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Dive into the research topics where Mehdi Ghommem is active.

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Featured researches published by Mehdi Ghommem.


Journal of Computational Physics | 2013

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

Mehdi Ghommem; Michael Presho; Victor M. Calo; Yalchin Efendiev

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.


Theoretical and Applied Mechanics Letters | 2013

Piezoelectric energy harvesting from morphing wing motions for micro air vehicles

Abdessattar Abdelkefi; Mehdi Ghommem

Wing flapping and morphing can be very beneficial to managing the weight of micro air vehicles through coupling the aerodynamic forces with stability and control. In this letter, harvesting energy from the wing morphing is studied to power cameras, sensors, or communication devices of micro air vehicles and to aid in the management of their power. The aerodynamic loads on flapping wings are simulated using a three-dimensional unsteady vortex lattice method. Active wing shape morphing is considered to enhance the performance of the flapping motion. A gradient-based optimization algorithm is used to pinpoint the optimal kinematics maximizing the propellent efficiency. To benefit from the wing deformation, we place piezoelectric layers near the wing roots. Gauss law is used to estimate the electrical harvested power. We demonstrate that enough power can be generated to operate a camera. Numerical analysis shows the feasibility of exploiting wing morphing to harvest energy and improving the design and performance of micro air vehicles.


Journal of Vibration and Control | 2013

Model reduction and analysis of a vibrating beam microgyroscope

Mehdi Ghommem; Ali H. Nayfeh; Slim Choura

The present work is concerned with the nonlinear dynamic analysis of a vibrating beam microgyroscope composed of a rotating cantilever beam with a tip mass at its end. The rigid mass is coupled to two orthogonal electrodes in the drive and sense directions, which are attached to the rotating base. The microbeam is driven by an AC voltage in the drive direction, which induces vibrations in the orthogonal sense direction due to rotation about the microbeam axis. The electrode placed in the sense direction is used to measure the induced motions and extract the underlying angular speed. A reduced-order model of the gyroscope is developed using the method of multiple scales and used to examine its dynamic behavior.


Journal of Computational Physics | 2014

Multiscale empirical interpolation for solving nonlinear PDEs

Victor M. Calo; Yalchin Efendiev; Juan Galvis; Mehdi Ghommem

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 Newtons 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.


Mathematical Problems in Engineering | 2010

Control of Limit Cycle Oscillations of a Two-Dimensional Aeroelastic System

Mehdi Ghommem; Ali H. Nayfeh; Muhammad R. Hajj

Linear and nonlinear static feedback controls are implemented on a nonlinear aeroelastic system that consists of a rigid airfoil supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. The normal form is used to investigate the Hopf bifurcation that occurs as the freestream velocity is increased and to analytically predict the amplitude and frequency of the ensuing limit cycle oscillations (LCO). It is shown that linear control can be used to delay the flutter onset and reduce the LCO amplitude. Yet, its required gains remain a function of the speed. On the other hand, nonlinear control can be effciently implemented to convert any subcritical Hopf bifurcation into a supercritical one and to significantly reduce the LCO amplitude.


Spe Journal | 2016

Complexity Reduction of Multiphase Flows in Heterogeneous Porous Media

Mehdi Ghommem; Eduardo Gildin; Mohammadreza Ghasemi

In this paper, we apply mode decomposition and interpolatory projection methods to speed up simulations of two-phase flows in heterogeneous porous media. We propose intrusive and nonintrusive model-reduction approaches that enable a significant reduction in the size of the subsurface flow problem while capturing the behavior of the fully resolved solutions. In one approach, we use the dynamic mode decomposition. This approach does not require any modification of the reservoir simulation code but rather postprocesses a set of global snapshots to identify the dynamically relevant structures associated with the flow behavior. In the second approach, we project the governing equations of the velocity and the pressure fields on the subspace spanned by their properorthogonal-decomposition modes. Furthermore, we use the discrete empirical interpolation method to approximate the mobilityrelated term in the global-system assembly and then reduce the online computational cost and make it independent of the fine grid. To show the effectiveness and usefulness of the aforementioned approaches, we consider the SPE-10 benchmark permeability field, and present a numerical example in two-phase flow. One can efficiently use the proposed model-reduction methods in the context of uncertainty quantification and production optimization.


Journal of Vibration and Control | 2015

A novel differential frequency micro-gyroscope

Ali H. Nayfeh; Eihab M. Abdel-Rahman; Mehdi Ghommem

We present a frequency-domain method to measure angular speeds using electrostatic micro-electro-mechanical system actuators. Towards this end, we study a single-axis gyroscope made of a micro-cantilever and a proof-mass coupled to two fixed electrodes. The gyroscope possesses two orthogonal axes of symmetry and identical flexural mode shapes along these axes. We develop the equations of motion describing the coupled bending modes in the presence of electrostatic and Coriolis forces. Furthermore, we derive a consistent closed-form higher-order expression for the natural frequencies of the coupled flexural modes. The closed-form expression is verified by comparing its results to those obtained from numerical integration of the equations of motion. We find that rotations around the beam axis couple each pair of identical bending modes to produce a pair of global modes. They also split their common natural frequency into a pair of closely spaced natural frequencies. We propose the use of the difference between this pair of frequencies, which is linearly proportional to the speed of rotation around the beam axis, as a detector for the angular speed.


Medical Physics | 2014

Real-time tumor ablation simulation based on the dynamic mode decomposition method

George C. Bourantas; Mehdi Ghommem; George C. Kagadis; Konstantinos Katsanos; Vassilis C. Loukopoulos; Vasilis N. Burganos; George Nikiforidis

PURPOSE The dynamic mode decomposition (DMD) method is used to provide a reliable forecasting of tumor ablation treatment simulation in real time, which is quite needed in medical practice. To achieve this, an extended Pennes bioheat model must be employed, taking into account both the water evaporation phenomenon and the tissue damage during tumor ablation. METHODS A meshless point collocation solver is used for the numerical solution of the governing equations. The results obtained are used by the DMD method for forecasting the numerical solution faster than the meshless solver. The procedure is first validated against analytical and numerical predictions for simple problems. The DMD method is then applied to three-dimensional simulations that involve modeling of tumor ablation and account for metabolic heat generation, blood perfusion, and heat ablation using realistic values for the various parameters. RESULTS The present method offers very fast numerical solution to bioheat transfer, which is of clinical significance in medical practice. It also sidesteps the mathematical treatment of boundaries between tumor and healthy tissue, which is usually a tedious procedure with some inevitable degree of approximation. The DMD method provides excellent predictions of the temperature profile in tumors and in the healthy parts of the tissue, for linear and nonlinear thermal properties of the tissue. CONCLUSIONS The low computational cost renders the use of DMD suitable for in situ real time tumor ablation simulations without sacrificing accuracy. In such a way, the tumor ablation treatment planning is feasible using just a personal computer thanks to the simplicity of the numerical procedure used. The geometrical data can be provided directly by medical image modalities used in everyday practice.


13th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference | 2010

Deterministic Global Optimization of Flapping Wing Motion for Micro Air Vehicles

Mehdi Ghommem; Muhammad R. Hajj; Layne T. Watson; Dean T. Mook; Richard D. Snyder; Philip S. Beran

The kinematics of a ∞apping plate are optimized by combining the unsteady vortex lattice method with a deterministic global optimization algorithm. A constraint to keep the lift from taking large negative values at anytime is also imposed by following a penalty function approach. The design parameters are the amplitudes, mean values, frequencies, and phase angles of the ∞apping motion. The results suggest that imposing a delay between the difierent oscillatory motions and controlling the way through which the wing rotates at the end of each half stroke would enhance the lift generation. The use of a general unsteady numerical aerodynamic model and the implementation of a deterministic global optimization algorithm provide guidance and a baseline for future efiorts to identify optimal stroke trajectories for micro air vehicles with higher fldelity models.


SPE Kuwait Oil and Gas Show and Conference | 2013

Complexity reduction of multi-phase flows in heterogeneous porous media

Mehdi Ghommem; Victor M. Calo; Yalchin Efendiev; Eduardo Gildin

In this paper, we apply mode decomposition and interpolatory projection methods to speed up simulations of two-phase flows in highly heterogeneous porous media. We propose intrusive and non-intrusive model reduction approaches that enable a significant reduction in the dimension of the flow problem size while capturing the behavior of the fully-resolved solutions. In one approach, we employ the dynamic mode decomposition (DMD) and the discrete empirical interpolation method (DEIM). This approach does not require any modification of the reservoir simulation code but rather postprocesses a set of global snapshots to identify the dynamically-relevant structures associated with the flow behavior. In a second approach, we project the governing equations of the velocity and the pressure fields on the subspace spanned by their proper orthogonal decomposition (POD) modes. Furthermore, we use DEIM to approximate the mobility related term in the global system assembly and then reduce the online computational cost and make it independent of the fine grid. To show the effectiveness and usefulness of the aforementioned approaches, we consider the SPE 10 benchmark permeability field and present a variety of numerical examples of two-phase flow and transport. The proposed model reduction methods can be efficiently used when performing uncertainty quantification or optimization studies and history matching. Introduction High fidelity reservoir simulation models have been shown to yield better predictions in optimization problems and in planning for new reservoir developments in green fields. In addition, exploring the capabilities of real-time surveillance data to improve the accuracy of such models has led to a new paradigm in reservoir monitoring, namely the closed-loop reservoir management (Gildin and Lopez , 2011; Jansen et al. , 2009). Even in the case of unconventional reservoirs, numerical reservoir simulation has been used with several modifications with the current models, in particular in the nature of the flow. To this end, natural fractures and pore-space networks have been incorporated in the simulation process to account for flow in the fractures and matrix (Moridis et al. , 2010; King , 2010). Despite the great advances in reservoir modeling tools and the advent of high-performance computing (HPC), highfidelity physics-based numerical simulation still remains a challenging step in understanding the physics of the reservoir due to the large scale nature of the discretized of the underlying partial differential equations. Computationally intensive simulations, such as in the case of history matching, optimization and uncertainty quantification, become impractical to be performed in a timely-manner if real-time data needs to be assimilated into the model (Gildin and Lopez , 2011; Jansen et al. , 2009). A variety of complexity reduction techniques have been proposed to ease this problem and reduce the computational cost in the optimization under the uncertainty paradigm (Antoulas , 2005; Heijn et al. , 2004; Gildin , 2010). In general, they can be classified in three broader areas depending if one is dealing with the forward simulations (production optimization) or the inverse problem (parameter estimation) (Oliver et al. , 2008): • Reduction of the cost of forward simulations: surrogate models, reduced-order models, multiscale, upscaling • Reduction of the input space dimension: parameterizations, direct cosine transformation, sparsity-based, polynomial chaos SPE 167

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Imran Akhtar

College of Electrical and Mechanical Engineering

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Nathan Collier

King Abdullah University of Science and Technology

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