Steady-state heat transfer problems in heterogeneous solid are simulated by developing an adaptive extended isogeometric analysis(XIGA)method based on locally refined non-uniforms rational B-splines(LR NURBS).In the X...Steady-state heat transfer problems in heterogeneous solid are simulated by developing an adaptive extended isogeometric analysis(XIGA)method based on locally refined non-uniforms rational B-splines(LR NURBS).In the XIGA,the LR NURBS,which have a simple local refinement algorithm and good description ability for complex geometries,are employed to represent the geometry and discretize the field variables;and some special enrichment functions are introduced into the approximation of temperature field,thus the computational mesh is independent of the material interfaces,which are described with the level setmethod.Similar to the approximation of temperature field,a temperature gradient recovery technique for heterogeneous media is proposed,and based on the Zienkiewicz–Zhu recovery technique a posteriori error estimator is defined to automatically identify the locally refined regions.The convergence and performance properties of the developed method are verified by using three numerical examples.The numerical results show that(1)The convergence speed of the adaptive local refinement is faster than that of the uniform global refinement;(2)The convergence rate of the high-order basis functions is faster than that of the low-order basis functions;and(3)The existing inclusions change the local distributions of the temperature,and the extreme values of the temperature gradients take place around the inclusion interfaces.展开更多
An efficient approximate scheme is presented for wave-propagation simulation in piecewise heterogeneous media by applying the Born-series approximation to volume-scattering waves. The numerical scheme is tested for di...An efficient approximate scheme is presented for wave-propagation simulation in piecewise heterogeneous media by applying the Born-series approximation to volume-scattering waves. The numerical scheme is tested for dimensionless frequency responses to a heterogeneous alluvial valley where the velocity is perturbed randomly in the range of 5 %–25 %,compared with the full-waveform numerical solution. Then,the scheme is extended to a heterogeneous multilayered model by calculating synthetic seismograms to evaluate approximation accuracies Numerical experiments indicate that the convergence rate of this method decreases gradually with increasing velocity perturbations. The method has a fast convergence for velocity perturbations less than 15 %. However,the convergence becomes slow drastically when the velocity perturbation increases to 20 %. The method can hardly converge for the velocity perturbation up to 25 %.展开更多
In this study,we propose a constraint learning strategy based on interpretability analysis to improve the convergence and accuracy of the enriched physics-informed neural network(EPINN),which is applied to simulate tw...In this study,we propose a constraint learning strategy based on interpretability analysis to improve the convergence and accuracy of the enriched physics-informed neural network(EPINN),which is applied to simulate two-phase flow in heterogeneous porous media.Specifically,we first analyze the layerwise outputs of EPINN,and identify the distinct functions across layers,including dimensionality adjustment,pointwise construction of non-equilibrium potential,extraction of high-level features,and the establishment of long-range dependencies.Then,inspired by these distinct modules,we propose a novel constraint learning strategy based on regularization approaches,which improves neural network(NN)learning through layer-specific differentiated updates to enhance cross-timestep generalization.Since different neu ral network layers exhibit varying sensitivities to global generalization and local regression,we decrease the update frequency of layers more sensitive to local learning under this constraint learning strategy.In other words,the entire neural network is encouraged to extract more generalized features.The superior performance of the proposed learning strategy is validated through evaluations on numerical examples with varying computational complexities.Post hoc analysis reveals that gradie nt propagation exhibits more pronounced staged characte ristics,and the partial differential equation(PDE)residuals are more uniformly distributed under the constraint guidance.Interpretability analysis of the adaptive constraint process suggests that maintaining a stable information compression mode facilitates progressive convergence acceleration.展开更多
Studying immiscible fluid displacement patterns can provide a better understanding of displacement processes within heterogeneous porous media,thereby helping improving oil recovery and optimizing geological CO_(2) se...Studying immiscible fluid displacement patterns can provide a better understanding of displacement processes within heterogeneous porous media,thereby helping improving oil recovery and optimizing geological CO_(2) sequestration.As the injection rate of water displacing oil increases and the displacement pattern transits from capillary fingering to viscous fingering,there is a broad crossover zone between the two that can adversely affect the oil displacement efficiency.While previous studies have utilized phase diagrams to investigate the influence of the viscosity ratio and wettability of the crossover zone,fewer have studied the impact of rock heterogeneity.In this study,we created pore network models with varying degrees of heterogeneity to simulate water flooding at different injection rates.Our model quantifies capillary and viscous fingering characteristics while investigating porous media heterogeneity's role in the crossover zone.Analysis of simulation results reveals that a higher characteristic front flow rate within the crossover zone leads to earlier breakthrough and reduced displacement efficiency.Increased heterogeneity in the porous media raises injection-site pressure,lowers water saturation,and elevates the characteristic front flow rate,thereby expanding the extent of crossover zone.展开更多
Elastic wave inverse scattering theory plays an important role in parameters estimation of heterogeneous media.Combining inverse scattering theory,perturbation theory and stationary phase approximation,we derive the P...Elastic wave inverse scattering theory plays an important role in parameters estimation of heterogeneous media.Combining inverse scattering theory,perturbation theory and stationary phase approximation,we derive the P-wave seismic scattering coefficient equation in terms of fluid factor,shear modulus and density of background homogeneous media and perturbation media.With this equation as forward solver,a pre-stack seismic Bayesian inversion method is proposed to estimate the fluid factor of heterogeneous media.In this method,Cauchy distribution is utilized to the ratios of fluid factors,shear moduli and densities of perturbation media and background homogeneous media,respectively.Gaussian distribution is utilized to the likelihood function.The introduction of constraints from initial smooth models enhances the stability of the estimation of model parameters.Model test and real data example demonstrate that the proposed method is able to estimate the fluid factor of heterogeneous media from pre-stack seismic data directly and reasonably.展开更多
This paper is devoted to studying the asymptotic behavior of the solution to nonlocal Fisher-KPP type reaction diffusion equations in heterogeneous media.The kernel K is assumed to depend on the media.First,we give an...This paper is devoted to studying the asymptotic behavior of the solution to nonlocal Fisher-KPP type reaction diffusion equations in heterogeneous media.The kernel K is assumed to depend on the media.First,we give an estimate of the upper and lower spreading speeds by generalized principal eigenvalues.Second,we prove the existence of spreading speeds in the case where the media is periodic or almost periodic by showing that the upper and lower generalized principal eigenvalues are equal.展开更多
This study investigates the impact of pore network characteristics on fluid flow through complex and heterogeneous porous media,providing insights into the factors affecting fluid propagation in such systems.Specifica...This study investigates the impact of pore network characteristics on fluid flow through complex and heterogeneous porous media,providing insights into the factors affecting fluid propagation in such systems.Specifically,high-resolution or micro X-ray computed tomography(CT)imaging techniques were utilized to examine outcrop stromatolite samples of the Lagoa Salgada,considered flow analogous to the Brazilian Pre-salt carbonate reservoirs.The petrophysical results comprised two distinct stromatolite depositional facies,the columnar and the fine-grained facies.By generating pore network model(PNM),the study quantified the relationship between key features of the porous system,including pore and throat radius,throat length,coordination number,shape factor,and pore volume.The study found that the less dense pore network of the columnar sample is typically characterized by larger pores and wider and longer throats but with a weaker connection of throats to pores.Both facies exhibited less variability in the radius of the pores and throats in comparison to throat length.Additionally,a series of core flooding experiments coupled with medical CT scanning was designed and conducted in the plug samples to assess flow propagation and saturation fields.The study revealed that the heterogeneity and presence of disconnected or dead-end pores significantly impacted the flow patterns and saturation.Two-phase flow patterns and oil saturation distribution reveal a preferential and heterogeneous displacement that mainly swept displaced fluid in some regions of plugs and bypassed it in others.The relation between saturation profiles,porosity profiles,and the number of fluid flow patterns for the samples was evident.Only for the columnar plug sample was the enhancement in recovery factor after shifting to lower salinity water injection(SB)observed.展开更多
The accurate simulation of wave propagation in real media requires properly taking the attenuation into account,which leads to wave dissipation together with its causal companion,wave dispersion.In this study,to obtai...The accurate simulation of wave propagation in real media requires properly taking the attenuation into account,which leads to wave dissipation together with its causal companion,wave dispersion.In this study,to obtain a weak formulation of heterogenous viscoacoustic wave propagation in an infinite domain,the viscoacoustic medium is first characterized by its frequency-dependent complex bulk compliance instead of the classically used complex bulk modulus.Then,a mechanical model using serially connected standard linear solids(SSLS)is built to obtain the rational approximation of the complex bulk compliance whose parameters are calculated via an adapted nonlinear optimization method.Utilizing the obtained bulk compliance-based constitutive relation,a novel second-order viscoacoustic wave equation in the frequency domain is derived,of which the weak formulation can be physically explained as the virtual work equation and can thus be discretized using a continuous spectral element method in space.Additionally,a new method is introduced to address the convolution terms involved in the inverse Fourier transform,whose accurate time integration can then be achieved using an explicit time scheme,which avoids the transient growth that exists in the classical method.The resulting full time-space decoupling scheme can handle wave propagation in arbitrary heterogeneous media.Moreover,to treat the wave propagation in an infinite domain,a perfectly matched layer in weak formulation is derived for the truncation of the infinite domain via complex coordinate stretching of the virtual work equation.With only minor modification,the resulting perfectly matched layer can be implemented using the same time scheme as for the wave equation inside the truncated domain.The accuracy,numerical stability,and versatility of the new proposed scheme are demonstrated with numerical examples.展开更多
This study presents a numerical solution to the three-dimensional solute transport in heterogeneous media by using a layer-integrated approach.Omitting vertical spatial variation of soil and hydraulic properties withi...This study presents a numerical solution to the three-dimensional solute transport in heterogeneous media by using a layer-integrated approach.Omitting vertical spatial variation of soil and hydraulic properties within each layer,a threedimensional solute transport can be simplified as a quasi-three-dimensional solute transport which couples a horizontal two-dimensional simulation and a vertical onedimensional computation.The finite analytic numericalmethod was used to discretize the derived two-dimensional governing equation.A quadratic function was used to approximate the vertical one-dimensional concentration distribution in the layer to ensure the continuity of concentration and flux at the interface between the adjacent layers.By integration over each layer,a set of system of equations can be generated for a single column of vertical cells and solved numerically to give the vertical solute concentration profile.The solute concentration field was then obtained by solving all columns of vertical cells to achieve convergence with the iterative solution procedure.The proposed model was verified through examples from the published literatures including four verifications in terms of analytical and experimental cases.Comparison of simulation results indicates that the proposed model satisfies the solute concentration profiles obtained from experiments in time and space.展开更多
We review some of our recent efforts in developing upscaling methods for simulating the flow transport through heterogeneous porous media. In particular, the steady flow transport through highly heterogeneous porous m...We review some of our recent efforts in developing upscaling methods for simulating the flow transport through heterogeneous porous media. In particular, the steady flow transport through highly heterogeneous porous media driven by extraction wells and the flow transport through unsaturated porous media will be considered.展开更多
The dispersion process in heterogeneous porous media is distance-dependent, which results from multi-scaling property of heterogeneous structure. An analytical model describing the dispersion with an exponential dispe...The dispersion process in heterogeneous porous media is distance-dependent, which results from multi-scaling property of heterogeneous structure. An analytical model describing the dispersion with an exponential dispersion function is built, which is transformed into ODE problem with variable coefficients, and obtained analytical solution for two type boundary conditions using hypergeometric function and inversion technique. According to the analytical solution and computing results the difference between the exponential dispersion and constant dispersion process is analyzed展开更多
We describe an operator splitting technique based on physics rather than on dimension for the numerical solution of a nonlinear system of partial differential equations which models three-phase flow through heterogene...We describe an operator splitting technique based on physics rather than on dimension for the numerical solution of a nonlinear system of partial differential equations which models three-phase flow through heterogeneous porous media.The model for three-phase flow considered in this work takes into account capillary forces,general relations for the relative permeability functions and variable porosity and permeability fields.In our numerical procedure a high resolution,nonoscillatory,second order,conservative central difference scheme is used for the approximation of the nonlinear system of hyperbolic conservation laws modeling the convective transport of the fluid phases.This scheme is combined with locally conservative mixed finite elements for the numerical solution of the parabolic and elliptic problems associated with the diffusive transport of fluid phases and the pressure-velocity problem.This numerical procedure has been used to investigate the existence and stability of nonclassical shock waves(called transitional or undercompressive shock waves)in two-dimensional heterogeneous flows,thereby extending previous results for one-dimensional flow problems.Numerical experiments indicate that the operator splitting technique discussed here leads to computational efficiency and accurate numerical results.展开更多
In this paper, we propose a tailored finite cell method for the computation of two- dimensional Helmholtz equation in layered heterogeneous medium. The idea underlying the method is to construct a numerical scheme bas...In this paper, we propose a tailored finite cell method for the computation of two- dimensional Helmholtz equation in layered heterogeneous medium. The idea underlying the method is to construct a numerical scheme based on a local approximation of the solution to Helmholtz equation. This provides a computational tool of achieving high accuracy with coarse mesh even for large wave number （high frequency）. The stability analysis and error estimates of this method are also proved. We present several numerical results to show its efficiency and accuracy.展开更多
We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling.This poroelasticity problem suffers from rapidly oscillating material parameters,which c...We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling.This poroelasticity problem suffers from rapidly oscillating material parameters,which calls for a thorough numerical treatment.In this paper,we propose a method based on the local orthogonal decomposition technique and motivated by a similar approach used for linear thermoelasticity.Therein,local corrector problems are constructed in line with the static equations,whereas we propose to consider the full system.This allows to benefit from the given saddle point structure and results in two decoupled corrector problems for the displacement and the pressure.We prove the optimal first-order convergence of this method and verify the result by numerical experiments.展开更多
In this article, the bounding surfaces of channels were modeled by Bayesian stochastic simulation, which is a boundary-valued problem with observed valley erosion thickness at the locations of wells （hard data）. In ...In this article, the bounding surfaces of channels were modeled by Bayesian stochastic simulation, which is a boundary-valued problem with observed valley erosion thickness at the locations of wells （hard data）. In this study, it was assumed that the cross-section of the channel shows a parabolic shape, and the case that the vertical well and the horizontal well are located in the channel was considered. Peaceman＇s equations were modified to simultaneously solve both the vertical well problem and the horizontal well problem. In porous media, a 3D fluid equation was solved with iteration in the spatial domain, which had channels, vertical wells, and horizontal wells. As an example, the spatial distributions of pressure were calculated for channel reservoirs containing vertical and horizontal wells.展开更多
For land seismic surveys, the surface waves are the dominant noises that mask the effective signals on seismograms.The conventional methods isolate surface waves from the effective signals by the differences in freque...For land seismic surveys, the surface waves are the dominant noises that mask the effective signals on seismograms.The conventional methods isolate surface waves from the effective signals by the differences in frequencies or apparent velocities,but may not perform well when these differences are not obvious. Since the original seismic interferometry can only predict inter-receiver surface waves, we propose the use of super-virtual interferometry(SVI), which is a totally data-driven method, to predict shot-to-receiver surface waves, since this method relieves the limitation that a real shot should collocate with one of the receivers for adaptive subtraction. We further develop the adaptive weighted SVI(AWSVI) to improve the prediction of dispersive surface waves, which may be generated from heterogeneous media at the near surface. Numerical examples demonstrate the effectiveness of AWSVI to predict dispersive surface waves and its applicability to the complex near surface. The application of AWSVI on the field data from a land survey in the east of China improves the suppression of the residual surface waves compared to the conventional methods.展开更多
We develop a framework for constructing mixed multiscale finite volume methods for elliptic equations with multiple scales arising from flows in porous media.Some of the methods developed using the framework are alrea...We develop a framework for constructing mixed multiscale finite volume methods for elliptic equations with multiple scales arising from flows in porous media.Some of the methods developed using the framework are already known[20];others are new.New insight is gained for the known methods and extra flexibility is provided by the new methods.We give as an example a mixed MsFV on uniform mesh in 2-D.This method uses novel multiscale velocity basis functions that are suited for using global information,which is often needed to improve the accuracy of the multiscale simulations in the case of continuum scales with strong non-local features.The method efficiently captures the small effects on a coarse grid.We analyze the new mixed MsFV and apply it to solve two-phase flow equations in heterogeneous porous media.Numerical examples demonstrate the accuracy and efficiency of the proposed method for modeling the flows in porous media with non-separable and separable scales.展开更多
文摘Steady-state heat transfer problems in heterogeneous solid are simulated by developing an adaptive extended isogeometric analysis(XIGA)method based on locally refined non-uniforms rational B-splines(LR NURBS).In the XIGA,the LR NURBS,which have a simple local refinement algorithm and good description ability for complex geometries,are employed to represent the geometry and discretize the field variables;and some special enrichment functions are introduced into the approximation of temperature field,thus the computational mesh is independent of the material interfaces,which are described with the level setmethod.Similar to the approximation of temperature field,a temperature gradient recovery technique for heterogeneous media is proposed,and based on the Zienkiewicz–Zhu recovery technique a posteriori error estimator is defined to automatically identify the locally refined regions.The convergence and performance properties of the developed method are verified by using three numerical examples.The numerical results show that(1)The convergence speed of the adaptive local refinement is faster than that of the uniform global refinement;(2)The convergence rate of the high-order basis functions is faster than that of the low-order basis functions;and(3)The existing inclusions change the local distributions of the temperature,and the extreme values of the temperature gradients take place around the inclusion interfaces.
基金supported by the National Natural Science Foundation of China (Grant Nos. 41204097 and 41130418)the China National Major Science and Technology Project (2011ZX05023-005-004)
文摘An efficient approximate scheme is presented for wave-propagation simulation in piecewise heterogeneous media by applying the Born-series approximation to volume-scattering waves. The numerical scheme is tested for dimensionless frequency responses to a heterogeneous alluvial valley where the velocity is perturbed randomly in the range of 5 %–25 %,compared with the full-waveform numerical solution. Then,the scheme is extended to a heterogeneous multilayered model by calculating synthetic seismograms to evaluate approximation accuracies Numerical experiments indicate that the convergence rate of this method decreases gradually with increasing velocity perturbations. The method has a fast convergence for velocity perturbations less than 15 %. However,the convergence becomes slow drastically when the velocity perturbation increases to 20 %. The method can hardly converge for the velocity perturbation up to 25 %.
基金supported by the National Key R&D Program of China(No.2023YFB4104200)the National Natural Science Foundation of China(Nos.52474067,52441411,52325402,52034010,and12131014)+2 种基金the Natural Science Foundation of Shandong Province,China(No.ZR2024ME005)Fundamental Research Funds for the Central Universities(Nos.25CX02025A and 21CX06031A)the Youth Innovation and Technology Support Program for Higher Education Institutions of Shandong Province,China(No.2022KJ070)。
文摘In this study,we propose a constraint learning strategy based on interpretability analysis to improve the convergence and accuracy of the enriched physics-informed neural network(EPINN),which is applied to simulate two-phase flow in heterogeneous porous media.Specifically,we first analyze the layerwise outputs of EPINN,and identify the distinct functions across layers,including dimensionality adjustment,pointwise construction of non-equilibrium potential,extraction of high-level features,and the establishment of long-range dependencies.Then,inspired by these distinct modules,we propose a novel constraint learning strategy based on regularization approaches,which improves neural network(NN)learning through layer-specific differentiated updates to enhance cross-timestep generalization.Since different neu ral network layers exhibit varying sensitivities to global generalization and local regression,we decrease the update frequency of layers more sensitive to local learning under this constraint learning strategy.In other words,the entire neural network is encouraged to extract more generalized features.The superior performance of the proposed learning strategy is validated through evaluations on numerical examples with varying computational complexities.Post hoc analysis reveals that gradie nt propagation exhibits more pronounced staged characte ristics,and the partial differential equation(PDE)residuals are more uniformly distributed under the constraint guidance.Interpretability analysis of the adaptive constraint process suggests that maintaining a stable information compression mode facilitates progressive convergence acceleration.
基金supported by the Research and Innovation Fund for Graduate Students of Southwest Petroleum University(No.2022KYCX027)supported by the National Natural Science Foundation for Youth Grant(No.41902157).
文摘Studying immiscible fluid displacement patterns can provide a better understanding of displacement processes within heterogeneous porous media,thereby helping improving oil recovery and optimizing geological CO_(2) sequestration.As the injection rate of water displacing oil increases and the displacement pattern transits from capillary fingering to viscous fingering,there is a broad crossover zone between the two that can adversely affect the oil displacement efficiency.While previous studies have utilized phase diagrams to investigate the influence of the viscosity ratio and wettability of the crossover zone,fewer have studied the impact of rock heterogeneity.In this study,we created pore network models with varying degrees of heterogeneity to simulate water flooding at different injection rates.Our model quantifies capillary and viscous fingering characteristics while investigating porous media heterogeneity's role in the crossover zone.Analysis of simulation results reveals that a higher characteristic front flow rate within the crossover zone leads to earlier breakthrough and reduced displacement efficiency.Increased heterogeneity in the porous media raises injection-site pressure,lowers water saturation,and elevates the characteristic front flow rate,thereby expanding the extent of crossover zone.
基金supported by the National Basic Research Program of China(Grant No.2013CB228604)the National Grand Project for Science and Technology(Grant Nos.2011ZX05030-004-002,2011ZX05019-003&2011ZX05006-002)
文摘Elastic wave inverse scattering theory plays an important role in parameters estimation of heterogeneous media.Combining inverse scattering theory,perturbation theory and stationary phase approximation,we derive the P-wave seismic scattering coefficient equation in terms of fluid factor,shear modulus and density of background homogeneous media and perturbation media.With this equation as forward solver,a pre-stack seismic Bayesian inversion method is proposed to estimate the fluid factor of heterogeneous media.In this method,Cauchy distribution is utilized to the ratios of fluid factors,shear moduli and densities of perturbation media and background homogeneous media,respectively.Gaussian distribution is utilized to the likelihood function.The introduction of constraints from initial smooth models enhances the stability of the estimation of model parameters.Model test and real data example demonstrate that the proposed method is able to estimate the fluid factor of heterogeneous media from pre-stack seismic data directly and reasonably.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11971454 and 12001514)the Fundamental Research Funds for the Central Universities and the Japan Society for the Promotion of Science。
文摘This paper is devoted to studying the asymptotic behavior of the solution to nonlocal Fisher-KPP type reaction diffusion equations in heterogeneous media.The kernel K is assumed to depend on the media.First,we give an estimate of the upper and lower spreading speeds by generalized principal eigenvalues.Second,we prove the existence of spreading speeds in the case where the media is periodic or almost periodic by showing that the upper and lower generalized principal eigenvalues are equal.
基金the support of EPIC—Energy Production Innovation Center,hosted by the University of Campinas(UNICAMP)sponsored by FAPESP—Sao Paulo Research Foundation(2017/15736—3 process)+2 种基金the support and funding from Equinor Brazil and the support of ANP(Brazil's National Oil,Natural Gas and Biofuels Agency)through the R&D levy regulationthe Center of Energy and Petroleum Studies(CEPETRO)the School of Mechanical Engineering(FEM)。
文摘This study investigates the impact of pore network characteristics on fluid flow through complex and heterogeneous porous media,providing insights into the factors affecting fluid propagation in such systems.Specifically,high-resolution or micro X-ray computed tomography(CT)imaging techniques were utilized to examine outcrop stromatolite samples of the Lagoa Salgada,considered flow analogous to the Brazilian Pre-salt carbonate reservoirs.The petrophysical results comprised two distinct stromatolite depositional facies,the columnar and the fine-grained facies.By generating pore network model(PNM),the study quantified the relationship between key features of the porous system,including pore and throat radius,throat length,coordination number,shape factor,and pore volume.The study found that the less dense pore network of the columnar sample is typically characterized by larger pores and wider and longer throats but with a weaker connection of throats to pores.Both facies exhibited less variability in the radius of the pores and throats in comparison to throat length.Additionally,a series of core flooding experiments coupled with medical CT scanning was designed and conducted in the plug samples to assess flow propagation and saturation fields.The study revealed that the heterogeneity and presence of disconnected or dead-end pores significantly impacted the flow patterns and saturation.Two-phase flow patterns and oil saturation distribution reveal a preferential and heterogeneous displacement that mainly swept displaced fluid in some regions of plugs and bypassed it in others.The relation between saturation profiles,porosity profiles,and the number of fluid flow patterns for the samples was evident.Only for the columnar plug sample was the enhancement in recovery factor after shifting to lower salinity water injection(SB)observed.
基金National Natural Science Foundation of China under Grant No.U2039209the National Key R&D Program of China under Grant No.2022YFC3004303+1 种基金the Heilongjiang Natural Science Foundation for Distinguished Young Scholars under Grant No.JQ2022E006Heilongjiang Natural Science Foundation Joint Guidance Project under Grant No.LH2021E122。
文摘The accurate simulation of wave propagation in real media requires properly taking the attenuation into account,which leads to wave dissipation together with its causal companion,wave dispersion.In this study,to obtain a weak formulation of heterogenous viscoacoustic wave propagation in an infinite domain,the viscoacoustic medium is first characterized by its frequency-dependent complex bulk compliance instead of the classically used complex bulk modulus.Then,a mechanical model using serially connected standard linear solids(SSLS)is built to obtain the rational approximation of the complex bulk compliance whose parameters are calculated via an adapted nonlinear optimization method.Utilizing the obtained bulk compliance-based constitutive relation,a novel second-order viscoacoustic wave equation in the frequency domain is derived,of which the weak formulation can be physically explained as the virtual work equation and can thus be discretized using a continuous spectral element method in space.Additionally,a new method is introduced to address the convolution terms involved in the inverse Fourier transform,whose accurate time integration can then be achieved using an explicit time scheme,which avoids the transient growth that exists in the classical method.The resulting full time-space decoupling scheme can handle wave propagation in arbitrary heterogeneous media.Moreover,to treat the wave propagation in an infinite domain,a perfectly matched layer in weak formulation is derived for the truncation of the infinite domain via complex coordinate stretching of the virtual work equation.With only minor modification,the resulting perfectly matched layer can be implemented using the same time scheme as for the wave equation inside the truncated domain.The accuracy,numerical stability,and versatility of the new proposed scheme are demonstrated with numerical examples.
文摘This study presents a numerical solution to the three-dimensional solute transport in heterogeneous media by using a layer-integrated approach.Omitting vertical spatial variation of soil and hydraulic properties within each layer,a threedimensional solute transport can be simplified as a quasi-three-dimensional solute transport which couples a horizontal two-dimensional simulation and a vertical onedimensional computation.The finite analytic numericalmethod was used to discretize the derived two-dimensional governing equation.A quadratic function was used to approximate the vertical one-dimensional concentration distribution in the layer to ensure the continuity of concentration and flux at the interface between the adjacent layers.By integration over each layer,a set of system of equations can be generated for a single column of vertical cells and solved numerically to give the vertical solute concentration profile.The solute concentration field was then obtained by solving all columns of vertical cells to achieve convergence with the iterative solution procedure.The proposed model was verified through examples from the published literatures including four verifications in terms of analytical and experimental cases.Comparison of simulation results indicates that the proposed model satisfies the solute concentration profiles obtained from experiments in time and space.
文摘We review some of our recent efforts in developing upscaling methods for simulating the flow transport through heterogeneous porous media. In particular, the steady flow transport through highly heterogeneous porous media driven by extraction wells and the flow transport through unsaturated porous media will be considered.
文摘The dispersion process in heterogeneous porous media is distance-dependent, which results from multi-scaling property of heterogeneous structure. An analytical model describing the dispersion with an exponential dispersion function is built, which is transformed into ODE problem with variable coefficients, and obtained analytical solution for two type boundary conditions using hypergeometric function and inversion technique. According to the analytical solution and computing results the difference between the exponential dispersion and constant dispersion process is analyzed
文摘We describe an operator splitting technique based on physics rather than on dimension for the numerical solution of a nonlinear system of partial differential equations which models three-phase flow through heterogeneous porous media.The model for three-phase flow considered in this work takes into account capillary forces,general relations for the relative permeability functions and variable porosity and permeability fields.In our numerical procedure a high resolution,nonoscillatory,second order,conservative central difference scheme is used for the approximation of the nonlinear system of hyperbolic conservation laws modeling the convective transport of the fluid phases.This scheme is combined with locally conservative mixed finite elements for the numerical solution of the parabolic and elliptic problems associated with the diffusive transport of fluid phases and the pressure-velocity problem.This numerical procedure has been used to investigate the existence and stability of nonclassical shock waves(called transitional or undercompressive shock waves)in two-dimensional heterogeneous flows,thereby extending previous results for one-dimensional flow problems.Numerical experiments indicate that the operator splitting technique discussed here leads to computational efficiency and accurate numerical results.
文摘In this paper, we propose a tailored finite cell method for the computation of two- dimensional Helmholtz equation in layered heterogeneous medium. The idea underlying the method is to construct a numerical scheme based on a local approximation of the solution to Helmholtz equation. This provides a computational tool of achieving high accuracy with coarse mesh even for large wave number （high frequency）. The stability analysis and error estimates of this method are also proved. We present several numerical results to show its efficiency and accuracy.
文摘We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling.This poroelasticity problem suffers from rapidly oscillating material parameters,which calls for a thorough numerical treatment.In this paper,we propose a method based on the local orthogonal decomposition technique and motivated by a similar approach used for linear thermoelasticity.Therein,local corrector problems are constructed in line with the static equations,whereas we propose to consider the full system.This allows to benefit from the given saddle point structure and results in two decoupled corrector problems for the displacement and the pressure.We prove the optimal first-order convergence of this method and verify the result by numerical experiments.
基金Project supported by the Scientific Research Common Program of Beijing Municipal Commission of Education (Grant No: KM200510015003)
文摘In this article, the bounding surfaces of channels were modeled by Bayesian stochastic simulation, which is a boundary-valued problem with observed valley erosion thickness at the locations of wells （hard data）. In this study, it was assumed that the cross-section of the channel shows a parabolic shape, and the case that the vertical well and the horizontal well are located in the channel was considered. Peaceman＇s equations were modified to simultaneously solve both the vertical well problem and the horizontal well problem. In porous media, a 3D fluid equation was solved with iteration in the spatial domain, which had channels, vertical wells, and horizontal wells. As an example, the spatial distributions of pressure were calculated for channel reservoirs containing vertical and horizontal wells.
基金supported by the National Basic Research Program of China (Grant No. 2013CB228602)the National Science and Technology Major Project of China (Grant No. 2016ZX05004003-002)the National High Technology Research and Development Program of China (Grant No. 2013AA064202)
文摘For land seismic surveys, the surface waves are the dominant noises that mask the effective signals on seismograms.The conventional methods isolate surface waves from the effective signals by the differences in frequencies or apparent velocities,but may not perform well when these differences are not obvious. Since the original seismic interferometry can only predict inter-receiver surface waves, we propose the use of super-virtual interferometry(SVI), which is a totally data-driven method, to predict shot-to-receiver surface waves, since this method relieves the limitation that a real shot should collocate with one of the receivers for adaptive subtraction. We further develop the adaptive weighted SVI(AWSVI) to improve the prediction of dispersive surface waves, which may be generated from heterogeneous media at the near surface. Numerical examples demonstrate the effectiveness of AWSVI to predict dispersive surface waves and its applicability to the complex near surface. The application of AWSVI on the field data from a land survey in the east of China improves the suppression of the residual surface waves compared to the conventional methods.
文摘We develop a framework for constructing mixed multiscale finite volume methods for elliptic equations with multiple scales arising from flows in porous media.Some of the methods developed using the framework are already known[20];others are new.New insight is gained for the known methods and extra flexibility is provided by the new methods.We give as an example a mixed MsFV on uniform mesh in 2-D.This method uses novel multiscale velocity basis functions that are suited for using global information,which is often needed to improve the accuracy of the multiscale simulations in the case of continuum scales with strong non-local features.The method efficiently captures the small effects on a coarse grid.We analyze the new mixed MsFV and apply it to solve two-phase flow equations in heterogeneous porous media.Numerical examples demonstrate the accuracy and efficiency of the proposed method for modeling the flows in porous media with non-separable and separable scales.
