Mass Conservation Analysis For The Lower St. Johns River Using Continuous And Discontinuous Galerkin Finite Element Methods

This thesis provides a mass conservation analysis of the Lower St. Johns River for the purpose of providing basis for future salinity transport modeling. The analysis provides an assessment of the continuous (CG) and discontinuous (DG) Galerkin finite element methods with respect to their mass conservation properties. The following thesis also presents a rigorous literature review pertaining to salinity transport in the Lower St. Johns River, from which this effort generates the data used to initialize and validate numerical simulations. Two research questions are posed and studied in this thesis: can a DG-based modeling approach produce mass conservative numerical solutions; and what are the flow interactions between the river and the marshes within the coastal region of the Lower St. Johns River? Reviewing the available data provides an initial perspective of the ecosystem. For this, salinity data are obtained and assembled for three modeling scenarios. Each scenario, High Extreme, Most Variable, and Low Extreme, is 30 days long (taken from year 1999) and represents a unique salinity regime in the Lower St. Johns River. Time-series of salinity data is collected at four stations in the lower and middle reaches of the Lower St. Johns River, which provides a vantage point for assessing longitudinal variation of salinity. As an aside, precipitation and evaporation data is presented for seven stations along the entire St. Johns River, which provides added insight into salinity transport in the river. A mass conservation analysis is conducted for the Lower St. Johns River. The analysis utilizes a segmentation of the Lower St. Johns River, which divides the domain into sections iv based on physical characteristics. Mass errors are then calculated for the CG and DG finite element methods to determine mass conservative abilities. Also, the flow interactions (i.e., volume exchange) between the river and marshes are evaluated through the use of tidal prisms. The CG- and DG- finite element methods are then tested in tidal simulation performance, which the results are then compared to observed tides and tidal currents at four stations within the lower portion of the Lower St. Johns River. Since the results show that the DG model outperforms the CG model, the DG model is used in the tidally driven salinity transport simulations. Using four stations within the lower and middle part of the Lower St. Johns River, simulated and observed water levels and salinity concentrations are compared

Thetis coastal ocean model: discontinuous Galerkin discretization for the three-dimensional hydrostatic equations

Unstructured grid ocean models are advantageous for simulating the coastal ocean and river–estuary–plume systems. However, unstructured grid models tend to be diffusive and/or computationally expensive, which limits their applicability to real-life problems. In this paper, we describe a novel discontinuous Galerkin (DG) finite element discretization for the hydrostatic equations. The formulation is fully conservative and second-order accurate in space and time. Monotonicity of the advection scheme is ensured by using a strong stability-preserving time integration method and slope limiters. Compared to previous DG models, advantages include a more accurate mode splitting method, revised viscosity formulation, and new second-order time integration scheme. We demonstrate that the model is capable of simulating baroclinic flows in the eddying regime with a suite of test cases. Numerical dissipation is well-controlled, being comparable or lower than in existing state-of-the-art structured grid models.</p

Numerical modeling of multiphase flow and phase separation phenomena in the system H2O−NaCl with applications to magmatic hydrothermal systems at fast-spreading mid-ocean ridges

At mid-ocean ridges, the inner workings of hydrothermal systems are difficult to access directly and have to be investigated indirectly through geophysical measurements, petrological studies of disclosed oceanic crust brought to the surface, or geochemical analysis of venting hydrothermal fluids. Numerical models have become a beneficial tool to study hydrothermal fluid dynamics and allow researchers to better synthesize and understand observations and interpretations obtained by other scientific disciplines. At fast-spreading ridges, hydrothermal fluids are heated by shallow magmatism separating the fluids into a high-salinity liquid and a low-salinity vapor phase. In the first application of a self-developed hydrothermal simulator, I investigate the brine formation and mobilization in hydrothermal systems driven by a transient basal temperature boundary condition, which represents the axial magma lens. It was found that basal heating results in rapid phase segregation and the formation of a stable brine layer that thermally insulates the driving heat source of flow circulation. While this brine layer is stable under steady-state conditions, a reduction of the heat input mobilizes the brines. The second application studies dike intrusions for conditions found at the East Pacific Rise (EPR). At EPR 9°50.3’N, vent fluid salinity and temperature at individual vents in the axial summit trough have been repeatedly measured over a 25+ year-long period. After the 1991/92 diking event it was observed that low salinities are followed by higher salinities after a few years. The simulation analysis includes brine accumulation close to the dike as well as two-phase flow and the delayed brine upflow when the dike has cooled. In a comprehensive suite of model runs, I have identified key parameters, which control the vent salinity evolution, These are rock permeability and porosity plus the background fluid temperature and salinity

Saltwater intrusion simulation in heterogeneous aquifer using lattice Boltzmann method

This study develops a saltwater intrusion simulation model using a lattice Boltzmann method (LBM) in a two-dimensional coastal confined aquifer. The saltwater intrusion is described by density-dependent groundwater flow and mass transport equations, where a freshwater-saltwater mixing zone is considered. The problem is formulated in terms of hydraulic head instead of pressure, which is recommended in those cases where static pressures dominate to reduce computational cost. The aquifer heterogeneity is explicitly a function of the speed of sound, relaxation parameter and time steps in the LBM. This study explores the equivalent squared sound speed to deal with the spatial-temporal heterogeneity arising from the inhomogeneous hydraulic conductivity and fluid density to update the equilibrium distribution functions in each time step. The Henry problem and its variants are used to demonstrate the LBM applicability to solve the saltwater intrusion problem. The inverse relationship between the time step and diffusion coefficient results in a very small time step for the groundwater flow problem due to the high hydraulic diffusion coefficient. The study demonstrates the ease of implementing the LBM to different salt concentration boundary conditions at the seaside and shows that the isochlors distributions are significantly different. Due to doubts regarding the validity of the Henry problem to test variable-density flows, numerical simulation of freshwater injection into a sediment saturated with saltwater have been carried out, showing the capability of the LBM to represent strong buoyancy effects. Some examples with correlated and uncorrelated random hydraulic conductivity (K) distributions show reasonable flow fields and isochlors distributions. It was found in the Henry problem that completely random heterogeneity in K is insignificant in changing the scale of the saltwater intrusion from that predicted using the mean K value. However, the correlated K field may have significant impact on the saltwater intrusion, resulting different from that obtained by the mean K field

Numerical modeling of flow and solute transport phenomena in subsurface and coupled surface-subsurface hydrology

The overall aim of the work described in this thesis is to bring a number of contributions to hydrology and hydrological modeling in the framework of a specific physically-based numerical model for integrated surface subsurface and flow-transport processes, the CATchment-HYdrology Flow-Transport (CATHY_FT) model. These contributions revolve around three main themes: the enhancement of the numerical performance of hydrological models for flow and transport phenomena, the improvement of our current understanding of complex boundary conditions in order to reduce the errors associated with their modeling, and the testing and benchmarking of distributed physically-based models for groundwater flow and transport processes. The work to achieve the general objective is elaborated into four stages. First, the Larson-Niklasson post-processing algorithm is implemented in CATHY_FT to reconstruct mass-conservative velocities from a linear, or P1, Galerkin solution of Richards' equation. This is done to improve the accuracy and mass balance properties of the companion advective transport model (finite volume-based), which rely on accurate velocity fields as input. Through a comparison between the results from the reconstructed velocities and the P1 Galerkin velocities, it is shown that a locally mass-conservative velocity field is necessary to obtain accurate transport results. Second, a detailed and novel analysis of the behavior of seepage face boundaries is performed with the flow model of CATHY_FT. The numerical simulations examine the model's performance under complex conditions such as heterogeneity and coupled surface/subsurface flow. It is shown that the overall numerical solution can be greatly affected by the way seepage face boundaries are handled in hydrological models and that careful considerations are required when using simple approximations, in the presence of heterogeneous slopes, and for seepage faces forming on a portion of the land surface. Third, CATHY_FT is implemented and run at the Landscape Evolution Observatory of the Biosphere 2 facility, Arizona. A detailed modeling analysis is performed of the experimental data collected during an isotope tracer experiment and from an intensively-measured hillslope, including quantity and quality of groundwater discharge and point-scale flow and transport data. This flow and tracer data is used to incrementally explore complex phenomena and associated hypotheses (e.g., heterogeneity, fractionation, and dispersion), progressing from flow to transport and from integrated to point-scale response analysis. This incremental approach highlights the challenges in testing and validating the new generation of integrated hydrological models when considering many types and levels of observation data. Finally, a concluding analysis is performed that relates to all three themes of the thesis, describing some of the features of the CATHY_FT model, discussing key issues associated to its further development, and testing its physical and numerical behavior for both real and synthetic scenarios. This final stage of the thesis addresses the myriad challenges faced in accurately and efficiently resolving the difficult behavior of the advection-dispersion equation for subsurface solute transport, in properly handling the complex boundary conditions for solute interactions across the land surface, and generally in capturing process interactions and feedbacks between flow and transport phenomena in surface and subsurface environments

Multiphase Thermohaline Convection in the Earth's Crust: I. A New Finite Element - Finite Volume Solution Technique Combined With a New Equation of State for NaCl-H2O

We present a new finite element - finite volume (FEFV) method combined with a realistic equation of state for NaCl-H2O to model fluid convection driven by temperature and salinity gradients. This method can deal with the nonlinear variations in fluid properties, separation of a saline fluid into a high-density, high-salinity brine phase and low-density, low-salinity vapor phase well above the critical point of pure H2O, and geometrically complex geological structures. Similar to the well-known implicit pressure explicit saturation formulation, this approach decouples the governing equations. We formulate a fluid pressure equation that is solved using an implicit finite element method. We derive the fluid velocities from the updated pressure field and employ them in a higher-order, mass conserving finite volume formulation to solve hyperbolic parts of the conservation laws. The parabolic parts are solved by finite element methods. This FEFV method provides for geometric flexibility and numerical efficiency. The equation of state for NaCl-H2O is valid from 0 to 750°C, 0 to 4000bar, and 0-100 wt.% NaCl. This allows the simulation of thermohaline convection in high-temperature and high-pressure environments, such as continental or oceanic hydrothermal systems where phase separation is commo

Lattice Boltzmann modeling for mass transport equations in porous media

The aim of this dissertation is to extend the lattice Boltzmann method (LBM) to cope with parameter heterogeneity and anisotropy in mass transport equations in porous media, as well as investigating the stability and accuracy. Although the LBM is a well known and effective numerical method to solve fluid flows, LBM has not been extensively applied to mass transport equations in porous medium flow yet, and only a few works can be found on improving LBM to cope with mass transport equations other than the diffusion and advection-diffusion equations. One of the reasons why LBM has not been extensively used is because it is not clearly understood how LBM solve mass transport equations. We first focus on investigating what type of partial differential equation (PDE) the LBM recovers. The recovery procedure is carried out in detail up to third order accuracy and including the effect of forcing terms. Once the recovered PDE is known, LBM can be tailored to solve targeted mass transport equations. In order to improve the accuracy of LBM, the analysis is based on the lattice Boltzmann equation with a two-relaxation-time collision operator. Regarding the stability of LBM, the von Neumann stability analysis is used and linear stability boundaries are found under different scenarios. By an appropriate selection of the equilibrium distribution functions (EDF) and forcing terms, LBM is able to cope with parameter heterogeneity and anisotropy in mass transport equations in porous media. The relaxation times offer some degrees of freedom that allows LBM to improve the accuracy without decreasing computational efficiency. For validation purposes LBM has been implemented to simulate saltwater intrusion in the Henry problem and modified versions, and the results are in good agreement with available analytical solutions and numerical solutions obtained by other methods

A review on reactive transport model and porosity evolution in the porous media

This work comprehensively reviews the equations governing multicomponent flow and reactive transport in porous media on the pore-scale, mesoscale and continuum scale. For each of these approaches, the different numerical schemes for solving the coupled advection–diffusion-reactions equations are presented. The parameters influenced by coupled biological and chemical reactions in evolving porous media are emphasised and defined from a pore-scale perspective. Recent pore-scale studies, which have enhanced the basic understanding of processes that affect and control porous media parameters, are discussed. Subsequently, a summary of the common methods used to describe the transport process, fluid flow, reactive surface area and reaction parameters such as porosity, permeability and tortuosity are reviewed