Assessment of numerical schemes for transient, finite-element ice flow models using ISSM v4.18

Time-dependent simulations of ice sheets require two equations to be solved: the mass transport equation, derived from the conservation of mass, and the stress balance equation, derived from the conservation of momentum. The mass transport equation controls the advection of ice from the interior of the ice sheet towards its periphery, thereby changing its geometry. Because it is based on an advection equation, a stabilization scheme needs to be employed when solved using the finite-element method. Several stabilization schemes exist in the finite-element method framework, but their respective accuracy and robustness have not yet been systematically assessed for glaciological applications. Here, we compare classical schemes used in the context of the finite-element method: (i) artificial diffusion, (ii) streamline upwinding, (iii) streamline upwind Petrov–Galerkin, (iv) discontinuous Galerkin, and (v) flux-corrected transport. We also look at the stress balance equation, which is responsible for computing the ice velocity that “advects” the ice downstream. To improve the velocity computation accuracy, the ice-sheet modeling community employs several sub-element parameterizations of physical processes at the grounding line, the point where the grounded ice starts to float onto the ocean. Here, we introduce a new sub-element parameterization for the driving stress, the force that drives the ice-sheet flow. We analyze the response of each stabilization scheme by running transient simulations forced by ice-shelf basal melt. The simulations are based on an idealized ice-sheet geometry for which there is no influence of bedrock topography. We also perform transient simulations of the Amundsen Sea Embayment, West Antarctica, where real bedrock and surface elevations are employed. In both idealized and real ice-sheet experiments, stabilization schemes based on artificial diffusion lead systematically to a bias towards more mass loss in comparison to the other schemes and therefore should be avoided or employed with a sufficiently high mesh resolution in the vicinity of the grounding line. We also run diagnostic simulations to assess the accuracy of the driving stress parameterization, which, in combination with an adequate parameterization for basal stress, provides improved numerical convergence in ice speed computations and more accurate results.

Assessment of groundwater contamination by chlorpyrifos using the PWC model in Valencia Region (Spain)

<p>Chlorpyrifos is commoly used as an pesticide to control weeds and prevent nondesirable grow of algae, fungi and bacteria in many agricultural applications. Despite its highly negative effects on human health, environmental modeling of this kind of pesticide in the groundwater is not commonly done in real situations. Predicting the fate of pesticides released into the natural environment is necessary to anticipate and minimize adverse effects both at close and long distances from the contamination source. A number of models have been developed to predict the behavior, mobility, and persistence of pesticides. These models should account for key hydrological and agricultural processes, such as crop growth, pesticide application patterns, transformation processes and field management practices.</p><p>This work shows results obtained by the Pesticide Water Calculator (PWC) model to simulate the behavior of chlorpyrifos. PWC model is used as a standard pesticide simulation model in USA and in this work it has been used to  simulate the fate and transport of chlorpyrifos in the unsaturated zone of the aquifer. The model uses a whole set of parameters to solve a modified version of the mass transport equation considering the combined effect of advection, dispersion and reactive transport processes. PWC is used to estimate the daily concentrations of chlorpyrifos in the Buñol-Cheste aquifer in Valencia Region(Spain).</p><p>A whole set of simulation scenarios have been designed to perform a parameter sensitivity analysis. Results of the PWC model obtained in this study represents a crucial first step towards the development of a pesticide risk assessment in Valencia Region. Results show that numerical simulation is a valid tool for the analysis and prediction of the fate  and transport of pesticides in the groundwater.</p>

Assessment of numerical schemes for transient, finite-element ice flow models using ISSM v4.18

Time dependent simulations of ice sheets require two equations to be solved: the mass transport equation, derived from the conservation of mass, and the stress balance equation, derived from the conservation of momentum. The mass transport equation controls the advection of ice from the interior of the ice sheet towards its periphery, thereby changing its geometry. Because it is based on a hyperbolic partial differential equation, a stabilization scheme needs to be employed when solved using the finite element method. Several stabilization schemes exist in the finite element method framework, but their respective accuracy and robustness have not yet been systematically assessed for glaciological applications. Here, we compare classical schemes used in the context of the finite element method: (i) Artificial Diffusion, (ii) Streamline Upwinding, (iii) Streamline Upwind Petrov-Galerkin, (iv) Discontinuous Galerkin, and (v) Flux Corrected Transport. We also look at the stress balance equation, which is responsible for computing the ice velocity that `advects' the ice dowstream. To improve the velocity computation accuracy, the ice sheet modeling community employs several sub-element parameterizations of physical processes at the grounding line, the point where the grounded ice starts to float onto the ocean. Here, we introduce a new sub-element parameterization for the driving stress, the force that drives the ice sheet flow. We analyze the response of each stabilization scheme by running transient simulations forced by ice shelf basal melt. The simulations are based on an idealized ice sheet geometry for which there is no influence of bedrock topography. We also perform transient simulations of the Amundsen Sea Sector, West Antarctica, where real bedrock and surface elevations are employed. In both idealized and real ice sheet experiments, stabilization schemes based on artificial diffusion lead systematically to a bias towards more mass loss in comparison to the other schemes, and therefore, should be avoided or employed with a sufficiently high mesh resolution in the vicinity of the grounding line. We also run diagnostic simulations to assess the accuracy of the driving stress parameterization, which in combination with an adequate parameterization for basal stress, provides improved numerical convergence in ice speed computations and more accurate results.

Determination of State Variables in Textile Composite with Membrane During Complex Heat and Moisture Transport

The cotton-based composite is equipped with a single/double semipermeable membrane made of polyurethane (PU) (100%), which blocks liquid transport to the surrounding environment. The complex problem analyzed involves the coupled transport of water vapor within the textile material, transport of liquid water in capillaries, as well as heat transport with vapor and liquid water. The problem can be described using the mass transport equation for water vapor, heat transport equation, and mass transport equation for liquid moisture, accompanied by the set of corresponding boundary and initial conditions. State variables are determined using a complex multistage solution procedure within the selected points for each layer. The distributions of state variables are determined for different configurations of membranes.

Numerical simulation of dissolution of solid particles in fluid flow using the SPH method

Purpose The purpose of this paper is to numerically study the dissolution of solid particles using the smoothed particle hydrodynamics (SPH) method. Design/methodology/approach To implement dissolution, an advection–diffusion mass transport equation is solved over computational particles. Subsequently, these particles disintegrate from the solute when their concentration falls below a certain threshold. Findings It is shown that the implementation of dissolution is in good agreement with available data in the literature. The dissolution of solid particles is studied for a wide range of Reynolds and Schmidt numbers. Two-dimensional (2D) results are compared with three-dimensional (3D) cases to identify where 2D results are accurate for modelling 3D dissolution phenomena. Originality/value The present numerical model is capable of addressing related problems in pharmaceutical, biochemical, food processing and detergent industries.

Concentration Distribution of Photosensitive Liquid in a Droplet Under UV Light

A semi-analytical solution for the concentration of photosensitive suspension is developed in a hemispherical droplet illuminated with UV laser. A biharmonic equation in stream function is analytically solved using toroidal coordinates and the velocity is then used to solve the mass transport equation for concentration. Flow pattern and photosensitive material concentration are affected by the peak location of the UV light intensity, which corresponds to a surface tension profile. When the laser beam is moved from the droplet center to its edge, a rotationally symmetric flow pattern changes from a single counter clockwise circulation to a circulation pair and finally to a single clockwise circulation. This modulation in the orientation of circulation modifies the concentration distribution of the photosensitive material. The distribution depends on both diffusion from the droplet surface as well as Marangoni convection. The region beneath the droplet surface away from the UV light intensity peak has low concentration, while the region near the downward dividing streamline has the highest concentration. When the UV light peak reaches the droplet edge, the concentration is high everywhere in the droplet.

On the Generalized Mass Transport Equation to the Concept of Variable Fractional Derivative

The hydrodynamic dispersion equation was generalized using the concept of variational order derivative. The modified equation was numerically solved via the Crank-Nicholson scheme. The stability and convergence of the scheme in this case were presented. The numerical simulations showed that, the modified equation is more reliable in predicting the movement of pollution in the deformable aquifers, than the constant fractional and integer derivatives.

Effects of convection and diffusion of the vapour in evaporating liquid films

We propose a novel model of a pure liquid film evaporating into an inert gas, taking into account an effect of convection of the vapour by the evaporation flow of the gas. For the liquid phase, the long-wave approximation is applied to the governing equations. Assuming that fluctuations of the vapour concentration in the gas phase are localized in the vicinity of the liquid–gas interface, we consider only the limit of the mass transport equation at the interface. The diffusion term in the vertical direction of the mass transport equation is modelled by introducing the concentration boundary layer above the liquid film and solving the stationary convection–diffusion equation for the concentration inside the boundary layer. We investigate the linear stability of a flat film based on our model. The effect of vapour diffusion along the interface mitigates the Marangoni effect for short-wavelength disturbances. The local variation of vertical advection is found to be negligible. A critical thickness above which the film is stable exists under the presence of gravity. The effect of fluctuation of mass loss of the liquid induced by horizontal vapour diffusion becomes the primary instability mechanism in a very thin region. The effects of the resistance of phase change and the time derivative of the interface concentration are also examined.