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

Prediction of biome-specific potential evapotranspiration in mongolia under a scarcity of weather data

We propose practical guidelines to predict biome-specific potential evapotranspiration (ETp) from the knowledge of grass-reference evapotranspiration (ET0) and a crop coefficient (Kc) in Mongolia. A paucity of land-based weather data hampers use of the Penman–Monteith equation (FAO-56 PM) based on the Food and Agriculture Organization (FAO) guidelines to predict daily ET0. We found that the application of the Hargreaves equation provides ET0 estimates very similar to those from the FAO-56 PM approach. The Kc value is tabulated only for crops in the FAO-56 guidelines but is unavailable for steppe grasslands. Therefore, we proposed a new crop coefficient, Kc adj defined by (a) net solar radiation in the Gobi Desert (Kc adjD) or (b) leaf area index in the steppe region (Kc adjS) in Mongolia. The mean annual ETp obtained using our approach was compared to that obtained by FAO-56 guidelines for forages (not steppe) based on tabulated Kc values in 41 lo-cations in Mongolia. We found the differences are acceptable (RMSE of 0.40 mm d−1) in northern Mongolia under high vegetation cover but rather high (RMSE of 1.69 and 2.65 mm d−1) in central and southern Mongolia. The FAO aridity index (AI) is empirically related to the ETp/ET0 ratio. Ap-proximately 80% and 54% reduction of ET0 was reported in the Gobi Desert and in the steppe loca-tions, respectively. Our proposed Kc adj can be further improved by considering local weather data and plant phenological characteristics

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

Impact of grassland conversion to forest on groundwater recharge in the Nebraska Sand Hills

Study region: Nebraska National Forest in the High Plains Aquifer, Nebraska Sand Hills, U.S.A. Study focus: This research aimed to investigate the effects of grassland conversions to forest on recharge rates in a century-old experimental forest. The DiffeRential Evolution Adaptive Metropolis (DREAMZS) global optimization algorithm was used to calibrate the effective soil hydraulic parameters from observed soil moisture contents for 220 cm deep uniform soil profiles. The historical recharge rates were then estimated by applying the numerical model HYDRUS 1-D for simulation of two plots representing grasslands and dense pine forest conditions. New hydrological insights: The results indicate that conversion from grasslands to dense pine forests led to vegetation induced changes in soil hydraulic properties, increased rooting depth, and greater leaf area index, which together altered the water budget considerably. The impacts of land use change, expressed in percent of gross precipitation, include a 7% increase in interception associated with an increase in leaf area index, a nearly 10% increase in actual evapotranspiration, and an overall reduction of groundwater recharge by nearly 17%. Simulated average annual recharge rates decreased from 9.65 cm yr−1 in the grassland to 0.07 cm yr−1 in the pine plot. These outcomes highlight the significance of the grassland ecology for water resources, particularly groundwater recharge, in the Nebraska Sand Hills and the overall sustainability and vitality of the High Plains Aquifer