:
- 5
- 10
- 20
- 40
- 60
- 80
- 100

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.

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.

Multiscale empirical interpolation for solving nonlinear PDEs

Calo, Victor M.; Efendiev, Yalchin R.; Galvis, Juan; Ghommem, Mehdi (Journal of Computational Physics, Elsevier BV, 2014-12) [Article]

In this paper, we propose a multiscale empirical interpolation method for solving nonlinear multiscale partial differential equations. The proposed method combines empirical interpolation techniques and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM). To solve nonlinear equations, the GMsFEM is used to represent the solution on a coarse grid with multiscale basis functions computed offline. Computing the GMsFEM solution involves calculating the system residuals and Jacobians on the fine grid. We use empirical interpolation concepts to evaluate these residuals and Jacobians of the multiscale system with a computational cost which is proportional to the size of the coarse-scale problem rather than the fully-resolved fine scale one. The empirical interpolation method uses basis functions which are built by sampling the nonlinear function we want to approximate a limited number of times. The coefficients needed for this approximation are computed in the offline stage by inverting an inexpensive linear system. The proposed multiscale empirical interpolation techniques: (1) divide computing the nonlinear function into coarse regions; (2) evaluate contributions of nonlinear functions in each coarse region taking advantage of a reduced-order representation of the solution; and (3) introduce multiscale proper-orthogonal-decomposition techniques to find appropriate interpolation vectors. We demonstrate the effectiveness of the proposed methods on several nonlinear multiscale PDEs that are solved with Newton's methods and fully-implicit time marching schemes. Our numerical results show that the proposed methods provide a robust framework for solving nonlinear multiscale PDEs on a coarse grid with bounded error and significant computational cost reduction.

Accelerating Monte Carlo molecular simulations by reweighting and reconstructing Markov chains: Extrapolation of canonical ensemble averages and second derivatives to different temperature and density conditions

Kadoura, Ahmad Salim; Sun, Shuyu; Salama, Amgad (Journal of Computational Physics, Elsevier BV, 2014-08) [Article]

Accurate determination of thermodynamic properties of petroleum reservoir fluids is of great interest to many applications, especially in petroleum engineering and chemical engineering. Molecular simulation has many appealing features, especially its requirement of fewer tuned parameters but yet better predicting capability; however it is well known that molecular simulation is very CPU expensive, as compared to equation of state approaches. We have recently introduced an efficient thermodynamically consistent technique to regenerate rapidly Monte Carlo Markov Chains (MCMCs) at different thermodynamic conditions from the existing data points that have been pre-computed with expensive classical simulation. This technique can speed up the simulation more than a million times, making the regenerated molecular simulation almost as fast as equation of state approaches. In this paper, this technique is first briefly reviewed and then numerically investigated in its capability of predicting ensemble averages of primary quantities at different neighboring thermodynamic conditions to the original simulated MCMCs. Moreover, this extrapolation technique is extended to predict second derivative properties (e.g. heat capacity and fluid compressibility). The method works by reweighting and reconstructing generated MCMCs in canonical ensemble for Lennard-Jones particles. In this paper, system's potential energy, pressure, isochoric heat capacity and isothermal compressibility along isochors, isotherms and paths of changing temperature and density from the original simulated points were extrapolated. Finally, an optimized set of Lennard-Jones parameters (ε, σ) for single site models were proposed for methane, nitrogen and carbon monoxide. © 2014 Elsevier Inc.

Hybrid nested sampling algorithm for Bayesian model selection applied to inverse subsurface flow problems

Elsheikh, Ahmed H.; Wheeler, Mary Fanett; Hoteit, Ibrahim (Journal of Computational Physics, Elsevier BV, 2014-02) [Article]

A Hybrid Nested Sampling (HNS) algorithm is proposed for efficient Bayesian model calibration and prior model selection. The proposed algorithm combines, Nested Sampling (NS) algorithm, Hybrid Monte Carlo (HMC) sampling and gradient estimation using Stochastic Ensemble Method (SEM). NS is an efficient sampling algorithm that can be used for Bayesian calibration and estimating the Bayesian evidence for prior model selection. Nested sampling has the advantage of computational feasibility. Within the nested sampling algorithm, a constrained sampling step is performed. For this step, we utilize HMC to reduce the correlation between successive sampled states. HMC relies on the gradient of the logarithm of the posterior distribution, which we estimate using a stochastic ensemble method based on an ensemble of directional derivatives. SEM only requires forward model runs and the simulator is then used as a black box and no adjoint code is needed. The developed HNS algorithm is successfully applied for Bayesian calibration and prior model selection of several nonlinear subsurface flow problems. © 2013 Elsevier Inc.

Mode decomposition methods for flows in high-contrast porous media. A global approach

Ghommem, Mehdi; Calo, Victor M.; Efendiev, Yalchin R. (Journal of Computational Physics, Elsevier BV, 2014-01) [Article]

We apply dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD) methods to flows in highly-heterogeneous porous media to extract the dominant coherent structures and derive reduced-order models via Galerkin projection. Permeability fields with high contrast are considered to investigate the capability of these techniques to capture the main flow features and forecast the flow evolution within a certain accuracy. A DMD-based approach shows a better predictive capability due to its ability to accurately extract the information relevant to long-time dynamics, in particular, the slowly-decaying eigenmodes corresponding to largest eigenvalues. Our study enables a better understanding of the strengths and weaknesses of the applicability of these techniques for flows in high-contrast porous media. Furthermore, we discuss the robustness of DMD- and POD-based reduced-order models with respect to variations in initial conditions, permeability fields, and forcing terms. © 2013 Elsevier Inc.

Mode decomposition methods for flows in high-contrast porous media. Global-local approach

Ghommem, Mehdi; Presho, Michael; Calo, Victor M.; Efendiev, Yalchin R. (Journal of Computational Physics, Elsevier BV, 2013-11) [Article]

In this paper, we combine concepts of the generalized multiscale finite element method (GMsFEM) and mode decomposition methods to construct a robust global-local approach for model reduction of flows in high-contrast porous media. This is achieved by implementing Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) techniques on a coarse grid computed using GMsFEM. The resulting reduced-order approach enables a significant reduction in the flow problem size while accurately capturing the behavior of fully-resolved solutions. We consider a variety of high-contrast coefficients and present the corresponding numerical results to illustrate the effectiveness of the proposed technique. This paper is a continuation of our work presented in Ghommem et al. (2013) [1] where we examine the applicability of POD and DMD to derive simplified and reliable representations of flows in high-contrast porous media on fully resolved models. In the current paper, we discuss how these global model reduction approaches can be combined with local techniques to speed-up the simulations. The speed-up is due to inexpensive, while sufficiently accurate, computations of global snapshots. © 2013 Elsevier Inc.

An iterative stochastic ensemble method for parameter estimation of subsurface flow models

Elsheikh, Ahmed H.; Wheeler, Mary Fanett; Hoteit, Ibrahim (Journal of Computational Physics, Elsevier BV, 2013-06) [Article]

Parameter estimation for subsurface flow models is an essential step for maximizing the value of numerical simulations for future prediction and the development of effective control strategies. We propose the iterative stochastic ensemble method (ISEM) as a general method for parameter estimation based on stochastic estimation of gradients using an ensemble of directional derivatives. ISEM eliminates the need for adjoint coding and deals with the numerical simulator as a blackbox. The proposed method employs directional derivatives within a Gauss-Newton iteration. The update equation in ISEM resembles the update step in ensemble Kalman filter, however the inverse of the output covariance matrix in ISEM is regularized using standard truncated singular value decomposition or Tikhonov regularization. We also investigate the performance of a set of shrinkage based covariance estimators within ISEM. The proposed method is successfully applied on several nonlinear parameter estimation problems for subsurface flow models. The efficiency of the proposed algorithm is demonstrated by the small size of utilized ensembles and in terms of error convergence rates. © 2013 Elsevier Inc.

The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

By default, clicking on the export buttons will result in a download of the allowed maximum amount of items. For anonymous users the allowed maximum amount is 50 search results.

To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.