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numerical computations of rock dissolution and geomechanical effects for CO₂ geological storage

INTERNATIONAL JOURNAL FOR numerical AND ANALYTICAL METHODS IN GEOMECHANICS 2015年第5期39卷 482-506页

作者： Wojtacki, K. Lewandowska, J. Gouze, Ph. Lipkowski, A. Univ Montpellier 2 Lab Mecan & Genie Civil Montpellier France Univ Montpellier 2 CNRS Geosci Montpellier France Gdansk Univ Technol Gdansk Poland Gdanskie Inwestycje Komunalne Gdansk Poland

The paper is motivated by the long-term safety analysis of the CO2 geological storage. We present a methodology for the assessment of the geomechanical impact of progressive rock dissolution. The method is based on the use of X-ray tomography and the numerical dissolution technique. The influence of evolution of the microstructure on the macroscopic properties of the rock is analysed by using periodic homogenization method. The numerical computations show progressive degradation of all components of the stiffness (orthotropic) tensor. Moreover, the evolution of associated mass transfer properties (as tortuosity and conductivity tensors), by using the periodic homogenization method, is also calculated. The correlation between the mechanical parameters and the transfer properties during the dissolution process is presented. The results show that the highest increase of the hydraulic conductivity (in direction Y) is not associated with the highest decrease of Young modulus in this direction. Moreover, the highest decrease of Young modulus (in the direction X) is not associated with percolation in this direction. Finally, an incremental law to calculate settlement, in case of a rock with evolving microstructure, is proposed. The solution of the macroscopic settlement problem under constant stress and drained conditions showed that the geomechanical effects of the rock dissolution are rather limited. Copyright (c) 2014 John Wiley & Sons, Ltd.

关键词： CO2 storage homogenization chemo-mechanical coupling microstructure X-ray tomography numerical computations

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numerical computations and mathematical modelling with infinite and infinitesimal numbers

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2009年第1-2期29卷 177-195页

作者： Sergeyev, Yaroslav D. Univ Calabria Dipartimento Elettron Informat & Sistemist I-87030 Arcavacata Di Rende CS Italy

Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not related to the non-standard analysis) is used to work with finite, infinite, and infinitesimal numbers numerically. This can be done on a new kind of a computer-the Infinity Computer-able to work with all these types of numbers. The new computational tools both give possibilities to execute computations of a new type and open new horizons for creating new mathematical models where a computational usage of infinite and/or infinitesimal numbers can be useful. A number of numerical examples showing the potential of the new approach and dealing with divergent series, limits, probability theory, linear algebra, and calculation of volumes of objects consisting of parts of different dimensions are given.

关键词： numerical computations Infinite and infinitesimal numbers The Infinity Computer

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TESTING FOR numerical computations

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IEE PROCEEDINGS-E COMPUTERS AND DIGITAL TECHNIQUES 1980年第2期127卷 69-76页

作者： KARPOVSKY, M Computer Science Department School of Advanced Technology State University of New York at Binghamton Binghamton USA

We consider the problem of error detection in programs or specialised devices computing real functions f(x), where the argument x is represented in binary form. For error detection we use the linear check inequalities |∑τεTf(x ⊕ τ) − C| ≤ ε, where ε ≥ 0 is some given small constant, ⊕denotes componentwise addition mod 2 of binary vectors, T is some set of binary vectors and C is a constant. A method for the construction of a minimal check set T and constant C for the given f(x) and ɛ is proposed. This method is based on the techniques of Walsh transforms and least-absolute-error polynomial approximation. Several important examples of optimal checks for programs computing exponential, logarithmic and trigonometric functions will be given.

关键词： numerical computations Diagnostic, testing, debugging and evaluating systems polynomial approximation program testing real functions exponential functions Walsh transforms check inequalities programs trigonometric functions minimal check set error detection logarithmic functions

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A displacement potential function using complex variables for numerical computations of three-dimensional elasticity problems

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ARCHIVE OF APPLIED MECHANICS 2021年第5期91卷 2331-2344页

作者： Mares Carreno, Jesus Ortega Herrera, Jose angel Lodegario Abarca Jimenez, Griselda Stephany Inst Politecn Nacl Unidad Profes Interdisciplinaria Ingn Campus Hida Pachuca 42162 Mexico Inst Politecn Nacl Escuela Super Ingn Mecan & Elect Unidad Zacatenco Secc Estudios Posgrad & Invest Mexico City 07738 DF Mexico

This paper shows the development of a displacement potential function based on the Galerkin potential using complex variables. The displacement potential function results in a more suitable method for numerical calculations since it avoids the strenuous integration process associated with stress potential methods. Completeness of the displacement potential function is demonstrated. The displacement potential function was applied to the solution of the first fundamental problem of elasticity over a three-dimensional domain with known boundary conditions. It's application for numerical calculations is demonstrated by solving the pure shear problem over a three-dimensional unit hexahedral cell. Finally, the obtained numerical results are compared against finite element results, proving the validity of the displacement potential function in solving three-dimensional linear elasticity problems.

关键词： Displacement potential function Functions of complex variable numerical computations Three-dimensional elasticity

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Vortex kinematics around a submerged plate under water waves. Part II: numerical computations

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EUROPEAN JOURNAL OF MECHANICS B-FLUIDS 2017年 65卷 368-383页

作者： Pinon, Gregory Perret, Gaele Cao, Lei Poupardin, Adrien Brossard, Jerome Rivoalen, Elie Normandie Univ UNIHAVRE CNRS LOMCLab Ondes & Milieux Complexes UMR 6295 F-76600 Le Havre France UTC BP 60319 Rue Roger Couttolenc F-60203 Compiegne France CEA DAM DIF F-91297 Arpajon France Normandie Univ INSAROUEN LOFIMS Lab Optimisat & Fiabilite Mecan Struct EA 3828 F-76800 St Etienne Du Rouvray France

This paper presents numerical computations of the flow generated by a horizontal plate immersed in a regular wave field, and associated loads acting on the plate. This numerical work is the continuation of the Poupardin et al. (2012) experimental study. This numerical study is original in the way that the vortical aspects of the flow are not neglected. Therefore, a 2D Lagrangian Vortex method is used as a numerical scheme. These methods are particularly well suited for the computation of unsteady and highly rotational flows in an open domain. The velocity field is decomposed into rotational and potential components, using the Helmholtz decomposition. The rotational part of the velocity is calculated by the Biot-Savart equation using vortex particles. The plate is modelled by a distribution of normal dipoles and the wave field is taken into account by means of a Stokes formulation, which completes the potential part of the velocity. Firstly, the numerical code is validated by means of comparison with the experimental results of Poupardin et al. (2012). In particular, the complex vortical activity and the mean flow velocity field are well reproduced and physically analysed. Secondly, forces acting on the plate are analysed on a wide range of parameters by varying the plate immersions and lengths. In the end, a new scaling is found for the lift forces acting on the plate based on the modified Stokes velocity (i.e. the bottom Stokes velocity for a water depth equals to the plate immersion) and the square of the plate length. (C) 2016 Elsevier Masson SAS. All rights reserved.

关键词： numerical computations Submerged plate Hydrodynamics Lagrangian vortex method Water wave Vortex dynamics

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Compute-in-Memory for numerical computations

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MICROMACHINES 2022年第5期13卷 731-731页

作者： Zhao, Dongyan Wang, Yubo Shao, Jin Chen, Yanning Guo, Zhiwang Pan, Cheng Dong, Guangzhi Zhou, Min Wu, Fengxia Wang, Wenhe Zhou, Keji Xue, Xiaoyong Beijing Smart Chip Microelect Technol Co Ltd State Grid Key Lab Power Ind Chip Design & Anal T Beijing 100192 Peoples R China Beijing Chip Identificat Technol Co Ltd Beijing 100192 Peoples R China Fudan Univ Sch Microelect State Key Lab ASIC & Syst Shanghai 201203 Peoples R China

In recent years, compute-in-memory (CIM) has been extensively studied to improve the energy efficiency of computing by reducing data movement. At present, CIM is frequently used in data-intensive computing. Data-intensive computing applications, such as all kinds of neural networks (NNs) in machine learning (ML), are regarded as 'soft' computing tasks. The 'soft' computing tasks are computations that can tolerate low computing precision with little accuracy degradation. However, 'hard' tasks aimed at numerical computations require high-precision computing and are also accompanied by energy efficiency problems. numerical computations exist in lots of applications, including partial differential equations (PDEs) and large-scale matrix multiplication. Therefore, it is necessary to study CIM for numerical computations. This article reviews the recent developments of CIM for numerical computations. The different kinds of numerical methods solving partial differential equations and the transformation of matrixes are deduced in detail. This paper also discusses the iterative computation of a large-scale matrix, which tremendously affects the efficiency of numerical computations. The working procedure of the ReRAM-based partial differential equation solver is emphatically introduced. Moreover, other PDEs solvers, and other research about CIM for numerical computations, are also summarized. Finally, prospects and the future of CIM for numerical computations with high accuracy are discussed.

关键词： compute-in-memory (CIM) numerical computations resistive random-access memory (ReRAM) partial differential equations (PDEs) crossbar

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numerical simulations of thermal convection in unsteady Darcy Forchheimer flow of radiative Ag - GO/KO hybrid nanofluid over a slipping spinning porous disk

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CASE STUDIES IN THERMAL ENGINEERING 2025年 68卷

作者： Iqbal, Zahoor Ali, Farhan Xu, Huiying Zhu, Xinzhong Alqarni, M. M. Hussain, Arafat Alhazmi, Sharifah E. Ragab, Ehab M. Ahmed, M. Faizan Zhejiang Normal Univ Sch Comp Sci & Technol Jinhua 321004 Peoples R China Zhejiang Normal Univ Zhejiang Inst Photoelect Jinhua 321004 Zhejiang Peoples R China Zhejiang Normal Univ Zhejiang Inst Adv Light Source Jinhua 321004 Zhejiang Peoples R China Zhejiang Normal Univ Res Inst Hangzhou Artificial Intelligence Hangzhou 311231 Zhejiang Peoples R China Wenzhou Univ Coll Comp Sci & Artificial Intelligence Wenzhou 325035 Peoples R China Fed Urdu Univ Arts Sci & Technol Dept Math Sci Karachi 75300 Pakistan King Khalid Univ Coll Sci Dept Math Abha 61413 Saudi Arabia Xinjiang Univ Coll Math & Syst Sci Urumqi Xinjiang Peoples R China Umm Al Qura Univ Al Qunfudah Univ Coll Math Dept Mecca Saudi Arabia Northern Border Univ Engn Coll Dept Civil Engn Ar Ar Saudi Arabia

The thermal transport in hybrid nanofluid flow across a rotating disk has numerous applications in technical and engineering fields, including thermal power systems, rotating machinery, gas turbines, and electronics. The Hybrid nanofluids offer better thermal efficiency than traditional single-component nanofluids due to the inclusion of two types of metallic nanoparticles. This study examines the thermal behavior of an Ag- GO/KO hybrid nanofluid flowing over a rotating, slippery disk under a highly oscillating magnetic field. The model incorporates a thermal sink/ source and thermal radiation to enhance its applicability in practical scenarios. The Tiwari and Das approach is used to examine the characteristics of the fluid flow. The model equations are obtained by applying the proper Von-Karman similarity transformations to the strongly nonlinear system of governing equations, which is then numerically solved using the bvp4c technique in MATLAB. The effects of physical parameters on thermal field, radial velocity, axial velocity, and tangential direction are visually displayed. The findings indicate that a rise in the inertia coefficient and porosity variable leads to produce a reducing effect on the radial velocity and tangential velocity. In contrast, the opposite impact is examined in the axial direction. Additionally, the result demonstrates the improved temperature distribution due to higher thermal radiation and unsteady variable. Moreover, tables are depicted to numerically discuss the impacts of slip variables, heat radiation and unsteady variables on drag coefficients and heat transport.

关键词： Rotating disk numerical computations Porous medium Hybrid nanofluid Darcy Forchheimer law Thermal radiations

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Analysis of heat and mass transport in Hiemenz viscoelastic fluid flow via modified Fourier and Fick's law

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MULTISCALE AND MULTIDISCIPLINARY MODELING EXPERIMENTS AND DESIGN 2025年第2期8卷 1-12页

作者： Sarfraz, Mahnoor Khan, Masood Quaid I Azam Univ Dept Math Islamabad 44000 Pakistan Ghulam Ishaq Khan Inst Engn Sci & Technol GIKI Dept Engn Sci Swabi 23640 Pakistan

This study analyzes Hiemenz flow to understand the fluid's behavior over a biaxial stretching/shrinking surface after applying boundary layer approximation. Cattaneo-Christov's model is used which addresses the physical controls of Fourier's law and expands the classical theory of heat conduction by incorporating the concepts of thermal and solutal relaxation time. This indicates that precise temperature control and thermal response are intensely beneficial in material processing and biomedical engineering applications. Furthermore, the mathematical model is formulated by considering thermal generation/absorption, Ohmic heating, and chemical reactions to investigate thermal and solutal distribution. The resulting nonlinear system equations contain singularity which is effectively managed by applying the perturbation technique. A built-in module in Python is used to obtain numerical solutions by converting highest-order equations to first-order equations. Graphical representations depict numerical solutions against the constraints on temperature, concentration distributions, fluid velocities, and friction drag. The numerical results indicate that the increase in the Prandtl number and relaxation time reduce heat transport due to decreased thermal diffusivity and slower response to temperature changes. Additionally, variations in molecular diffusion rates decrease mass transfer. The results are validated and compared with previously published results in tabular form. The novelty of this study lies in the implementation of Cattaneo-Christov theory, which effects the thermal and solutal transfer mechanisms by propagating thermal waves with finite speed and incorporates non-Fourier thermal behavior. Due to its practical and scientific importance in preservation of solar energy, biomedical science, food industries, oil spill clean-up and textile industries, the study holds significant importance.

关键词： Cattaneo-Christov heat flux Chemical reaction Heat source/sink Jeffrey fluid numerical computations Ohmic heating Viscoelastic fluids

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Modeling and analysis of heat transfer in Eyring-Powell fluids with magnetic and viscous dissipation: applications to MHD systems

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MULTISCALE AND MULTIDISCIPLINARY MODELING EXPERIMENTS AND DESIGN 2025年第3期8卷 1-13页

作者： Afaq, Harsa Azhar, Ehtsham Kamran, Abid PMAS Arid Agr Univ Dept Math Rawalpindi Punjab Pakistan Capital Univ Sci & Technol Dept Math Islamabad 44000 Pakistan

This study aims to numerically investigate the heat transfer characteristics and flow behavior of a non-Newtonian Eyring-Powell fluid. The model considers the non-Newtonian properties of the Eyring-Powell fluid, a magnetic dipole, and viscous dissipation, while also incorporating micropolar and mixed convection effects to create a comprehensive analysis. This model is relevant for engineering applications such as the design of MHD generators, cooling of electronic devices, and thermal management in processes involving fluid transport under magnetic fields. The challenge of numerically solving magnetic dipole-related mathematical problems underscores the importance of this research. The mathematical model includes the governing equations for flow and energy. Similarity transformations are employed to convert these into a set of coupled nonlinear ordinary differential equations (ODEs), which are then solved using the Runge-Kutta method. The study provides an in-depth analysis of the key parameters influencing the flow problem, supported by diagrams and tables. Additionally, the local Nusselt number and the skin-friction coefficient are calculated and presented in tabular form. The numerical results yield several significant conclusions, with the most notable being that the fluid parameter & varepsilon;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document} reduces heat dissipation, thereby decreasing the heat transfer rate at the sheet surface. Higher material fluid parameters can result in stronger coupling between rotational and translational motions, leading to a decrease in velocity.

关键词： Eyring fluid model Micropolar Magnetic dipole numerical computations

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Theoretical and numerical results on the control of type III thermoelastic porous system

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2025年第7期48卷 8385-8399页

作者： Messaoudi, Salim A. Al-Mahdi, Adel M. Alahyane, Mohamed Univ Sharjah Dept Math Sharjah U Arab Emirates King Fahd Univ Petr & Minerals Preparatory Year Program Dhahran Saudi Arabia King Fahd Univ Petr & Minerals Interdisciplinary Res Ctr Construct & Bldg Mat Dhahran Saudi Arabia La Rochelle Univ MIA Lab La Rochelle France King Fahd Univ Petr & Minerals Preparatory Year Program Dhahran 31261 Saudi Arabia

In this work, a type III thermo-porous elastic system is considered. First, we use the semigroup theory to demonstrate that the system is well-posed. Second, we show that the system is exponentially stable under a natural constraint on its parameters. Finally, we provide various numerical examples to illustrate numerically our theoretical findings.

关键词： exponential decay numerical computations semigroup theory swelling porous thermoelasticity of type III

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