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Complexity reduction of multi-phase flows in heterogeneous porous media

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Complexity reduction of multi-phase flows in heterogeneous p...

Kuwait Oil and Gas Show and Conference, KOGS 2013

作者： Ghommem, Mehdi Calo, Victor M. Efendiev, Yalchin Gildin, Eduardo Center for Numerical Porous Media Applied Mathematics and Computational Science Earth and Environmental Sciences and Engineering King Abdullah University of Science and Technology Thuwal Saudi Arabia Department of Mathematics and ISC Texas A and M University College Station TX United States Department of Petroleum Engineering Texas A and M University College Station TX United States

ISBN: (纸本)9781629932149

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. Copyright 2013, Society of Petroleum Engineers.

关键词： Two phase flow

Nonlinear interaction of waves in elastodynamics and an inverse problem

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arXiv 2018年

作者： de Hoop, Maarten Uhlmann, Gunther Wang, Yiran Computational and Applied Mathematics and Earth Science Rice University Department of Mathematics University of Washington Institute for Advanced Study Hong Kong University of Science and Technology Department of Mathematics University of Washington

We consider nonlinear elastic wave equations generalizing Gol’dberg’s five constants model. We analyze the nonlinear interaction of two distorted plane waves and characterize the possible nonlinear responses. Using the boundary measurements of the nonlinear responses, we solve the inverse problem of determining elastic parameters from the displacement-to-traction map. Copyright © 2018, The Authors. All rights reserved.

关键词： Elastic waves

The Phonon Quasiparticle Approach for Anharmonic Properties of Solids 32

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The Phonon Quasiparticle Approach for Anharmonic Properties ...

32nd IUPAP Conference in computational Physics, CCP 2021

作者： Zhang, Zhen Zhang, Dong-Bo Sun, Tao Wentzcovitch, Renata M. Department of Applied Physics and Applied Mathematics Columbia University New YorkNY10027 United States College of Nuclear Science and Technology Beijing Normal University Beijing100875 China Beijing Computational Science Research Center Beijing100193 China Key Laboratory of Computational Geodynamics Chinese Academy of Sciences Beijing100049 China Department of Earth and Environmental Sciences Columbia University New YorkNY10027 United States Lamont-Doherty Earth Observatory Columbia University PalisadesNY10964 United States

Knowledge of lattice anharmonicity is essential to elucidate distinctive thermal properties in crystalline solids. Yet, accurate ab initio investigations of lattice anharmonicity encounter difficulties owing to the cumbersome computations. Here we introduce the phonon quasiparticle approach and review its application to various materials. This method efficiently and reliably addresses lattice anharmonicity by combining ab initio molecular dynamics and lattice dynamics calculations. Thus, in principle, it accounts for full anharmonic effects and overcomes finite-size effects typical of ab initio molecular dynamics. The validity and effectiveness of the current approach are demonstrated in the computation of thermodynamic and heat transport properties of weakly and strongly anharmonic systems. © Published under licence by IOP Publishing Ltd.

关键词： Calculations

Analysis of leaky modes or wavenumber resonances for the Rayleigh system in a half space

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arXiv 2022年

作者： de Hoop, Maarten V. Iantchenko, Alexei SIMONS CHAIR IN COMPUTATIONAL AND APPLIED MATHEMATICS AND EARTH SCIENCE RICE UNIVERSITY HoustonTX77005 United States DEPARTMENT OF MATERIALS SCIENCE AND APPLIED MATHEMATICS FACULTY OF TECHNOLOGY AND SOCIETY MALMÖ UNIVERSITY Malmö Sweden

We present a comprehensive analysis of wavenumber resonances or leaky modes associated with the Rayleigh operator in a half space containing a heterogeneous slab, being motivated by seismology. To this end, we introduce Jost solutions on an appropriate Riemann surface, a boundary matrix and a reflection matrix in analogy to the studies of scattering resonances associated with the Schrödinger operator. We analyze their analytic properties and characterize the distribution of these wavenumber resonances. Furthermore, we show that the resonances appear as poles of the meromorphic continuation of the resolvent to the nonphysical sheets of the mentioned Riemann surface as expected. Copyright © 2022, The Authors. All rights reserved.

关键词： Surface waves

Geometric inverse problems on gas giants

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arXiv 2024年

作者： de Hoop, Maarten V. Ilmavirta, Joonas Kykkänen, Antti Mazzeo, Rafe Computational and Applied Mathematics and Earth Science Rice University United States Department of Mathematics and Statistics University of Jyväskylä Finland Department of Mathematics Stanford University United States

On gas giant planets the speed of sound is isotropic and goes to zero at the surface. Geometrically, this corresponds to a Riemannian manifold whose metric tensor has a conformal blow-up near the boundary. The blow-up is tamer than in asymptotically hyperbolic geometry: the boundary is at a finite distance. We study the differential geometry of such manifolds, especially the asymptotic behavior of geodesics near the boundary. We relate the geometry to the propagation of singularities of a hydrodynamic PDE and we give the basic properties of the Laplace–Beltrami operator. We solve two inverse problems, showing that the interior structure of a gas giant is uniquely determined by different types of boundary *** Codes 53C22, 37D40, 53C65, 35R30 Copyright © 2024, The Authors. All rights reserved.

关键词： Geometry

Efficient mesh management in Firedrake using PETSc DMPlex

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Efficient mesh management in Firedrake using PETSc DMPlex

作者： Lange, Michael Mitchell, Lawrence Knepley, Matthew G. Gorman, Gerard J. Department of Earth Science and Engineering Imperial College London LondonSW7 2AZ United Kingdom Department of Mathematics Department of Computing Imperial College London LondonSW7 2AZ United Kingdom Computational and Applied Mathematics Rice University HoustonTX77005 United States

The use of composable abstractions allows the application of new and established algorithms to a wide range of problems, while automatically inheriting the benefits of well-known performance optimizations. This work highlights the composition of the PETSc DMPlex domain topology abstraction with the Firedrake automated finite element system to create a PDE solving environment that combines expressiveness, flexibility, and high performance. We describe how Firedrake utilizes DMPlex to provide the indirection maps required for finite element assembly, while supporting various mesh input formats and runtime domain decomposition. In particular, we describe how DMPlex and its accompanying data structures allow the generic creation of user-defined discretizations, while utilizing data layout optimizations that improve cache coherency and ensure overlapped communication during assembly computation. © 2016 SIAM.

关键词： Topology

Diffusive Wave Approximation to the Shallow Water Equations: computational Approach

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Procedia Computer science 2011年 4卷 1828-1833页

作者： Nathan Collier Hany Radwan Lisandro Dalcin Victor M. Calo Applied Mathematics and Computational Science and Earth and Environmental Sciences and Engineering King Abdullah University of Science and Technology Thuwal Saudi Arabia Centro Internacional de Ḿetodos Computacionales en Ingenieŕıa Santa Fe Argentina

We discuss the use of time adaptivity applied to the one dimensional diffusive wave approximation to the shallow water equations. A simple and computationally economical error estimator is discussed which enables time-step size adaptivity. This robust adaptive time discretization corrects the initial time step size to achieve a user specified bound on the discretization error and allows time step size variations of several orders of magnitude. In particular, in the one dimensional results presented in this work feature a change of four orders of magnitudes for the time step over the entire simulation.

关键词： time adaptivity shallow water flow overland flow

STABLE RECOVERY OF COEFFICIENTS IN AN INVERSE FAULT FRICTION PROBLEM

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arXiv 2023年

作者： de Hoop, Maarten V. Lassas, Matti Lu, Jinpeng Oksanen, Lauri Computational and Applied Mathematics and Earth Science Rice University HoustonTX77005 United States Department of Mathematics and Statistics University of Helsinki HelsinkiFI-00014 Finland

We consider the inverse fault friction problem of determining the friction coefficient in the Tresca friction model, which can be formulated as an inverse problem for differential inequalities. We show that the measurements of elastic waves during a rupture uniquely determine the friction coefficient at the rupture surface with explicit stability *** Codes 35R30, 35Q86 Copyright © 2023, The Authors. All rights reserved.

关键词： Elastic waves

QUANTITATIVE UNIQUE CONTINUATION FOR THE ELASTICITY SYSTEM WITH APPLICATION TO THE KINEMATIC INVERSE RUPTURE PROBLEM

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arXiv 2022年

We obtain explicit estimates on the stability of the unique continuation for a linear system of hyperbolic equations. In particular our result applies to the elasticity system and also the Maxwell system. As an application, we study the kinematic inverse rupture problem of determining the jump in displacement and the friction force at the rupture surface, and we obtain new features on the stable unique continuation up to the rupture *** Codes 35L10, 35R30, 35Q86 Copyright © 2022, The Authors. All rights reserved.

关键词： Elasticity