On a Doubly Reduced Model for Dynamics of Heterogeneous Mixtures of Stiffened Gases, its Regularizations and their Implementations

We deal with the reduced four-equation model for the dynamics of heterogeneous compressible binary mixtures with the stiffened gas equations of state. We study its further reduced form, with the excluded volume concentrations, and with a quadratic equation for the common pressure of the components; this form can be called a quasi-homogeneous form. We prove new properties of the equation, derive simple formulas for the squared speed of sound and present an alternative proof for a formula that relates it to the squared Wood speed of sound; also, a short derivation of the pressure balance equation is given. For the first time, we introduce regularizations of the heterogeneous model (in the quasi-homogeneous form). Previously, regularizations of such type were developed only for the homogeneous mixtures of perfect polytropic gases, and it was unclear how to cover the case considered here. In the 1D case, based on these regularizations, we construct new explicit two-level in time and symmetric three-point in space finite-difference schemes without limiters, and provide numerical results for various flows with shock waves.Comment: 19 pages, 7 figures, 3 table

Field Study of Hydraulic Conductivity in a Heterogeneous Aquifer: Comparison of Single-Borehole Measurements Using Different Instruments

This field study compares three techniques for estimating the vertical distribution of horizontal hydraulic conductivity Kr in a heterogeneous aquifer and evaluates possible support volume effects. The dipole flow test (DFT), multilevel slug test (MLST), and borehole flowmeter test (BFT) are based on different kinematic flow structures and the shape and the size of the support volumes. The experiment design employed an identical characteristic linear scale for all tests. Vertical profiles of Kr ranging up to 260 m/day from tested wells in an alluvial aquifer exhibit a strong correlation in spite of the differences between test hydraulics. Results suggest that tested screen length is an important indicator of the averaging mechanism for hydraulic tests. Correlation between the DFT and MLST is especially strong. Correlation between data from the BFT and other tests is not as strong due to the absence of a distinct physical vertical scale, among other factors. The differences between the tests are discussed using the concept of a weighting function associated with the magnitude of instantaneous local velocity

Reply to comment by H. Lough, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand, on the paper “Stream depletion predictions using pumping test data from a heterogeneous stream–aquifer system (a case study from the Great Plains, USA)”

1. General remark 2. The study by Kollet and Zlotnik (2003) 3. Remark on the explanation of the drawdown behavior 4. Remark on the re-analysis of the data from piezometer C2d 5. Summar

Proper generalized decomposition for parameterized Helmholtz problems in heterogeneous and unbounded domains: Application to harbor agitation

Solving the Helmholtz equation for a large number of input data in an heterogeneous media and unbounded domain still represents a challenge. This is due to the particular nature of the Helmholtz operator and the sensibility of the solution to small variations of the data. Here a reduced order model is used to determine the scattered solution everywhere in the domain for any incoming wave direction and frequency. Moreover, this is applied to a real engineering problem: water agitation inside real harbors for low to mid-high frequencies. The Proper Generalized Decomposition (PGD) model reduction approach is used to obtain a separable representation of the solution at any point and for any incoming wave direction and frequency. Here, its applicability to such a problem is discussed and demonstrated. More precisely, the separability of the operator is addressed taking into account both the non-constant co

Mary\u27s Flowers: A Matching Game

Matching game using images of flowers named for the Blessed Virgin Mary. Illustrations by Brother A. Joseph Barrish, S.M

An approach to hydrogeological modeling of a large system of groundwater-fed lakes and wetlands in the Nebraska Sand Hills, USA

The feasibility of a hydrogeological modeling approach to simulate several thousand shallow groundwater-fed lakes and wetlands without explicitly considering their connection with groundwater is investigated at the regional scale (~40,000 km2) through an application in the semi-arid Nebraska Sand Hills (NSH), USA. Hydraulic heads are compared to local land-surface elevations from a digital elevation model (DEM) within a geographic information system to assess locations of lakes and wetlands. The water bodies are inferred where hydraulic heads exceed, or are above a certain depth below, the land surface. Numbers of lakes and/or wetlands are determined via image cluster analysis applied to the same 30-m grid as the DEM after interpolating both simulated and estimated heads. The regional water-table map was used for groundwater model calibration, considering MODIS-based net groundwater recharge data. Resulting values of simulated total baseflow to interior streams are within 1% of observed values. Locations, areas, and numbers of simulated lakes and wetlands are compared with Landsat 2005 survey data and with areas of lakes from a 1979–1980 Landsat survey and the National Hydrography Dataset. This simplified process-based modeling approach avoids the need for field-based morphology or water-budget data from individual lakes or wetlands, or determination of lake-groundwater exchanges, yet it reproduces observed lake-wetland characteristics at regional groundwater management scales. A better understanding of the NSH hydrogeology is attained, and the approach shows promise for use in simulations of groundwater-fed lake and wetland characteristics in other large groundwater systems. Includes supplementary materials

Analysis of Groundwater Recharge in Mongolian Drylands Using Composite Vadose Zone Modeling

Knowledge of groundwater recharge (GR) is important for the effective management of water resources under semi-arid continental climates. Unfortunately, studies and data in Mongolia are limited due to the constraints in funding and lack of research infrastructures. Currently, the wide accessibility of freely available global-scale digital datasets of physical and chemical soil properties, weather data, vegetation characteristics, and depths to the water table offers new tools and basic information that can support low-cost physically based and process-oriented models. Estimates of GR over 41 study sites in Mongolia were obtained using HYDRUS-1D in a 2-m-thick soil profile with root depths of either 0.30 or 0.97 m by exploiting the daily precipitation and biome-specific potential evapotranspiration values. The GR simulated by HYDRUS-1D arrives at the water table and becomes the actual GR with a lag time that has been calculated using a simplified form of the Richards equation and a traveling wave model. The mean annual precipitation ranges from 57 to 316 mm year−1, and on average about 95% of it is lost by mean annual actual evapotranspiration. In the steppe region, the vegetation cover induces higher-than-normal actual transpiration losses and consequently lower GR. The mean annual GR rates span between 0.3 and 12.0 mm year−1, while travel times range between 4 and 558 years. Model prediction uncertainty was quantified by comparing actual evapotranspiration and GR with available maps and by a sensitivity assessment of lag time to the soil moisture in the deep vadose zone. The partial least squares regression (PLSR) was used to evaluate the impact of available environmental properties in explaining the 47.1 and 59.1% variability of the spatially averaged mean annual GR and travel time, respectively. The most relevant contributors are clay content, aridity index, and leaf area index for GR, and depth to the water table and silt content for the lag time. In data-poor, arid, and semi-arid regions such as Mongolia, where the mean annual GR rates are low and poorly correlated to precipitation, the ever-increasing availability of world databases and remote sensing products offers promise in estimating GR

Analysis of Groundwater Recharge in Mongolian Drylands Using Composite Vadose Zone Modeling

Knowledge of groundwater recharge (GR) is important for the effective management of water resources under semi-arid continental climates. Unfortunately, studies and data in Mongolia are limited due to the constraints in funding and lack of research infrastructures. Currently, the wide accessibility of freely available global-scale digital datasets of physical and chemical soil properties, weather data, vegetation characteristics, and depths to the water table offers new tools and basic information that can support low-cost physically based and process-oriented models. Estimates of GR over 41 study sites in Mongolia were obtained using HYDRUS-1D in a 2-m-thick soil profile with root depths of either 0.30 or 0.97m by exploiting the daily precipitation and biome-specific potential evapotranspiration values. The GR simulated by HYDRUS-1D arrives at the water table and becomes the actual GR with a lag time that has been calculated using a simplified form of the Richards equation and a traveling wave model. The mean annual precipitation ranges from 57 to 316mm year−1, and on average about 95% of it is lost by mean annual actual evapotranspiration. In the steppe region, the vegetation cover induces higher-than-normal actual transpiration losses and consequently lower GR. The mean annual GR rates span between 0.3 and 12.0mm year−1, while travel times range between 4 and 558 years. Model prediction uncertainty was quantified by comparing actual evapotranspiration and GR with available maps and by a sensitivity assessment of lag time to the soil moisture in the deep vadose zone. The partial least squares regression (PLSR) was used to evaluate the impact of available environmental properties in explaining the 47.1 and 59.1%variability of the spatially averaged mean annual GR and travel time, respectively. The most relevant contributors are clay content, aridity index, and leaf area index for GR, and depth to the water table and silt content for the lag time. In data-poor, arid, and semi-arid regions such as Mongolia, where the mean annual GR rates are low and poorly correlated to precipitation, the ever-increasing availability of world databases and remote sensing products offers promise in estimating GR