Coupling geological and numerical models to simulate groundwater flow and contaminant transport in fractured media

A new modeling approach is presented to improve numerical simulations of groundwater flow and contaminant transport in fractured geological media. The approach couples geological and numerical models through an intermediate mesh generation phase. As a first step, a platform for 3D geological modeling is used to represent fractures as 2D surfaces with arbitrary shape and orientation in 3D space. The advantage of the geological modeling platform is that 2D triangulated fracture surfaces are modeled and visualized before building a 3D mesh. The triangulated fractures are then transferred to the mesh generation software that discretizes the 3D simulation domain with tetrahedral elements. The 2D triangular fracture elements do not cut through the 3D tetrahedral elements, but they rather form interfaces with them. The tetrahedral mesh is then used for 3D groundwater flow and contaminant transport simulations in discretely fractured porous media. The resulting mesh for the 2D fractures and 3D rock matrix is checked to ensure that there are no negative transmissibilities in the discretized flow and transport equation, to avoid unrealistic results. To test the validity of the approach, flow and transport simulations for a tetrahedral mesh are compared to simulations using a block-based mesh and with results of an analytical solution. The fluid conductance matrix for the tetrahedral mesh is also analyzed and compared with known matrix values.     

A numerical study on the fluid compressibility effects in strongly coupled fluid–solid interaction problems

Interactions between an incompressible fluid passing through a flexible tube and the elastic wall is one of the strongly coupled fluid–solid interaction (FSI) problems frequently studied in the literature due to its research importance and wide range of applications. Although incompressible fluid is a prevalent model in many simulation studies, the assumption of incompressibility may not be appropriate in strongly coupled FSI problems. This paper narrowly aims to study the effect of the fluid compressibility on the wave propagation and fluid–solid interactions in a flexible tube. A partitioned FSI solver is used which employs a finite volume-based fluid solver. For the sake of comparison, both traditional incompressible (ico) and weakly compressible (wco) fluid models are used in an Arbitrary Lagrangian–Eulerian (ALE) formulation and a PISO-like algorithm is used to solve the unsteady flow equations on a collocated mesh. The solid part is modeled as a simple hyperelastic material obeying the St-Venant constitutive relation. Computational results show that not only use of the weakly compressible fluid model makes the FSI solver in this case more efficient, but also the incompressible fluid model may produce largely unrealistic computational results. Therefore, the use of the weakly compressible fluid model is suggested for strongly coupled FSI problems involving seemingly incompressible fluids such as water especially in cases where wave propagation in the solid plays an important role.

     

Numerical Modeling of Degenerate Equations in Porous Media Flow

In this paper is introduced a new numerical formulation for solving degenerate nonlinear coupled convection dominated parabolic systems in problems of flow and transport in porous media by means of a mixed finite element and an operator splitting technique, which, in turn, is capable of simulating the flow of a distinct number of fluid phases in different porous media regions. This situation naturally occurs in practical applications, such as those in petroleum reservoir engineering and groundwater transport. To illustrate the modelling problem at hand, we consider a nonlinear three-phase porous media flow model in one- and two-space dimensions, which may lead to the existence of a simultaneous one-, two- and three-phase flow regions and therefore to a degenerate convection dominated parabolic system. Our numerical formulation can also be extended for the case of three space dimensions. As a consequence of the standard mixed finite element approach for this flow problem the resulting linear algebraic system is singular. By using an operator splitting combined with mixed finite element, and a decomposition of the domain into different flow regions, compatibility conditions are obtained to bypass the degeneracy in order to the degenerate convection dominated parabolic system of equations be numerically tractable without any mathematical trick to remove the singularity, i.e., no use of a parabolic regularization. Thus, by using this procedure, we were able to write the full nonlinear system in an appropriate way in order to obtain a nonsingular system for its numerical solution. The robustness of the proposed method is verified through a large set of high-resolution numerical experiments of nonlinear transport flow problems with degenerating diffusion conditions and by means of a numerical convergence study.     

A high-resolution method for the depth-integrated solute transport equation based on an unstructured mesh

This paper presents a high-resolution numerical method for solving mass transport problems involving advection and anisotropic diffusion in shallow water based on unstructured mesh. An alternating operator-splitting technique is adopted to advance the numerical solution with advection and diffusion terms solved separately in two steps. By introducing a new r-factor into the Total Variation Diminishing (TVD) limiter, an improved finite-volume method is developed to solve the advection term with significant reduction of numerical diffusion and oscillation errors. In addition, a coordinate transformation is introduced to simplify the diffusion term with the Green-Gauss theorem used to deal with the anisotropic effect based on unstructured mesh. The new scheme is validated against three benchmark cases with separated and combined advection and diffusion transport processes involved. Results show that the scheme performs better than existing methods in predicting the advective transport, particularly when a sharp concentration front is in presence. The model also provides a sound solution for the anisotropic diffusion phenomenon. Anisotropic diffusion has been largely neglected by existing flow models based on unstructured mesh, which usually treat the diffusion process as being isotropic for simplicity. Based on the flow field provided by the ELCIRC model, the developed transport model was successfully applied to simulate the transport of a hypothetical conservative tracer in a bay under the influence of tides.     

A coupled discrete-continuum approach to simulate moisture effects on damage processes in porous materials

In the present paper, a coupled model for the prediction of damage under hygro-mechanical loading is developed. The model combines a mechanical and a moisture transport model within a poromechanical framework. Damage is incorporated by embedded displacement discontinuities, allowing an accurate prediction of the crack path within a coarse finite element mesh. To simulate the preferential wetting around a crack, a discrete front tracking method to predict the fluid transport through cracks is incorporated in a continuous moisture transport model. The computational features and capabilities of the coupled model and the effects of moisture on dimensional stability, crack opening evolution and cracking behaviour are illustrated with different examples of combined mechanical and moisture loading during three point bending tests on a fictitious sandstone.     

多介质拉氏自适应流体动力学软件LAD2D研制及其应用

拉氏方法是内爆动力学过程数值模拟的主要方法.针对高温、高压、多介质和大变形等内爆问题,采用非结构任意多边形网格底层管理、计算过程中网格邻域可变技术,以及拉氏自适应网格加密方法和层次化、模块化程序设计思想,自主研发非结构拉氏自适应网格流体动力学软件LAD2D.从物理模型、计算方法、程序设计、程序验证与确认、大变形问题数值模拟等方面系统地介绍LAD2D.LAD2D对多介质爆轰弹塑性流体大变形问题有很强的适应能力.     

A full-Eulerian solid level set method for simulation of fluid–structure interactions

We present a full Eulerian method, termed solid level set (SLS) method, for modeling of a class of fluid–structure interactions (FSI) problems soft solid body can deform significantly but remains nearly incompressible. The SLS method is based on the unified momentum equation framework in which the solid–fluid interactions are modeled by introducing a solid body force term and a solid–fluid interfacial force term into the Navier–Stokes equation. The key idea of the SLS method is that the deformation of the solid body is no longer tracked using a Lagrangian mesh. Instead, the solid body is tracked by introducing a reference coordinate for describing the reference state of the solid body and by introducing three dynamic level set functions on the Cartesian coordinate and one static level set functions on the reference coordinate. The SLS method is easy to implement and addresses several challenges in the simulation of FSIs in which a fixed Cartesian mesh is used for fluid flow and a Lagrangian mesh is used for tracking the solid deformation. The effectiveness of the SLS method is demonstrated by studying two FSI problems. The method is suitable for studying a wide range of problems in microfluidics, e.g., manipulation of cells in confined space and ink-jet printing of biological samples.     

Scaling law for cross-stream diffusion in microchannels under combined electroosmotic and pressure driven flow

This paper presents an analytical study of the cross-stream diffusion of an analyte in a rectangular microchannel under combined electroosmotic flow (EOF) and pressure driven flow to investigate the heterogeneous transport behavior and spatially dependent diffusion scaling law. An analytical model capable of accurately describing 3D steady-state convection–diffusion in microchannels with arbitrary aspect ratios is developed based on the assumption of the thin electric double layer. The model is verified against high-fidelity numerical simulation in terms of flow velocity and analyte concentration profiles with excellent agreement (<0.5 % relative error). An extensive parametric analysis is then undertaken to interrogate the effect of the combined flow velocity field on the transport behavior in both the positive pressure gradient (PPG) and negative pressure gradient cases. For the first time, the evolution from the spindle-shaped concentration profile in the PPG case, via the stripe-shaped profile (pure EOF), and finally to the butterfly shaped profile in the PPG case is obtained using the analytical model along with a quantitative depiction of the spatially dependent diffusion layer thickness and scaling law across a wide range of the parameter space.     

A coupled flow and transport model for simulation of groundwater reservoirs

As in many cases the quality of water, rather than the available amount restricts water use, a management of groundwater reservoirs has to include the investigation of the transport of dissolved solids in many cases. A special problem of coastal aquifers is a density dependent groundwater flow, caused by different saltwater concentration. For the efficient simulation of aquifer reaction a model is described, which permits the simultaneous computation of groundwater flow and mass transport.     

Numerical simulations of particle migration in a viscoelastic fluid subjected to shear flow

Particle migration is a relevant transport mechanism whenever suspensions flow in channels with gap size comparable to particle dimensions (e.g. microfluidic devices). Several theoretical as well as experimental studies have been performed on this topic, showing that the occurring of this phenomenon and the migration direction are related to particle size, flow rate, and the nature of the suspending liquid.In this work we perform a systematic analysis on the migration of a single particle in a sheared viscoelastic fluid through 2D finite element simulations in a Couette planar geometry. To focus on the effects of viscoelasticity alone, inertia is neglected. The suspending medium is modeled as a Giesekus fluid.An ALE particle mover is combined with a DEVSS/SUPG formulation with a log-representation of the conformation tensor giving stable and convergent results up to high flow rates. To optimize the computational effort and reduce the remeshing and projection steps, needed as soon as the mesh becomes too distorted, a ‘backprojection’ of the flow fields is performed, through which the particle in fact moves along the cross-streamline direction only, and the mesh distortion is hence drastically reduced.Our results, in agreement with recent experimental data, show a migration towards the closest walls, regardless of the fluid and geometrical parameters. The phenomenon is enhanced by the fluid elasticity, the shear thinning and strong confinements. The migration velocity trends show the existence of a master curve governing the particle dynamics in the whole channel. Three different regimes experienced by the particle are recognized, related to the particle-wall distance. The existence of a unique migration behavior and its qualitative aspects do not change by varying the fluid parameters or the particle size.     

A finite difference real ghost fluid method on moving meshes with corner-transport upwind interpolation

The real ghost fluid method (RGFM) [Wang CW, Liu TG, Khoo BC. A real-ghost fluid method for the simulation of multi-medium compressible flow. SIAM J Sci Comput 2006;28:278–302] has been shown to be more robust than previous versions of GFM for simulating multi-medium flow problems with large density and pressure jumps. In this paper, a finite difference RGFM is combined with adaptive moving meshes for one- and two-dimensional problems. A high resolution corner-transport upwind (CTU) method is used to interpolate approximate solutions from old quadrilateral meshes to new ones. Unlike the dimensional splitting interpolation, the CTU method takes into account the transport across corner points, which is physically more sensible. Several one- and two-dimensional examples with large density and pressure jumps are computed. The results show the present moving mesh method can effectively reduce the conservative errors produced by GFM and can increase the computational efficiency.     

Computation of flow problems with the Mixed Interface-Tracking/Interface-Capturing Technique (MITICT)

In computation of flow problems with fluid-solid interfaces, an interface-tracking technique, where the fluid mesh moves to track the interface, would allow us to have full control of the resolution of the fluid mesh in the boundary layers. With an interface-capturing technique (or an interface locator technique in the more general case), on the other hand, independent of how accurately the interface geometry is represented, the resolution of the fluid mesh in the boundary layer will be limited by the resolution of the fluid mesh at the interface. In computation of flow problems with fluid-fluid interfaces where the interface is too complex or unsteady to track while keeping the remeshing frequency under control, interface-capturing techniques, with enhanced-discretization as needed, could be used as more flexible alternatives. Sometimes we may need to solve flow problems with both fluid-solid interfaces and complex or unsteady fluid-fluid interfaces. The Mixed Interface-Tracking/Interface-Capturing Technique (MITICT) was introduced for computation of flow problems that involve both interfaces that can be accurately tracked with a moving mesh method and interfaces that are too complex or unsteady to be tracked and therefore require an interface-capturing technique. As the interface-tracking technique, we use the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation. The interface-capturing technique rides on this, and is based on solving over a moving mesh, in addition to the Navier-Stokes equations, the advection equation governing the time-evolution of the interface function. For the computations reported in this paper, as interface-capturing technique we are using one of the versions of the Edge-Tracked Interface Locator Technique (ETILT).     

Cellular automata simulation of saltwater intrusion in coastal aquifer

The wasteful consumption of freshwater in heavily populated coastal areas usually consist the basic reason for the intrusion of saltwater into the coastal aquifers. In order to avoid such catastrophic scenarios, their prediction is of utter significance. Underground water systems are highly complex and the water flow is extremely dynamic, thus making the prediction of this phenomenon a difficult task. For this reason, a two dimensional Cellular Automaton (CA) was designed enabling both the qualitative and quantitative simulation and illustration of the saltwater intrusion into an unconfined coastal aquifer. The presented results ensure the robustness of the proposed CA model taking full advantage of its inherent parallelism and local connectivity.     

Multiple stream superposition of a two-stream combined analytical numerical initial value problem solver for aerodynamic mixing

In spite of the rapid advances in both scalar and parallel computational flow simulation tools, the large number and breadth of variables involved in both design and inverse problems make the use of complex fluid flow models impractical. With this restriction, it may be concluded that an important family of methods for mathematical/computational development are reduced or approximate models. An approximate model for two stream mix problems utilizing a combined perturbation/numerical modelling methodology has been developed [1]. The numerical portion of the model uses a compact finite difference scheme, while analytical solutions are used to resolve singular behavior that is inherent to this flow. Approximate representation of the flow in terms of flux variables yields a linear transport operator, thus facilitating the additive decomposition of the solution into numerical and analytical portions. Additionally, linearity permits superposition of the basic two-stream initial value problem to construct multiple stream mixing problems. Multiple stream results are presented to illustrate the efficiency of this methodology.     

A comprehensive modeling environment for the simulation of groundwater flow and transport

A comprehensive graphical modeling environment has been developed to address the needs of the computer simulation of groundwater flow and transport. The Department of Defense Groundwater Modeling Systems (GMS), developed at the Engineering Computer Graphics Laboratory at Brigham Young University, is part of a multi-year project funded through the Department of Defense, Department of Energy and Environmental Protection Agency. GMS is a graphically based software tool providing facility through all aspects of the groundwater flow and transport modeling process. Facilities include geometric modeling of hydrostratigraphy, two- and three-dimensional mesh generation, graphically based model input for specific flow and transport codes, interpolation and geostatistics as well as complete three-dimensional scientific visualization.     

Modelling the effects of reservoir construction on tidal hydrodynamics and suspended sediment distribution in Danshuei River estuary

A vertical (laterally integrated) two-dimensional numerical model was implemented to study the hydrodynamics, saltwater intrusion, and suspended sediment in the Danshuei River–Tahan Stream due to the Shihmen Reservoir construction in the upriver reaches. The construction of the reservoir and water diversion in the upper reaches of the river system significantly reduces the freshwater inflow and drastically changes the river bathymetry. The model was calibrated and verified with the available hydrographic data measured in 1977, 1978, and 1999 as well as measured salinity and suspended sediment concentration in 1999. The overall performance of the model is in reasonable agreement with the field data. The validated model was then used to investigate the change in hydrodynamics, saltwater intrusion, suspended sediment distribution, and flushing time as a result of reservoir construction in upper river of Tahan Stream. The model simulations indicate that more tidal energy propagates into the estuarine system after reservoir construction because of the substantial increase in river cross-sections. The limits of saltwater intrusion after reservoir construction extended farther inland 2–3 km than those after reservoir construction. The modelling results also reveal that the suspended sediment concentration before reservoir construction was higher than that after reservoir construction along the river mouth to Kuan-Du due to the significant bathymetric change after the reservoir construction. The calculated estuary flushing time was strongly dependent on river flow and reduced 2.3–25 h under different river discharges after reservoir construction due to the change in river bathymetry.     

Multi-level adaptive simulation of transient two-phase flow in heterogeneous porous media

An implicit pressure and explicit saturation (IMPES) finite element method (FEM) incorporating a multi-level shock-type adaptive refinement technique is presented and applied to investigate transient two-phase flow in porous media. Local adaptive mesh refinement is implemented seamlessly with state-of-the-art artificial diffusion stabilization allowing simulations that achieve both high resolution and high accuracy. Two benchmark problems, modelling a single crack and a random porous medium, are used to demonstrate the robustness of the method and illustrate the capabilities of the adaptive refinement technique in resolving the saturation field and the complex interaction (transport phenomena) between two fluids in heterogeneous media.     

Numerical modeling of heat exchange and unsaturated–saturated flow in porous media

We discuss the numerical modeling of heat and mass transport in unsaturated–saturated porous media. The heat is transported by infiltrated water underlying capillary and gravitation driven forces. Heat energy is governed by molecular diffusion, convection, dispersion and exchange between the infiltrated water and porous media matrix. An unsaturated–saturated flow is considered with boundary conditions reflecting the external driven forces. The presented mathematical model is motivated by analysis of hygrothermal isolation properties of facades. The main contribution is focused on the determination of model parameters including soil parameters, dispersion coefficients, thermal transmission coefficient, thermal conductivity of porous media matrix and external transmission coefficients. The used mathematical model does not include the vapor transport and its phase exchange with water due to vaporization and condensation. It will be the next step of our research. Thus, practical applications of our model are limited. The developed numerical method is a good candidate for solving corresponding inverse problems. Numerical experiments support our method.     

珠三角地区咸潮入侵预警预报信息系统的总体设计

珠江口由于淡水径流量小、河口较宽,潮水比较容易进入,每年都会发生不同程度的咸潮现象,咸潮对珠三角城市群构成整体威胁。本文提出预警预报系统设计思想,旨在从计算机软件层面通过预警系统加以模拟实现咸潮发生、发展的整个侵入过程,从而更加科学合理地制定珠三角咸潮的应对措施,为咸潮入侵应急预案提供决策依据。     

High-Order Accurate Adaptive Kernel Compression Time-Stepping Schemes for Fractional Differential Equations

We present a goal-oriented a posteriori error estimator for finite element approximations of a class of homogenization problems. As a rule, homogenization problems are defined through the coupling of a macroscopic solution and the solution of auxiliary problems. In this work we assume that the homogenized problem is known and that it depends on a finite number of auxiliary problems. The accuracy in the goal functional depends therefore on the discretization error of the macroscopic and the auxiliary solutions. We show that it is possible to compute the error contributions of all solution components separately and use this information to balance the different discretization errors. Additionally, we steer a local mesh refinement for both the macroscopic problem and the auxiliary problems. The high efficiency of this approach is shown by numerical examples. These include the upscaling of a periodic diffusion tensor, the case of a Stokes flow over a porous bed, and the homogenization of a fuel cell model which includes the flow in a gas channel over a porous substrate coupled with a multispecies nonlinear transport equation.