Mass Conservation Research Articles

A staggered Lagrangian magnetohydrodynamics method based on subcell Riemann solver

This paper uses a general formalism to derive staggered Lagrangian method for 2D compressible magnetohydrodynamics (MHD) flows. A subcell method is introduced to discretize the MHD system and some Riemann problems over subcells are solved at the cell center and grid node respectively. In these solvers, only the fast-waves in all jumping relations are considered and thus the solution structure is simple. The discrete conservations of mass, momentum and energy are preserved naturally in the proposed numerical method. In order to meet the thermodynamic Gibbs relation in isentropic flows, an adaptive Riemann solver is implemented at the cell center, in which a criterion is proposed to reduce overheating errors in the rarefying problems and maintains the excellent shock-capturing ability simultaneously. It is worth to be noticed that the divergence-free condition is naturally satisfied in the Lagrangian method. Various numerical tests are presented to demonstrate the accuracy and robustness of the algorithm.

Computation of the sound transmission loss of heterogeneous periodic structure using the wave finite element-based methodology

In the present study, a Wave Finite Element-based method is introduced to estimate the Sound Transmission Loss (STL) of periodic structures with contrasting properties. This method addresses the precision and computational speed limitations of existing methodologies. It calculates the wave STL by applying a plane wave excitation from the ambient medium to a Unit Cell (UC), which is representative of the periodic structure. The STL under Diffuse Acoustic Field (DAF) is then computed by integrating the wave STL over all possible incidence angle ranges. The advantages of this methodology are demonstrated through various configurations, ranging from simple plates to complex laminated structures. Additionally, the study investigates the Mass Law of STL.

A vibroacoustic model for low-frequency sound transmission loss in circular membranes with added strip mass

Noise control strategies involve physical barriers in the transmission path. Conventional barriers conform to the mass law which states an inverse relation between sound transmission, barrier mass, and incident frequency. Practical scenarios for low-frequency noise attenuation require prohibitively thick barriers making them infeasible. Mass-loaded membranes exhibit marked differences in their dynamic nature from that of bare membranes as they do not necessarily conform to the mass law. Being thin, compact, and lightweight makes them geometrically ideal for most applications. The paper presents an analytical model based on the Newtonian approach for the vibroacoustic behavior of a pre-stretched elastic circular membrane with rigidly attached strip mass under normal incidence. The point collocation approach distributes the effect of the strip mass on the membrane as a collection of discretized concentrated loads along the interfacial boundary resulting in a summation that is easier to solve. The peak and dip frequencies of sound transmission are determined for circular membranes with eccentric and central strip mass. The present study evaluates strip mass-loaded membranes' capability to attenuate noise at low frequencies as an unconventional physical barrier.

A sub-wavelength metamaterial layer for reducing underwater noise radiation of marine structures

Reducing the underwater noise radiated by marine structures is a critical issue for improving submarine stealth or limiting the anthropogenic impact of commercial ships. In this study, we propose a lightweight passive solution based on a metamaterial to efficiently reduce the noise at low frequency (< 1000 Hz) that can be transmitted through the shell plating of a marine vessel. This solution is made of a soft acoustically impervious poro-elastic foam in which inclusions are periodically positioned. Added to a plate, this metamaterial outperforms the mass law in the sub-wavelength domain when separating two air domains. This performance is due to the periodic arrangement of inclusions in the foam, creating a vibro-acoustic bandgap. The aim of this study is therefore to assess this solution where the domain of the transmitted acoustic wave is water. Firstly, numerical results on an unbounded plate are validated alongside the theoretical model of a flexible partition. When the metamaterial layer is added to the plate, it is shown that a vibro-acoustic bandgap still exists in the transmitted wavenumber domain, and that this solution is a good candidate for achieving the objectives. Experimental measurements on a finite structure are then conducted and compared to numerical results

Numerical simulation of three-phase mud invasion using an epidermal effect model and adaptive time-stepping

Abstract The numerical simulation of reservoir mud invasion is widely used for studying the dynamic invasion process. To investigate the saturation changes of the three phases (water, oil, and mud filtrate) during mud infiltration into intact formations, this study presents a mathematical model for three-phase invasion in cylindrical coordinates. The principle of mud intrusion into the reservoir allows the derivation of the basic equation of three-phase mud seepage from Darcy's law and the law of mass conservation. This is followed by the derivation of the differential equations of pressure and three-phase saturation during mud intrusion. A numerical simulation program for the three-phase seepage flow of mud intrusion is written using the finite-difference method. An adaptive time-step algorithm is developed to address the inadaptability of the intrusion algorithm in the case of mud surges. Additionally, an epithermal effect algorithm is developed to address the problem of mud particles entering the stratum and affecting the absolute permeability. The results show that, as the porosity increases, the radial depth of intrusion decreases, along with a reduction in the invaded annulus range. It can be demonstrated that, when the reservoir pressure is maintained at a constant level, the size of the borehole pressure leads to an increase in the depth of radial intrusion and the extent of the intrusion annulus, under different differential pressure conditions.

Thermo-economic investigation and comparative multi-objective optimization of dual-pressure evaporation ORC using binary zeotropic mixtures as working fluids for geothermal energy application

This contribution performs an energy, exergy, and exergoeconomic (3E) analysis of a dual-pressure evaporation organic Rankine cycle system employing twenty different binary zeotropic mixtures as working fluids for power production from a geothermal field. To this end, the designed system is modeled, invoking the mass and energy conservation laws and the exergy and cost balance analyses. Specific Exergy Costing (SPECO) procedure is utilized to provide practical insights into the exergoeconomic aspect of the system. Comparative optimization based on the multi-objective genetic algorithm is accomplished for each mixture in order to simultaneously maximize the exergy efficiency and minimize the total cost rate using the design variables of pressure factor in low-pressure and high-pressure stages, mixture fraction, pinch point temperature differences in low-pressure and high-pressure heat exchangers, and degree of superheat in the high-pressure heat exchanger. In this regard, the Pareto frontiers are drawn for the system with all twenty different binary zeotropic mixtures. The optimal point for each mixture is obtained via the decision-making technique of LINMAP. Subsequently, the LINMAP is re-utilized to find the preferred mixture. The optimization results suggest the R123/C2Butene (96.89/3.11) mixture for this system as the optimum working fluid, considering a trade-off between a low-cost rate of $88.0651 per hr and a high exergy efficiency of 64.07 %. Finally, the exergy flow diagram is plotted to provide the exergy flow rate and the amount of exergy destruction in each segment of the system considering the optimal working fluid. In the proposed system, exergy destruction chiefly occurs within the low-pressure preheater with a value of 1061 kW, followed by the low-pressure turbine and condenser with magnitudes of about 669 kW and 266 kW, respectively.

Heat Transfer Flow of Ternary Hybrid Nanofluid (Al2o3-Zro2-Mgo) Over A Sinusoidal Wavy Surface

This study examines how the hybrid nanofluid over a vertically wavy surface enhances heat transmission. The flow through a porous media is investigated using Darcy law. The sine wave characterizes the non-uniform behaviour of the vertical wall. The governing equations1 for the conservation of mass, momentum in the x and y directions, and energy are obtained. With the help of the proper transformations, they are non-dimensionalized. The PDE is converted to an ODE using the Similarity transformation. The resulting ODEs are solved using the spectral collocation method, and the results are shown together with several nanoparticle thermos-physical parameters.

Characterizing the evolution of the Daguangbao landslide nearly 15 years after the 2008 Wenchuan earthquake by InSAR observations

The Daguangbao landslide (DGBL), the largest landslide triggered by the 2008 Ms 8.0 Wenchuan earthquake, has received much attention, but its long-term post-earthquake evolution and driving force of activity are still poorly understood. As the evolutionary behavior of the DGBL is complicated by the influence of mainshock, aftershocks and rainfall, it is of great significance to study the dynamics of the landslide. In this study, a systematic and comprehensive framework for assessing the long-term stability and risk of co-seismic landslides was proposed. Based on ALOS-1 and Sentinel-1 data, time-series InSAR technology was used to reveal the nearly 15-year post-seismic evolution characteristics of the DGBL at different stages, followed by the prediction of the stabilization time, the estimation of the landslide thickness and risk assessment. The first stage was identified as three years after the earthquake (2008–2011). During this stage, ALOS-1 results show that the deformation of DGBL was intense (300 mm/year) with uneven spatial distribution, and an aftershock (Ms 5.3), along with increased rainfall, triggered its acceleration in 2009. The second stage was the period from 2014 to 2022. For this stage, we used the mass conservation approach to invert the thickness of the DGBL, revealing that a new sliding surface and thickness center had formed following the co-seismic failure in 2008. Sentinel-1 time series results indicated that the DGBL remains active even 15 years after the Wenchuan earthquake, but the deformation of DGBL has significantly slowed down (50 mm/year). The stabilization time for different segments of DGBL was predicted to range from 2027 to 2040 according to an exponential model. Beyond the overall trend of recovery, seasonal movements (including localized acceleration in 2021) closely related to rainfall remained evident, but the impact of aftershocks on the DGBL was severely weakened over time. UAV and field survey results suggested that the risk of localized debris flows at DGBL still exists. Our study improves our understanding of the long-term evolutionary pattern of DGBL and provides an important reference for post-earthquake landslide risk assessment and disaster prevention.

Physics-informed neural networks for inversion of river flow and geometry with shallow water model

The river flow transports sediment, resulting in the formation of alternating sandbars in the riverbed. The underlying physics is characterized by the interaction between flow and river geometry, necessitating an understanding of their inseparable relationship. However, the dynamics of river flow with alternating sandbars are hard to understand due to the difficulty of measuring flow depth and riverbed geometry during floods with current technology. This study implements an innovative approach utilizing physics-informed neural networks (PINNs) to estimate important hydraulic variables in rivers that are difficult to measure directly. The method uses sparse yet obtainable flow velocity and water level data. The governing equations of motion, continuity, and the constant discharge condition based on the mass conservation principle are integrated into the neural network as physical constraints. This approach enables the completion of sparse velocity fields and the inversion of flow depth, riverbed elevation, and roughness coefficients without requiring direct training data for these variables. Validation was performed using model experiment data and numerical simulations derived from these experiments. Results indicate that the accuracy of the estimations is relatively robust to the number of training data points, provided their spatial resolution is finer than the wavelength of the sandbars. The inclusion of mass conservation as a redundant constraint significantly improved the convergence and accuracy of the model. This PINNs-based approach, using measurable data, offers a new way to quantify complex river flows on alternating sandbars without significant updates to conventional methods, providing new insights into river physics.

Development of a smoothed particle hydrodynamics model for porous media flows with enhanced volume conservation and the revisit of the mass conservation equation

Porous media exist extensively in hydraulic and coastal engineering structures, while the modeling of wave/flow interaction with porous media remains challenging. This work develops a smoothed particle hydrodynamics (SPH) model for accurately simulating wave/flow interaction with porous media. The mass and momentum conservation equations incorporating the mixture theory are adopted. The resistant forces of the solid skeleton of porous media on fluid flows are described by the nonlinear empirical formula. The research contributions of the work lie in two aspects. First, two categories of mass conservation equations for porous media flow are revisited and analyzed to examine the influences of the local time derivative term of fluid volume fraction on simulation results. Second, the Volume Conservation Shifting scheme is, for the first time, introduced into SPH to enhance volume conservation for simulating porous media flows. The developed SPH model is validated by an analytical case of seepage flows in a U-tube with porous media and then applied to study four benchmark examples involving both saturated and unsaturated porous media, i.e., dam-break flow through a crushed stone dam, rapid seepage flow through a rockfill dam, solitary wave propagation over a porous seabed, and solitary wave propagation over a submerged porous breakwater. The morphological features and dynamic pressure heads of the porous media flows have been satisfactorily predicted, demonstrating the good accuracy and enhanced volume conservation of the developed SPH model.

An operational discontinuous Galerkin shallow water model for coastal flood assessment

Hydrodynamic modeling for coastal flooding risk assessment is a highly relevant topic. Many operational tools available for this purpose use numerical techniques and implementation paradigms that reach their limits when confronted with modern requirements in terms of resolution and performances. In this work, we present a novel operational tool for coastal hazards predictions, currently employed by the BRGM agency (the French Geological Survey) to carry out its flooding hazard exposure studies and coastal risk prevention plans on International and French territories. The model, called UHAINA (wave in the Basque language), is based on an arbitrary high-order discontinuous Galerkin discretization of the nonlinear shallow water equations with SSP Runge–Kutta time stepping on unstructured triangular grids. It is built upon the finite element library AeroSol, which provides a modern C++ software architecture and high scalability, making it suitable for HPC applications. The paper provides a detailed development of the mathematical and numerical framework of the model, focusing on two key-ingredients : (i) a pragmatic P0 treatment of the solution in partially dry cells which garantees efficiently well-balancedness, positivity and mass conservation at any polynomial order; (ii) an artificial viscosity method based on the physical dissipation of the system of equations providing nonlinear stability for non-smooth solutions. A set of numerical validations on accademic benchmarks is performed to highlight the efficiency of these approaches. Finally, UHAINA is applied on a real operational case of study, demonstrating very satisfactory results.

An Electro-Chemo-Mechanic Model Resolving Delamination between Components in Complex Microstructures of Solid-State Batteries

A novel approach is presented to model delamination and recontacting at internal interfaces of three-dimensional resolved microstructures of solid-state batteries. To resolve the effect of delaminations, we incorporate the consistent enforcement of contact constraints at those interfaces using Nitsche’s method. The model incorporates charge, mass, and momentum conservation to consider electrochemistry, solid mechanics, and their interaction. After introducing and verifying the model, we examine various scenarios to quantify the effect of delaminations at the electrode-solid electrolyte interface on cell performance. The simulations show that increased mechanical stack pressure during cycling mitigates delamination tendencies at the electrode-solid electrolyte interface. Consistent with existing literature, the simulations demonstrate that delaminations increase the internal resistance and reduce the amount of transferred charge. In contrast to experimental analyses, the presented model allows quantitative and in-depth investigations of delamination effects. Furthermore, our analysis of two cell concepts—one assembled in the discharged state and another assembled in the charged state—indicates that half-cells assembled in an initial state from which the active material shrinks in volume upon first charge or discharge show a higher delamination risk at the electrode-solid electrolyte interface. The study highlights the critical relationship between solid mechanics and electrochemistry in consideration of delamination phenomena in solid-state batteries, offering valuable insights for optimizing battery design and performance.

Mathematical Modelling of Hydrogen-Enriched Combustion

This article presents a mathematical model developed in ANSYS CFX 17.2 software to analyse the combustion process of hydrogen-enriched natural gas. The study investigates the concentrations of various flue gas components at hydrogen enrichments of 10% and 20%, compared to a baseline of pure natural gas. A three-dimensional model of the experimental setup was created allowing for detailed simulation of combustion dynamics under controlled conditions. The model incorporates the governing equations for mass conservation, momentum, energy, and turbulence, facilitating comprehensive analysis of combustion behaviour and pollutant formation. The simulations reveal that increased hydrogen enrichment raises combustion temperatures but also leads to higher carbon monoxide (CO) emissions due to incomplete combustion. The results indicate a corresponding decrease in carbon dioxide (CO₂) emissions, showcasing the environmental implications of hydrogen mixing. However, nitrogen oxide (NOx) emissions increase significantly with higher combustion temperatures. The mathematical model was validated against experimental data, demonstrating less than 10% deviation in temperature measurements and providing accurate predictions for pollutant concentrations.

Inundation Processes with Active Sediment Transportation in the Floodplain of West Rapti River, Nepal

The present study discusses flood hazard characteristics in the lower reaches of the West Rapti River based on the results obtained from field surveys and numerical computations using depth averaged 2-D numerical models for flood flow and associated sediment transportation. To evaluate the inundation process with sediment erosion and deposition in the floodplain, a new erosion term was introduced into the mass conservation equations for suspended sediment and bed sediment. The results obtained from numerical computations indicated that field data on the spatial distributions of depths for inundation, and sediment erosion and deposition can be evaluated by the numerical model. Thus, numerical predictions were performed for the inundated areas, and the accumulated volumes of sediment erosion/deposition for floods with return periods of 50, 100, and 200 years, as a step towards damage assessment and risk assessment due to floods with active sediment transportation in the floodplains.

3D-Numerical simulation of free convection inside a cubical cavity filled with non-Newtonian-Bingham fluid

This work focuses on a numerical study of the natural convection of a non-Newtonian viscoplastic fluid within a cubic enclosure. The viscoplastic behavior is described by the Bingham model. The considered three-dimensional convective flow is confined within a cavity, subjected to a horizontal temperature gradient, where the vertical walls have two imposed temperatures while the rest of the walls are adiabatic. The Navier-Stokes equations, along with the mass and energy conservation equations, are numerically solved. Fluid flow and heat transfer characteristics are systematically studied over a wide range of Rayleigh numbers Ra (103 - 106) and Bingham number Bn (0 - 20). Finally, comparisons were made with previous results obtained in two dimensions in order to analyze the existence of a three-dimensional effect on the flow of the Bingham fluid. The results show that the Nusselt number decreases with the increase of the Bingham number, and for the large values ​​of the latter the heat transfer is done by conduction. It is also noteworthy that the critical Bn of the 2D model is higher than that of the 3D model, which confirms the existence of the three-dimensional effect. This is attributed to the presence of a wall along the Z axis which hinders and limits the flow of fluid within the enclosure.

Leaching Thermodynamics of Low-Grade Copper Oxide Ore from [(NH4)2SO4]-NH3-H2O Solution.

This paper describes a highly alkaline low-grade copper oxide ore. Copper can be selectively leached out while other metals are retained. A thermodynamic model of the CuO-(NH4)2SO4-NH3-H2O system was established for the leaching of tenorite (CuO) under conditions of mass and charge conservation. MATLAB's fitting functions, along with the diff and solve functions, were used to calculate the optimal ammonia concentration and total copper ion concentration of tenorite under different ammonium sulfate concentrations. The effects of various ammonia-ammonium salt solutions (ammonium sulfate, ammonium carbonate, ammonium chloride) on the copper leaching rate were investigated. Results show that under the conditions of an ammonia concentration of 1.2 mol/L, an ammonia-ammonium ratio of 2:1, a liquid-solid ratio of 3:1, a temperature of 25 °C, and a leaching time of 4 h, the copper leaching rate from the ammonium sulfate and ammonium chloride solutions reaches 70%, which is slightly higher than that of ammonium carbonate. Therefore, an ammonia-ammonium sulfate system is selected for leaching low-grade copper oxide due to its lower corrosion to equipment compared to the chlorination system. The impact of this study on industrial applications includes the potential to find more sustainable and cost-effective methods for resource recovery. The industry can reduce its dependence on resources and mitigate its environmental impact. Readers engaged in low-grade oxidized copper research will benefit from this study.

Sound Insulation Characteristics of Sandwich Thin-Plate Acoustic Metamaterial: Analysis and Optimization

Addressing the demand for low-frequency noise control in ships and aiming to overcome the limitations imposed by the mass law of traditional materials, a sandwich thin-plate acoustic metamaterial (SPAM) was developed in this study. This structure is characterized by its simplicity and superior sound insulation performance. A sound insulation test was conducted to validate the exceptional low-frequency acoustic suppression capability of SPAM, and the effectiveness of the analytical model was also demonstrated. Subsequently, based on this model, a sensitivity analysis of the sound insulation characteristics of the SPAM relative to structural parameters was carried out. For the optimization process, the Logistic-Sine fusion chaotic mapping was employed to refine the dung beetle optimizer (DBO), enhancing the initial population distribution. The improved dung beetle optimizer (IDBO) was then used to further optimize and elevate the sound insulation performance of the SPAM. The outcomes indicate that the IDBO boasts superior optimization proficiency and accelerated convergence, while the optimized SPAM exhibits more remarkable sound insulation capabilities. Within the frequency range of 100–315[Formula: see text]Hz, the average sound transmission loss (STL) has increased by 11.94[Formula: see text]dB when compared to the pre-optimization values.

Effect of Different Basal Media and Organic Supplements on In Vitro Seedling Development of the Endangered Orchid Species Dendrobium moniliforme (L.) Swartz

The orchid Dendrobium moniliforme faces endangerment due to habitat loss and illegal harvesting, necessitating the development of an optimized artificial propagation system to aid conservation and reintroduction efforts. This study evaluated the effects of three plant growth media, namely Murashige and Skoog (MS), Hyponex, and Orchid Maintenance Medium (OMM) (P668), and various organic additives (apple homogenate, banana homogenate, and coconut water) on the in vitro seedling growth of D. moniliforme. The results reveal that, in early postgermination stages, seedlings achieve maximum growth in the Hyponex medium, with a fresh weight (92 mg) and root length (2.7 cm) approximately 20-fold greater than those in the MS medium and OMM. After 6 months, for seedlings grown in MS medium and OMM with banana (50 g·L−1), the mean fresh weights were 29 and 107 mg, respectively; however, the highest biomass was observed in seedlings grown in the Hyponex medium with coconut water (50 mL·L−1), exhibiting a mean fresh weight of 201 mg. This study highlights Hyponex medium with coconut water as the most effective combination for promoting D. moniliforme growth and identifies suitable organic supplements for the in vitro cultivation of seedlings from asymbiotic seed culture. This propagation system offers valuable technical support for the mass production and conservation of this epiphytic orchid.

Mass conservation in the validation of fluid-poroelastic structure interaction solvers

Benchmark problems commonly used to test numerical methods for fluid-poroelastic structure interaction often rely on simple examples constructed using the method of manufactured solutions. In this work, we show that such examples are not adequate to demonstrate the performance of the method, especially in cases when the poroelastic system is written in the primal or primal-mixed formulation, and when the dynamics of the poroelastic structure are driven only by dynamic loading from the fluid, which often occurs in biomedical applications. In those cases, the only forcing on the structure comes from the interaction with the fluid at the fluid-structure interface, where the coupling conditions are imposed. One of those conditions is a kinematic condition which enforces the conservation of mass. If this condition is not accurately satisfied, the resulting dynamics might lead to highly inaccurate results in the entire domain. We present three benchmark problems: Example 1 is based on the method of manufactured solutions; Example 2 is based on parameters used in geomechanics; and Example 3 is a benchmark problem with parameters from hemodynamics. Using these examples, we test the performance of the primal, primal-mixed and dual-mixed formulations. While all methods perform well in the first two examples, the primal and primal-mixed formulations exhibit large errors in Example 3, where the densities of the fluid and solid are comparable, and the structure dynamics is purely driven by the fluid loading. To recover the accuracy, we propose to use the primal and primal-mixed methods with a penalty term, which helps to enforce the conservation of mass.

Genetic-algorithm-assisted design of chiral honeycomb membrane acoustic metamaterials for broadband noise suppression

Low-frequency sound wave reduction is hardly feasible for traditional sound absorbers such as porous media. In contrast, locally resonant acoustic metamaterials act as spatial frequency filters, effectively reducing low-frequency noise. However, these materials can have narrow bandgaps, add extra mass to the main system, and function only within a specifically adjusted frequency range. Therefore, this paper proposes a methodology for designing three-dimensional (3D) chiral honeycomb membrane-type acoustic metamaterials (MAM) based on acoustic circular dichroism (ACD), negative effective mass, and local resonance mechanisms (LRM). The paper also uses the genetic algorithm (GA) to maximize sound transmission attenuation and widen bandgaps. The accuracy of the simulations is validated with available experimental data. The key idea of the present study is to automatically design a MAM structure using modern optimization tools. A developed GA aims to maximize the average sound transmission loss (STL) across the desired low-frequency range of 0–850 Hz by optimizing the value of structural parameters associated with the configurations of masses, including rotation and linear offset, as well as their geometrical dimensions, including length and width. COMSOL Livelink with MATLAB is employed as a practical co-simulation tool to find an optimum value for structural parameters. Results indicate a 35% improvement in average STL along with an ultra-wide bandgap with a 507% bandgap coverage factor (BGCF) in the frequency range of interest, verifying the reliability of the developed algorithm. In addition, sound mitigation incidence is justified by exploring the negative effective parameters of the unit cell and displacement vector fields. The proposed designs demonstrate superior performance as both initial and optimized models broke the mass law within the investigated frequency range. Finally, the effect of the selected geometrical parameters on the objective function is observed through sensitivity analysis. This study presents the practical use of optimization algorithms to develop MAMs.