Multiple factors, many of them environmental, coalesce to inform agricultural decisions. Farm planning is often done months in advance. These decisions have to be made with the information available at the time, including current trends, historical data, or predictions of what future weather patterns may be. The effort described in this work is geared towards a flexible mathematical and software framework for simulating the impact of meteorological variability on future crop yield. Our framework is data driven and can easily be applied to any location with suitable historical observations. This will enable site-specific studies that are needed for rigorous risk assessments and climate adaptation planning. The framework combines a physics-based model of crop yield with stochastic process models for meteorological inputs. Combined with techniques from uncertainty quantification, global sensitivity analysis, and machine learning, this hybrid statistical–physical framework allows studying the potential impacts of meteorological uncertainty on future agricultural yields and identify the environmental variables that contribute the most to prediction uncertainty. To highlight the utility of our general approach, we studied the predicted yields of multiple crops in multiple scenarios constructed from historical data. Using global sensitivity analysis, we then identified the key environmental factors contributing to uncertainty in these scenarios’ predictions.

In this work, we describe a simulation framework for fluid movement in a corrugated sawtooth channel whose walls are undergoing periodic repeated oscillations. The sawtooth geometry of the channel walls creates a fluid ratchet by generating an anisotropy in the fluid impedance. The simulations are developed using an immersed boundary method, and we present numerical results for both Newtonian and non-Newtonian fluids. These results are in agreement with physical studies of ratchets in the literature and with general flow behaviors expected for non-Newtonian fluids. In particular, we find enhanced mean flow rates for non-Newtonian fluids up to a critical value of the Weissenberg number. Existence of such a critical value has been shown for non-Newtonian flows in other environments, but has not been explored computationally for fluid ratchets. We also provide results which highlight the difference in movement of ratcheted non-Newtonian versus Newtonian fluids.

The development of appropriate water management strategies requires, in part, a methodology for quantifying and evaluating the impact of water policy decisions on regional stakeholders. In this work, we describe the framework we are developing to enhance the body of resources available to policy makers, farmers, and other community members in their efforts to understand, quantify, and assess the often competing objectives water consumers have with respect to usage. The foundation for the framework is the construction of a simulation-based optimization software tool using two existing software packages. In particular, we couple a robust optimization software suite (DAKOTA) with the USGS MF-OWHM water management simulation tool to provide a flexible software environment that will enable the evaluation of one or multiple (possibly competing) user-defined (or stakeholder) objectives. We introduce the individual software components and outline the communication strategy we defined for the coupled development. We present numerical results for case studies related to crop portfolio management with several defined objectives. The objectives are not optimally satisfied for any single user class, demonstrating the capability of the software tool to aid in the evaluation of a variety of competing interests.

Farmers in regions experiencing water stress or drought conditions can struggle to balance their crop portfolios. Periods of low precipitation often lead to increased, unsustainable reliance on groundwater-supplied irrigation. As a result, regional water management agencies place limits on the amount of water which can be obtained from groundwater, requiring farmers to reduce acreage for more water-intensive crops or remove them from the portfolio entirely. Real-time decisions must be made by the farmer to ensure viability of their farming operation and reduce the impacts associated with limited water resources. Evolutionary algorithms, coupled with accurate, flexible, realistic simulation tools, are ideal mechanisms to allow farmers to assess scenarios with regard to multiple, competing objectives. In order to effective, however, one must be able to select among a variety of simulation tools and optimization algorithms. Many simulation tools allow no access to the source code, and many optimization algorithms are now packaged as part of a suite of tools available to a user. In this work, we describe a framework for integrating these different software components using only their associated input and output streams. We analyze our strategy by coupling a multi-objective genetic algorithm available in the DAKOTA optimization suite (developed and distributed by Sandia National Laboratory) with the MODFLOW-FMP2 simulation tool (developed and distributed by the United States Geological Survey). MODFLOW-FMP2 has been used extensively to model hydrological and farming processes in agriculture-dominated regions, allowing us to represent both farming and conservation interests. We evaluate our integration by considering a case study related to planting decisions facing farmers experiencing water stress. We present numerical results for three competing objectives associated with stakeholders in a given region (i.e., profitability, meeting demand targets, and water conservation). The data obtained from the optimization are robust with respect to algorithmic parameter choices, validating the ability of the associated evolutionary algorithm to perform well without expert guidance. This is integral to our approach, as a motivation for this work is providing decision-making tools. In addition, the results from this study demonstrate that output from the chosen evolutionary algorithm provides a suite of feasible planting scenarios, giving farmers and policy makers the ability to compromise solutions based on realistic simulation data.

Over the last few decades, groundwater resources in many regions have been depleted at a faster rate than the underlying aquifers have been replenished. This imbalance has led water management agencies to consider managed aquifer recharge networks, where infiltration basins are used to replenish the aquifers using previously-uncaptured storm water runoff. In this work, we utilize optimization to evaluate the costs associated with constructing such a network and the ability of the network to meet demands placed on the aquifer. Our objective function incorporates land and construction costs, along with rewards for effective aquifer recharge. We enforce capture of a minimum volume of storm water runoff by penalizing the cost. We present results for two basin networks, one based on results from the literature and another based on a study of the Pajaro Valley region in California. The Pajaro Valley example is used as our realistic test case, and we use the analysis to suggest the viability of a managed aquifer recharge network in a particular sub-watershed associated with the area.

In this work, we couple a multi-objective genetic algorithm from the DAKOTA optimization software suite with the MODFLOW-FMP2 simulation tool, which was developed to help guide policy makers in agricultural regions. The proposed optimization framework allows for the output from the hydrological and farming processes simulated in MODFLOWFMP2 to be used to represent the various stakeholders in a farming community. We present numerical results for a case study related to decisions faced by farmers in regions experiencing water stress and asses the ability of this approach on three competing objectives (profit, demand, and water usage). This simulation data files for this example as well as the python wrappers needed to evaluate the objective function are provided to the public to facilitate future studies. This work has been submitted for publication and is under review.

We adapt the classic Taylor swimming sheet set-up to investigate both the transient and long-time dynamics of an actuated elastic sheet immersed in a viscoelastic fluid as it interacts with neighboring structures. While the preferred kinematics of the sheet are specified, the flexible sheet interacts with the surrounding fluid and other structures, and its realized kinematics emerges from this coupling. We use an immersed boundary framework to evolve the Oldroyd-B/Navier-Stokes equations and capture the spatial and temporal development of viscoelastic stresses and sheet shape. We compare the dynamics when the actuated sheet swims next to a free elastic membrane, with and without bending rigidity, and next to a fixed wall. We demonstrate that the sheets can exploit the neighboring structures to enhance their swimming speed and efficiency, and also examine how this depends upon fluid viscoelasticity. When the neighboring structure is likewise an actuated elastic sheet, we investigate the viscoelastic dynamics of phase-locking.

Increased demands for water from a variety of sources has placed severe stresses on the groundwater aquifers near the Pajaro Valley region in northern California. Initially developed as an agricultural region in the late 1800s, decades of pumping to serve the needs of the agricultural industry have caused significant saltwater intrusion into the underlying aquifer. The classification of the groundwater basin as one with critical conditions of overdraft has resulted in water use restrictions being placed on the entire Pajaro Valley region. Representatives of a berry-farming consortium in the region are working to mitigate the saltwater intrusion while studying strategies for profitable farming under water use restrictions. In this paper, we discuss the results of an optimization study designed to uncover optimal crop rotation and planting scenarios while incorporating possible grass roots solutions for aquifer recharge.

— A Navier-Stokes/Oldroyd-B immersed boundary algorithm is used to examine the interaction of swimming infinite sheets with a viscoelastic fluid. In par-ticular, we examine the spatial and temporal evolution of the polymer stress field. The effects of the bulk viscoelasticity on hydrodynamic synchronization of swimming sheets and sheets swimming next to solid walls is analyzed.

We present a Navier–Stokes/Oldroyd-B immersed boundary algorithm that captures the interaction of a flexible structure with a viscoelastic fluid. In particular, we study the effects of bulk viscoelasticity on freely decaying shape oscillations of an Oldroyd-B fluid droplet suspended in an Oldroyd-B matrix. Our numerical data indicate that if the fluid viscosity is low, viscoelasticity plays a modulating role in the drop shape relaxation; specifically, it increases the oscillation frequency and decreases the decay rate when the fluid relaxation time is above a critical value. In the high viscosity limit, i.e., when a Newtonian droplet is expected to return to a spherical shape with an aperiodic decay, an increase in the relaxation time eventually results in the reappearance of the oscillations. Both these results are in line with the prediction of small deformation theory for viscoelastic droplet oscillations. The algorithm was also validated by direct comparison with linear asymptotics.

ABSTRACT: Many biological fluids are viscoelastic and require a nonlinear constitutive equation to describe the evolution of the extrastress tensor. We use an immersed boundary framework to model processes that involve the movement of immersed elastic boundaries interacting with a surrounding viscoelastic fluid. We present recent results on applications including dynamics of a closed membrane moving under surface tension, and phase-locking of swimming sheets.

A fractional step θ-method for the approximation of time-dependent viscoelastic fluid flow equations is described and analyzed in this article. The algorithm uses substeps within a time step to sequentially update velocity, pressure, and stress. This lagged approach to temporal integration requires a resolution of smaller systems than a fully implicit approach while achieving a second order temporal accuracy. We establish a priori error estimates for our scheme, and provide numerical computations to support the theoretical results and demonstrate the capability of this method.

In this article a fractional step θ-method is described and studied for the approximation of time dependent viscoelastic fluid flow equations, using the Johnson-Segalman constitutive model. The θ-method implementation allows the velocity and pressure approximations to be decoupled from the stress, reducing the number of unknowns resolved at each step of the method. The constitutive equation is stabilized using a Streamline Upwinded Petrov-Galerkin (SUPG)-method. A priori error estimates are given for the approximation scheme. Numerical computations supporting the theoretical results and demonstrating the θ-method are also presented.

In this article, we analyze the fractional step θ-method for the time-dependent convection–diffusion equation. In our implementation, we completely separate the convection operator from the diffusion operator, and stabilize the convective problem using a Streamline Upwinded Petrov–Galerkin (SUPG) method. We establish a priori error estimates and show that the optimal value of θ yields a scheme that is second-order in time. Numerical computations are presented which demonstrate the method and support the theoretical results.

We investigate an operator splitting method for time-dependent partial differential equations. The goal of the method is to decouple mixed operators in PDE systems. This allows the user to implement operator specific solution techniques and also reduces the size of the approximating system. We apply the method to a convection-diffusion problem, and provide analysis and numerical results.