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A combined method using Lattice Boltzmann method(LBM)and finite volume method(FVM)to simulate geothermal reservoirs in Enhanced Geothermal System(EGS)

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Journal of Groundwater Science and Engineering 2024年第2期12卷 132-146页

作者： Xiang Gao Tai-lu Li Yu-wen Qiao Yao Zhang Ze-yu Wang School of Energy and Environmental Engineering Hebei University of TechnologyTianjin 300401China

With the development of industrial activities,global warming has accelerated due to excessive emission of CO_(2).Enhanced Geothermal System(EGS)utilizes deep geothermal heat for power *** porous medium theory is commonly employed to model geothermal reservoirs in EGS,Hot Dry Rock(HDR)presents a challenge as it consists of impermeable granite with zero porosity,potentially distorting the physical *** address this,the Lattice Boltzmann method(LBM)is employed to simulate CO_(2)flow within geothermal reservoirs and the finite volume method(FVM)to solve the energy conservation equation for temperature *** combined method of LBM and FVM is imple-mented using *** results showed that the Reynolds numbers(Re)of 3,000 and 8,000 lead to higher heat extraction rates from geothermal ***,higher Re values may accelerate thermal breakthrough,posing challenges to EGS ***,non-equilibrium of density in fractures becomes more pronounced during the system's life cycle,with non-Darcy's law becoming significant at Re values of 3,000 and 8,*** stratification due to buoyancy effects significantly impacts temperature distribution within geothermal reservoirs,with buoyancy effects at Re=100 under gravitational influence being *** Re values(3,000 and 8,000)induce stronger forced convection,leading to more uniform density *** addition of proppant negatively affects heat transfer performance in geothermal reservoirs,especially in single *** engineering considerations should determine the quantity of proppant through detailed numerical simulations.

关键词： Lattice boltzmann method finite volume method Enhanced geothermal system Geothermal reservoir Proppant Re Heat extraction rate

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A finite volume method for global electromagnetic induction forward modeling on collocated unstructured grids

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Earth and Planetary Physics 2023年第1期7卷 57-65页

作者： Liang Yin ZhengYong Ren HongBo Yao Cong Yang State Key Laboratory of Lunar and Planetary Sciences Macao University of Science and TechnologyMacaoChina CNSA Macao Center for Space Exploration and Science MacaoChina School of Geosciences and Info-Physics Central South UniversityChangsha 410083China Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring Ministry of Education(Central South University)Changsha 410083China Hunan Key Laboratory of Nonferrous Resources and Geological Hazards Exploration Central South UniversityChangsha 410083China

Global electromagnetic induction provides an efficient way to probe the electrical conductivity in the Earth’s deep *** to the increasing geomagnetic data especially from high-accuracy geomagnetic satellites,inverting the Earth’s three-dimensional conductivity distribution on a global scale becomes attainable.A key requirement in the global conductivity inversion is to have a forward solver with high-accuracy and *** this study,a finite volume method for global electromagnetic induction forward modeling is developed based on unstructured *** polyhedral grids are supported in our algorithms to obtain high geometric *** employ a cell-centered collocated variable arrangement which allows convenient discretization for complex geometries and straightforward implementation of multigrid *** validate the method,we test our code with two synthetic models and compare our finite volume results with an analytical solution and a finite element numerical *** agreements are observed between our solution and other results,indicating acceptable accuracy of the proposed method.

关键词： global electromagnetic induction mantle electrical conductivity finite volume method unstructured grids

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finite volume method FOR SIMULATION OF VISCOELASTIC FLOW THROUGH A EXPANSION CHANNEL

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Journal of Hydrodynamics 2009年第3期21卷 360-365页

作者： FU Chun-quan JIANG Hai-mei YIN Hong-jun SU Yu-chi ZENG Ye-ming Key Laboratory of Enhanced Oil and Gas Recovery of Ministry of Education Daqing Petroleum Institute Daqing 163318 China China National Offshore Oil Company Research Center Beijing 100027 China China National Offshore Oil Corporation Limited Beijing 100010 China Oil Recovery Plant No.1 Daqing Oilfield Corp. Ltd. Daqing 163001 China

A finite volume method for the numerical solution of viscoelastic flows is given. The flow of a differential Upper-Convected Maxwell （UCM） fluid through an abrupt expansion has been chosen as a prototype example. The conservation and constitutive equations are solved using the finite volume method （FVM） in a staggered grid with an upwind scheme for the viscoelastic stresses and a hybrid scheme for the velocities. An enhanced-in-speed pressure-correction algorithm is used and a method for handling the source term in the momentum equations is employed. Improved accuracy is achieved by a special discretization of the boundary conditions. Stable solutions are obtained for higher Weissenberg number （We）, further extending the range of simulations with the FVM. Numerical results show the viscoelasticity of polymer solutions is the main factor influencing the sweeo efficiency.

关键词： Upper-Convected Maxwell (UCM) model finite volume method viscoelasticity sweep efficiency

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A finite volume method with Unstructured Triangular Grids for Numerical Modeling of Tidal Current

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China Ocean Engineering 2005年第4期19卷 693-700页

作者：史宏达刘臻 Engineering College Ocean University of China Qingdao 266071China

The finite volume method （FVM） has many advantages in 2-D shallow water numerical simulation. In this study, the finite volume method is used with unstructured triangular grids to simulate the tidal currents. The Roe scheme is applied in the calculation of the intercell numerical flux, and the MUSCL method is introduced to improve its accuracy. The time integral is a two-step scheme of forecast and revision. For the verification of the present method, the Stoker＇s problem is calculated and the result is compared with the mathematically analytic solutions. The comparison indicates that the method is feasible. A sea area of a port is used as an example to test the method established here. The result shows that the present computational method is satisfactory, and it could be applied to the engineering fields.

关键词： finite volume method numerical modeling unstructured triangular grids tidal currents

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NUMERICAL INVESTIGATION ON NON-NEWTONIAN FLOWS THROUGH DOUBLE CONSTRICTIONS BY AN UNSTRUCTURED finite volume method

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Journal of Hydrodynamics 2009年第5期21卷 622-632页

作者： GAO Wei LIU Ru-xun DUAN Ya-li Department of Mathematics University of Science and Technology of China Hefei 230026 China

This article presents a numerical investigation on a steady non-Newtonian flow through a two-dimensional channel with double constrictions. The power-law mode is employed in describing the non-Newtonian behavior of the flow. An unstructured finite volume method combined with a fractional-step projection method is developed for the discretization of incompressible equations governing the non-Newtonian flows. The important flow dynamics related with the arterial diseases, such as the wall shear stress and vortex generation, are also numerically studied in detail. Numerical results reveal that there are marked differences between Newtonian and non-Newtonian models.

关键词： double constrictions power-law fluid finite volume method unstructured grids

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Integrating 1D and 2D hydrodynamic,sediment transport model for dam-break flow using finite volume method

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Science China(Physics,Mechanics & Astronomy) 2014年第4期57卷 774-783页

作者： ZHANG MingLiang XU YuanYuan HAO ZiNing QIAO Yang School of Ocean Science and Environment Dalian Ocean University

The purpose of this study is to set up a dynamically linked 1D and 2D hydrodynamic and sediment transport models for dam break *** 1D-2D coupling model solves the generalized shallow water equations,the non-equilibrium sediment transport and bed change equations in a coupled fashion using an explicit finite volume *** considers interactions among transient flow,strong sediment transport and rapid bed change by including bed change and variable flow density in the flow continuity and momentum *** unstructured Quadtree rectangular grid with local refinement is used in the 2D *** intercell flux is computed by the HLL approximate Riemann solver with shock captured capability for computing the dry-to-wet interface for all *** effects of pressure and gravity are included in source term in this coupling model which can simplify the computation and eliminate numerical imbalance between source and flux *** developed model has been tested against experimental and real-life case of dam-break flow over fix bed and movable *** results are compared with analytical solution and measured data with good *** simulation results demonstrate that the coupling model is capable of calculating the flow,erosion and deposition for dam break flows in complicated natural domains.

关键词： 1D/2D coupling model finite volume method HLL approximate Riemann solver non-equilibrium sediment transport

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A STABILIZED EQUAL-ORDER finite volume method FOR THE STOKES EQUATIONS

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Journal of Computational Mathematics 2012年第6期30卷 615-628页

作者： Wanfu Tian Liqiu Song Yonghai Li School of Science Shenyang Aerospace University Shenyang 110136 China Institute of Mathematics Jilin University Changchun 130012 China School of Mathematics Jilin University Changchun 130012 China

We construct a new stabilized finite volume method on rectangular grids for the Stokes equations. The lowest equal-order conforming finite element pair （piecewise bilinear veloc- ities and pressures） and piecewise constant test spaces for both the velocity and pressure are employed in this method. We show the stability of this method and prove first optimal rate of convergence for the velocity in the H1 norm and the pressure in the L2 norm. In addition, a second order optimal error estimate for the velocity in the L2 norm is derived. Numerical experiments illustrating the theoretical results are included.

关键词： Stokes equations Equal-order finite element pair finite volume method Errorestimate.

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High Accuracy finite volume method for Solving Nonlinear Aeroacoustics Problems on Unstructured Meshes

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Chinese Journal of Aeronautics 2006年第2期19卷 97-104页

作者： Ilya ABALAKIN Alain DERVIEUX Tatiana KOZUBSKAYA Institute for Mathematical Modelling RAS . MoscowRussia INRIA Sophia-Antipolis France Institute for Mathematical Modelling RAS . MoscowRussia

The paper presents a finite volume numerical method universally applicable for solving both linear and nonlinear aeroacoustics problems on arbitrary unstructured meshes. It is based on the vertexcentered multi-parameter scheme offering up to the 6th accuracy order achieved on the Cartesian meshes. An adaptive dissipation is added for the numerical treatment of possible discontinuities. The scheme properties are studied on a series of test cases, its efficiency is demonstrated at simulating the noise suppression in resonance-type liners.

关键词： nonlinear aeroacoustics Euler based models finite volume method high accuracy approximation unstructured meshes liners

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Simulation of unconventional well tests with the finite volume method

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Petroleum Science 2012年第3期9卷 317-329页

作者： CANCELLIERE Michel VERGA Francesca Politecnico di Torino DITAGTorino (TO) 10129 Italy

The finite volume method has been successfully applied in several engineering fields and has shown outstanding performance in fluid dynamics simulation. In this paper, the general framework for the simulation ofnear-wellbore systems using the finite volume method is described. The mathematical model and the numerical model developed by the authors are presented and discussed. A radial geometry in the vertical plane was implemented so as to thoroughly describe near-wellbore phenomena. The model was then used to simulate injection tests in an oil reservoir through a horizontal well and proved very powerful to correctly reproduce the transient pressure behavior. The reason for this is the robustness of the method, which is independent of the gridding options because the discretization is performed in the physical space. The model is able to describe the phenomena taking place in the reservoir even in complex situations, i.e. in the presence of heterogeneities and permeability barriers, demonstrating the flexibility of the finite volume method when simulating non-conventional tests. The results are presented in comparison with those obtained with the finite difference numerical approach and with analytical methods, if possible.

关键词： finite volume method numerical methods horizontal well modeling injection testing gridding

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finite volume method BASED ON THE CROUZEIX-RAVIART ELEMENT FOR THE STOKES EQUATION

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2001年第2期2卷 45-49页

作者：李大明 Dept. of Mathmatics Zhejiang University Hangzhou China

The author provides a new discretization method-the finite volume method(FVM).For the Stokes equation the velocity space is approximated by the nonconforming linear element based on the dual partition and the pressure by the piecewise constant based on the primal triangulation .Under the suitable smoothness of the solution, the optimal convergence rate \%O(h)\% is obtained,where \%h\% denotes the parameter of the space discretization.

关键词： Stokes equation finite volume method Crouzeix-Raviart element

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