Impermeable Boundary Research Articles

The 3D Euler equations with inflow, outflow and vorticity boundary conditions

The 3D incompressible Euler equations in a bounded domain are most often supplemented with impermeable boundary conditions, which constrain the fluid to neither enter nor leave the domain. We establish well-posedness with inflow, outflow of velocity when either the full value of the velocity is specified on inflow, or only the normal component is specified along with the vorticity (and an additional constraint). We derive compatibility conditions to obtain regularity in a Hölder space with prescribed arbitrary index, and allow multiply connected domains. Our results apply as well to impermeable boundaries, establishing higher regularity of solutions in Hölder spaces.

CFD–DEM comparison of slurry infiltration in laboratory column tests and in real-world tunnelling

Slurry infiltration and filter cake formation are critical for excavation surface stability in slurry shield tunnelling. Laboratory column tests are frequently adopted to study macroscopic infiltration. However, these tests, in a vertical orientation and confined by an impermeable cylindrical boundary, may not be a good representation of horizontal infiltration into an unbounded stratum in real-world tunnelling. In this paper, a more realistic slurry pressure balance (SPB) tunnelling model was created to overcome the limitations of simulated laboratory column tests. Coupled computational fluid dynamics (CFD)–discrete element method (DEM) numerical simulations were carried out to study the slurry infiltration into sand for this model and compare the results with the conventional laboratory column test model. Both models produced the same types of filter cakes. The SPB tunnelling model yielded larger infiltration distances and ranges, but a lower normalised permeability in the sand region in front of the tunnel face. The fluid pressure within this region dissipated much faster in the SPB tunnelling model, resulting in rapid velocity decreases and a faster infiltration process. Although the SPB tunnelling model is more representative of real-world tunnelling, the conventional laboratory column test is conservative, producing similar types of filter cakes over a longer timeframe.

Rayleigh wave propagation in a modified couple stress visco-thermoelastic diffusion medium

The present investigation is devoted to Rayleigh wave propagation in modified couple stress visco-thermoelastic medium with mass diffusion under Lord–Shulman and Green–Lindsay theories of thermoelasticity. After formulating the problem mathematically, the secular equation is derived for stress free, insulated, and impermeable boundary. The wave characteristics like phase velocity and attenuation coefficient have been obtained numerically by developing numerical algorithm. For a particular material, the numerically simulated results are shown graphically to display the physical meaning of the phenomenon. The current inquiry also leads to several specific cases of interest. A comparison has been conducted with the earlier findings that suggested how the additional parameters might affect the phenomena of Rayleigh waves propagating. The results obtained indicate to the strong impact for the diffusivity and viscosity of Rayleigh thermoelastic waves propagation and applicable on the related phenomenon in geology, geophysics, acoustics, astronomy, and geophysics and agreement with the physical meaning of the phenomenon.

Asymptotic stability of rarefaction wave with non-slip boundary condition for radiative Euler flows

This paper is devoted to studying the initial-boundary value problem for the radiative full Euler equations, which are a fundamental system in the radiative hydrodynamics with many practical applications in astrophysical and nuclear phenomena, with the non-slip boundary condition on an impermeable wall. Due to the difficulty from the disappearance of the velocity on the impermeable boundary, quite few results for compressible Navier-Stokes equations and no result for the radiative Euler equations are available at this moment. So the asymptotic stability of the rarefaction wave proven in this paper is the first rigorous result on the global stability of solutions of the radiative Euler equations with the non-slip boundary condition. It also contributes to our systematical study on the asymptotic behaviors of the rarefaction wave with the radiative effect and different boundary conditions such as the inflow/outflow problem and the impermeable boundary problem in our series papers including [5,6].

Imperfectly Impermeable Boundaries and Variable Viscosity Perspectives on the Stability of Natural Convection in a Vertical Porous Layer

Imperfectly Impermeable Boundaries and Variable Viscosity Perspectives on the Stability of Natural Convection in a Vertical Porous Layer

Minimum Cost Pathfinding Algorithm for the Determination of Optimal Paths under Airflow Constraints

Pathfinding algorithms allow for the numerical determination of optimal paths of travel across many applications. These algorithms remain poorly defined for additional consideration of outside parameters, such as fluid flow, while considering contaminant transport problems. We have developed a pathfinding algorithm based on the A* search algorithm which considers the effect of fluid flow behaviors in two dimensions. This search algorithm returns the optimal path between two points in a setting containing impermeable boundaries, allowing for a computational approach to the determination of the most likely path of travel for contaminants or hazards of concern due to fluid flow. This modified A* search algorithm has applications in the statistical modeling of airborne contamination distributions, providing a relative estimate of the statistical relationship between two points in an underground mine’s ventilation system. This method provides a significant improvement to the spatial resolution of minimum-cost path methods currently in use in mine ventilation network software.

On steady solutions to the MHD equations with inhomogeneous generalized impermeability boundary conditions for the magnetic field

The paper deals with the steady MHD equations for a viscous incompressible fluid in a bounded and generally multiply connected domain with the no‐slip boundary condition for the velocity and inhomogeneous generalized impermeability boundary conditions for the magnetic field . The main results concern an appropriate definition of the weak solution , its existence, continuous dependence on the data when the data tend to zero, and uniqueness in a “small” neighborhood of the zero solution .

Stimulation effect of network fracturing combined with sealing boundaries on the depressurization development of hydrate reservoir in China's offshore test site

This study investigated the stimulation of reservoir reconstruction by network fracturing combined with sealing boundaries (RC-HFBS) for hydrate development in China's offshore test site. We first studied the influence of different boundary-sealing characters on development performance. Then, the response of development performance to key production parameters including fracture conductivity (CF), fracture spacing (SF), and production pressure (Pp) under permeable and impermeable boundaries was studied. Lastly, the long-term commercial CH4 production potentials were evaluated. Results showed that compared to unreconstruction reservoirs, the CH4 production of RC-HFBS increased by 11.1 times, and the gas-to-water ratio increased by 13.3 times. The harm of permeable boundaries on reservoir depressurization leads to a short effective stimulation time of fractures (about 1000 out of 3650 days) and results in the insensitivity of exploitation performance to production parameters. However, the impermeable boundaries improve the fractures' stimulation, meanwhile, making exploitation performance extremely sensitive to production parameters. For RC-HFBS, commercial production can be realized by diverse production parameter combinations, including SF, CF, and Pp are 15 m, 10D•cm, 4 MPa; 15 m, 10D•cm, 2 MPa; 25 m, 10D•cm, 2 MPa; 5 m, 40D•cm, 4.5 MPa.

Setting our boundaries: The role of gender, values, and role salience in work–home boundary permeability

AbstractAlthough women make up nearly half of the U.S. workforce, gender role stereotypes persist, and gender roles may relate to how men and women manage work–home boundaries. In this study, we explore gender differences in how employee values (tradition, achievement) translate into role identity salience, and in turn, boundary management preferences and behaviour. With data collected in two waves from 200 employees, we examined how the personal values of tradition and achievement relate differently by gender to role identity salience and in turn, boundary management. We found that men who more strongly value tradition have higher levels of work identity salience and both prefer and create an impermeable boundary around work to prevent intrusion from home. Men who valued tradition more also preferred and crafted a permeable home boundary to allow work intrusion. In contrast, women with higher tradition values reported higher home identity salience, which was associated with preferring segmentation in both work‐to‐home and home‐to‐work directions, and to behaviorally protecting home from work. Contrary to expectations, achievement values did not relate to a boundary management process via role identity salience for either gender. We discuss implications for a more nuanced, values‐driven, and gendered perspective on boundary management.

Generation of runoff in an alpine meadow hillslope underlain by permafrost

Permafrost plays an important role in hydrological processes of alpine regions. The frost table in the active layer on the permafrost acts as an impermeable boundary and regulates water generation from hillslopes and its routing to streams. Past studies focused on modes or critical conditions of flow generation, rather than on the capacity of the active layer on the permafrost to recharge flow. This study aimed to characterize the role of supra-permafrost groundwater in the generation of runoff on hillslopes during the active layer thawing processes. The study focused on an alpine meadow permafrost hillslope located in the northeastern Tibet Plateau during the months of July and August in both 2021 and 2022. Hydrometeorological variables, including precipitation, air temperature, soil temperature, soil moisture, thaw depths, supra-permafrost groundwater level, and runoff generation were monitored in field. Partial Least Squares Path Modeling was selected to analyze the relations between the above variables. The results showed that infiltrated rainwater tended to move into deep thawed soil, following which the frozen layer forced horizontal transport along the hillslope. This indicated that thaw depths along the soil profile regulated the dominant runoff path. The accumulated precipitation of the previous days had a significant impact on runoff generation. There was minimal lateral subsurface flow when the saturated zone was absent, whereas lateral subsurface flow increased with increasing thickness of the saturated zone. Runoff generation on the hillslope was regulated by both thaw depths and the thickness of the saturated zone along the soil profile. This study can act as a reference for runoff generation processes of permafrost hillslopes.

Hydrologic windows into the crystalline basement and their controls on groundwater flow patterns across the Paradox Basin, western USA

Conceptual models of sedimentary basin groundwater flow systems typically assume that the crystalline basement acts as an impermeable boundary and can be neglected. In this study, we use hydrologic models constrained by isotopic and geochemical datasets to argue that the La Sal Mountains, Utah, USA, act as a hydrologic window into the Paradox Basin’s lower aquifer system and underlying crystalline basement. We conducted a sensitivity study in which we varied crystalline basement/laccolith permeability as well as fault zone connectivity along a cross-sectional transect from the La Sal Mountains to Lisbon Valley. When the crystalline basement/laccolith units are set at relatively permeable levels (10−14 m2), simulated tracers that include total dissolved solids, oxygen isotopic composition of pore fluids (δ18O), and groundwater residence times are in closest agreement with field measurements. Model results indicate that pore fluids in the basal aquifer system underlying the Paradox Formation confining unit are a mixture of relatively young meteoric fluids and older Paradox Formation brines. The presence of faults did not significantly modify fluid exchange between the upper and lower aquifer systems. This was due, in part, to underpressuring within the Paradox Formation. Our study concludes that the Paradox Basin represents a regional recharge area for the Colorado Plateau, with groundwater discharge occurring along the Colorado River within the Grand Canyon some 375 km away to the southwest. This is only possible with a permeable crystalline basement. Our findings help explain the genesis of Mississippi Valley-type ore deposits of the US Midcontinent, where the presence of a permeable basement may be useful in addressing issues related to solute mass and energy balance.

Analytical Solution for the Steady Seepage Field of an Anchor Circular Pit in Layered Soil

An analytical study was carried out on an anchored circular pit with a submerged free surface in layered soil. The seepage field around the anchor circular pit was divided into three zones. Separate variable method was used to obtain the graded solution forms of head distribution in the column coordinate system for each of the three regions. Combined with the continuity condition between the regions the Bessel function orthogonality was used to obtain the explicit analytical solution of the seepage field in each region, and the infiltration line was determined. Comparison with the calculation results of Plaxis 2D 8.5 software verified the correctness of the analytical solution. Based on the analytical solution, the influence of the radius of the pit and the distance of the retaining wall from the top surface of the impermeable layer on the total head distribution on both sides of the retaining wall was analyzed. And the variation in the infiltration line was determined with the above parameters. The results show that as the pit radius, r, decreased, the total head on both sides of the retaining wall gradually increased, and the height of the submerged surface drop also increased. As the distance, a, between the retaining wall and the impermeable boundary at the bottom increased, the hydraulic head on the outer side of the retaining wall decreased and the head on the inner side increased. The height of the submerged surface drop increased with decreasing depth of insertion of the retaining wall. The depth of insertion of the retaining wall had a greater influence on the degree of diving surface drop than the pit radius.

Uniform approximation of 2D Navier-Stokes equations with vorticity creation by stochastic interacting particle systems

We consider a stochastic interacting particle system in a bounded domain with reflecting boundary, including creation of new particles on the boundary prescribed by a given source term. We show that such particle system approximates 2D Navier–Stokes equations in vorticity form and impermeable boundary, the creation of particles modeling vorticity creation at the boundary. Kernel smoothing, more specifically smoothing by means of the Neumann heat semigroup on the space domain, allows to establish uniform convergence of regularized empirical measures to (weak solutions of) Navier–Stokes equations.

Effects of Neumann and Robin boundaries on the thermal instability

AbstractThe thermo convective instability of the Darcy-Benard problem (DB) using Robin (third-kind) thermal conditions is investigated here. We consider a viscous Newtonian fluid saturating a porous layer in which the layer is sandwiched between two impermeable boundaries. The upper and the lower walls are modelled in the form of the Neumann (second-kind) and the Robin (third-kind) thermal conditions, respectively. The difference in the temperature distribution between both phases allows the lack of a local thermal equilibrium model to be present. As a consequence, the third kind of thermal condition brings about one extra dimensionless parameter of the Biot number to the usual one of the inter-heat transfer coefficient and the thermal conductivity ratio. The normal modes method adopted in a linear stability analysis gives rise to perturbed governing equations. The eigenvalue problem is handled numerically as a result of the perturbed governing equations leading to the marginal stability condition.

Temporal to spatial instability in a flow system: a comparison

AbstractThe definitions of temporal instability and of spatial instability in a flow system are comparatively surveyed. The simple model of one-dimensional Burgers’ flow is taken as the scenario where such different conceptions of instability are described. The temporal analysis of instability stems from Lyapunov’s theory, while the spatial analysis of instability interchanges time and space in defining the evolution variable. Thus, the growth rate parameter for temporally unstable perturbations of a basic flow state is to be replaced by a spatial growth rate when a coordinate assumes the role of evolution variable. Finally, the idea of spatial instability is applied to a Rayleigh-Bénard system given by a fluid-saturated horizontal porous layer with an anisotropic permeability and impermeable boundaries kept at different uniform temperatures.

Stabilized immersed isogeometric analysis for the Navier–Stokes–Cahn–Hilliard equations, with applications to binary-fluid flow through porous media

Binary-fluid flows can be modeled using the Navier–Stokes–Cahn–Hilliard equations, which represent the boundary between the fluid constituents by a diffuse interface. The diffuse-interface model allows for complex geometries and topological changes of the binary-fluid interface. In this work, we propose an immersed isogeometric analysis framework to solve the Navier–Stokes–Cahn–Hilliard equations on domains with geometrically complex external binary-fluid boundaries. The use of optimal-regularity B-splines results in a computationally efficient higher-order method. The key features of the proposed framework are a generalized Navier-slip boundary condition for the tangential velocity components, Nitsche’s method for the convective impermeability boundary condition, and skeleton- and ghost-penalties to guarantee stability. A binary-fluid Taylor–Couette flow is considered for benchmarking. Porous medium simulations demonstrate the ability of the immersed isogeometric analysis framework to model complex binary-fluid flow phenomena such as break-up and coalescence in complex geometries.

Nonlinear consolidation analysis of saturated multi‐layered soil with continuous drainage boundary

AbstractContinuous drainage boundary is widely accepted to overcome the shortcoming of the traditional assumption of fully permeable or impermeable drainage boundary in consolidation theories. This study presents an analytical solution for one‐dimensional small‐strain nonlinear consolidation of saturated multi‐layered soil with constant consolidation coefficients under continuous drainage boundary condition. The proposed solution is validated by comparison with the existing solutions in literature, which shows that the existing solutions are special cases of this solution. A parametric study performed on saturated four‐layered soil with continuous drainage boundary indicates that the interface parameter and the loading stress ratio have great influences on the nonlinear consolidation of saturated multi‐layered soil. The present solution can be effectively applied to provide more reasonable design for soil foundation.

Bulges at vortical outflows

This paper constructs steady solutions of the two-dimensional Euler equations corresponding to a line source of vortical fluid on the impermeable boundary of a quiescent flow. The nonlinear, free-boundary problem is solved by mapping the flow domain to the hodograph plane. A vortex dipole or, equivalently, a source–sink doublet is superposed on the source leading to flow patterns that model the ballooning outflows observed where rivers and straits discharge into the open ocean and in the rotating flow experiments and numerical simulations designed to reflect these observations.

The Rayleigh–Bénard problem for water with maximum density effects

Linear stability and weakly nonlinear stability analyses are developed for Rayleigh–Bénard convection in water near 3.98 °C subject to isothermal boundary conditions. The density–temperature relationship (equation of state) is approximated by a cubic polynomial, including linear, quadratic, and cubic terms. The continuity equation, the Navier–Stokes momentum equation, the equation of state, and the energy equation constitute the governing system. Linear stability analysis is used to investigate how the maximum density property of water affects the onset of convective instability and the choice of unstable wave number for four different types of boundary conditions. Then, a weakly nonlinear stability study is done using the spectral Fourier method for isothermal tangential stress-free boundary conditions to quantify the heat transport of the system and demonstrate the transition from regular/periodic convection to chaotic convection. A Stuart-Ginzburg–Landau equation is obtained using the multiscale expansion method. Streamlines and isotherms are presented and analyzed. The influence of maximum density has been shown to delay the onset of instability and is, therefore, a stabilizing mechanism for thermal instability. Due to the maximum density, the onset of chaotic convection is also delayed. Among four different boundaries, the impermeable rigid boundaries require the highest Rayleigh number for instability to begin. Increasing boundary temperatures advance the onset of chaotic convection and improve the heat transport situation.

New Insights from Legacy Seismic Data regarding Basalt Elevations and Variability on the Hanford Site

Abstract Migration of groundwater contaminants in the Gable Gap area of the Hanford Site in southeastern Washington State is strongly influenced by the distribution and permeability of basalts that lie beneath an unconfined aquifer. Locally, folding and faulting of the Columbia River Basalt associated with the Yakima fold and thrust belt followed by erosion due to the Lake Missoula floods resulted in a complex basalt surface that represents either an impermeable lower boundary to the unconfined aquifer system or localized regions of increased permeability that potentially promote communication between the unconfined aquifer system and deeper, confined aquifer systems. Paleo-channels carved into the basalt by floodwaters are thought to provide preferential flow paths for groundwater contaminants. In 2011, a seismic landstreamer campaign was carried out to image the basalt surface and produced pre-stack depth migrated p-wave reflection images. The reflection images identified two large troughs that may represent paleo-channels and several areas of possible faulting. Here, the streamer data are re-analyzed using refraction travel-time and Rayleigh wave dispersion analyses to obtain images of compressional and shear wave velocities within the suprabasalt sediment sections and the upper basalt surface. The combined interpretation of reflection and seismic velocity images shows complexity in the basalt velocity and elevation, which varies by 50 m or more within the study area. These results, along with other ongoing geophysical investigations, will be used to inform the site geologic model and potentially guide placement of future boreholes needed to quantify vertical flow between the confined and unconfined aquifers.