Gas Flow Model Research Articles

A peridynamics approach modeling gas flow in porous media with damaged regions

The study of gas flow within porous media, particularly those characterized by complex pore-fracture networks, is critical for applications in fields such as shale gas engineering, gas extraction, and hydrogeology. This paper proposes a convenient and novel peridynamics approach to describe gas flow behavior in fracture regions and transition regions between fractured and intact regions in porous media, where the bonds naturally describe the interactions between material points in damaged areas. For implementation, we interpolate the permeability of the bonds in the transition region by using local damage values, and adopt a meshfree discretization approach that does not require additional mesh refinement for damaged or fractured regions. Numerical examples are provided and compared with the traditional finite element method to verify the accuracy and effectiveness of the proposed method.

Lattice Boltzmann Model for Rarefied Gaseous Mixture Flows in Three-Dimensional Porous Media Including Knudsen Diffusion

Numerical modeling of gas flows in rarefied regimes is crucial in understanding fluid behavior in microscale applications. Rarefied regimes are characterized by a decrease in molecular collisions, and they lead to unusual phenomena such as gas phase separation, which is not acknowledged in hydrodynamic equations. In this work, numerical investigation of miscible gaseous mixtures in the rarefied regime is performed using a modified lattice Boltzmann model. Slip boundary conditions are adapted to arbitrary geometries. A ray-tracing algorithm-based wall function is implemented to model the non-equilibrium effects in the transition flow regime. The molecular free flow defined by the Knudsen diffusion coefficient is integrated through an effective and asymmetrical binary diffusion coefficient. The numerical model is validated with mass flow measurements through microchannels of different cross-section shapes from the near-continuum to the transition regimes, and gas phase separation is studied within a staggered arrangement of spheres. The influence of porosity and mixture composition on the gas separation effect are analyzed. Numerical results highlight the increase in the degree of gas phase separation with the rarefaction rate and the molecular mass ratio. The various simulations also indicate that geometrical features in porous media have a greater impact on gaseous mixtures’ effective permeability at highly rarefied regimes. Finally, a permeability enhancement factor based on the lightest species of the gaseous mixture is derived.

Modeling the stability of air flows in inclined workings in case of fire

Purpose. Development of a mathematical model and study of the processes occurring during conveyor belt fires in inclined mines to determine the mechanism of air flow distribution under appropriate conditions. Methods. Practical measurements of the distribution of air flows in an inclined conveyor operated at the mining and processing plant of PJSC ArcelorMittal Kryvyi Rih were carried out. Based on the obtained data, a mathematical model was crea-ted, which was then used to perform Computational Fluid Dynamics (CFD) modeling of gas flows in the mine under normal conditions and in the event of a fire with a thermal capacity of 9 MW. Findings. The study reveals the peculiarities of gas flows during the combustion of a conveyor belt in inclined workings, as well as the influence of turbulence on the flow, changes in the density of gases during heating, and the impact of gravity on the distribution of gases in the cross-section and along the length of the workings. A fire centre with a heat output of 9 MW has a significant impact on the distribution of air flows. The phenomenon of thermal expansion results in a 59.2% increase in the volume of gases behind the fire. The thermal expansion of gases and their low density have a significant impact on the formation of gas flows in inclined workings. As the jet moves away from the centre of the fire, the velocity of the jet gradually increases, reaching a value of 12.4 m/s. This results in a notable alteration in the distribution of total pressure across adjacent workings, accompanied by an increase in flow turbulence. Consequently, the mass of air exiting the right branch is observed to have a five-fold increase in comparison to the pre-fire state. The overturning of the jet from the left branch of the workings gives rise to the exclusive distribution of combustion products along the right branch. Originality. The study helps to understand the mechanism of jet overturning and the peculiarities of the distribution of combustion products in case of fire in inclined conveyor workings. Practical implications. The results of the research allow us to predict the probability of fire, identify the most dangerous areas for fire, and plan the most rational actions for firefighting in specific unique conditions.

Effect of Blade Material of Steam Turbine Rotor on Aeroelastic Characteristics

Elements of powerful steam turbines are subjected to significant unsteady loads, in particular the rotor blades of the last stages. These loads, in some cases, can cause self-excited oscillations, which are extremely dangerous and have a negative impact on the efficiency and service life of the blade cascade. Therefore, when designing new or modernizing existing steam turbine stages, it is recommended to study the aeroelastic characteristics of the blades. The conditions for the occurrence of self-excited oscillations are influenced by both the geometric characteristics and the alloy from which the blade is made. To determine the effect of the blade material on the aeroelastic behaviour, a numerical analysis of the aeroelastic characteristics of the last stage blades made of steel and titanium alloy was performed. For the analysis, the method of simultaneous modeling of unsteady gas flow through the blade cascades and elastic vibrations of the blades (coupled problem) was used, which allows obtaining the amplitude-frequency spectrum of the interaction of unsteady loads and blade vibrations. The paper presents the results of numerical analysis for harmonic oscillations with a given amplitude and a given inter-blade phase angle, as well as for the regime of coupled vibration of blades under the action of unsteady aerodynamic forces. The dependences of the aerodamping coefficient on the inter-blade phase angle and the distribution of the coefficient along the blade are presented. The results of modeling the coupled vibration of the blades for the first six natural forms are presented in the form of a time-evolving displacement of the blade peripheral section, as well as forces and moments acting on the peripheral section. The corresponding amplitude-frequency spectra of displacements and loads in the peripheral section are also presented. The analysis of the results showed an insignificant difference in the characteristics of the proposed blade materials. For the first natural form of blade oscillations, the possibility of self-excited oscillations was found, and for the second form, there are conditions for the appearance of stable self-oscillations.

Novel irreversibility modeling of non-homogeneous charged gas flow by solving Maxwell–Boltzmann PDEs system: irreversibility analysis for multi-component plasma

Novel irreversibility modeling of non-homogeneous charged gas flow by solving Maxwell–Boltzmann PDEs system: irreversibility analysis for multi-component plasma

A multiscale stochastic particle method based on the Fokker-Planck model for nonequilibrium gas flows

The Fokker-Planck (FP) model characterizes the intermolecular collisions as continuous stochastic processes in velocity space. Compared to the Direct Simulation Monte Carlo (DSMC) method, which is grounded in the Boltzmann equation, the stochastic particle method based on the FP model, referred to as the SP-FP method, demonstrates a relative improvement in computational efficiency. However, the traditional SP-FP method, utilizing operator splitting scheme, encounters analogous limitations to DSMC, thereby limiting the application of large temporal-spatial discretization for simulating near-continuum and continuum flows. In this study, two critical advancements are introduced to improve the traditional SP-FP method. First, the exact integration scheme of the ellipsoidal-statistical FP (ESFP) model is derived, enabling the replication of the theoretical solutions for homogeneous relaxation with any time step. Furthermore, leveraging the integration scheme of the ESFP model, we propose a Multiscale Stochastic Particle (MSP) method. The MSP method quantifies the numerical errors stemming from the operator splitting scheme and corrects them in the relaxation step. This capability allows the MSP method to be employed with larger temporal-spatial discretization for inhomogeneous problems, achieving second-order accuracy while retaining implementation simplicity. Application of the MSP method to various benchmark problems, including Couette flow, Fourier flow, Poiseuille flow, Sod tube flow, Lid-driven cavity flow, and flow through a slit, demonstrates its promise for simulating multiscale nonequilibrium gas flows with high computational efficiency and accuracy.

Dynamic gas emission during coal seam drilling under the thermo-hydro-mechanical coupling effect: A theoretical model and numerical simulations

The potential risk of coal and gas outbursts has increased with the depth of coal mining, posing the threat of heavy casualties, vast economic losses, and harm to the ecological environment. Considering the limitations of existing coal and gas outburst prediction methods, novel indicators or methods are needed. In this study, a fully coupled dynamic drilling gas emission THM model of gas diffusion, seepage, and flow is established, and the reliability of the model was verified by the measured data. The validated model was applied to single-factor and multi-factor impact analysis of dynamic drilling gas emission. The simulation results showed that (1) During the drilling process, the increase in permeability is mainly attributed to the coal seam damage and disturbance caused by the borehole and the coupling effects of the THM model, which increase the porosity around the borehole. Driven by the pressure gradient and temperature gradient, the gas pressure and temperature of the coal seam around the borehole show a conical distribution. (2) In the single-factor analysis, increasing the values of coal seam parameters (initial gas pressure, initial permeability, and initial coal temperature) and drilling parameters (borehole radius) will promote gas emissions in the drilling process to different degrees. The most significant promoting effect is the initial permeability, and the weakest is the initial coal temperature. (3) The response surface analysis results of the four factors show that the interaction between initial coal temperature C and borehole radius D is the least significant, and the interaction between initial gas pressure A and initial permeability B is the most significant. Meanwhile, the established multiple regression model characterizes the relationship between borehole gas emissions and initial coal seam gas pressure, and the idea of using drilling gas emission volume to predict coal and gas outbursts was proposed.

Gas flow in frozen hydrate-bearing sediments exposed to compression and high-pressure gradients: Experimental modeling

Changes in temperature and pressure patterns in gas- and hydrate-saturated permafrost caused by natural geodynamic processes or human impacts can lead to the active flow of gas through unfrozen zones, and its explosive emission is often accompanied by crater formation. Gas flow and accumulation in the shallow permafrost can be explained by the conditions of gas pressure equal to or exceeding the overburden pressure and high-pressure gradients. For the first time, filtration tests were conducted on ice- and hydrate-saturated rocks under uniaxial compression at various negative temperatures using a developed methodology. The modeling of gas flow in a mixture of ice-saturated sand and 25 % montmorillonite at gas pressure gradients within 2 MPa, shows that gas flow can start at warm negative temperatures near the thaw point. Pore hydrate formation in frozen sand heated to positive temperatures and frozen back led to a linear decrease in gas permeability by up to eight times. However, the behavior of gas permeability during hydrate dissociation is nonlinear as it increased within a few hours after the onset of dissociation, but then decreased exponentially in the following 24 h.

High-velocity compressible gas flow modelling through porous media considering the quadratic pressure gradient: Part 2. experimental investigations and numerical analysis

This research investigates reliability of existing methods for analysis of transient Pressure Pulse Decay (PPD) test results. Analysis of experimental data reported by previous studies using existing conventional analysis methods revealed significant discrepancies, in some cases with more than 300% error between different experiments on the same sample. New experiments (Knudsen number ranged from 0.22 to 0.34) were designed and conducted in our laboratory, reducing the uncertainty by eliminating slip flow and net stress effects under low and high-pressure conditions. These experimental results aligned much better with the recently proposed analytical solution for improved interpretation of PPD experimental results. The differences are around 25% between different pulses, confirming the reliability of the conducted experiments and newly proposed methodology.Numerical simulations using a commercial software package were conducted to complement experimental and analytical findings. The simulator, which demonstrated good agreement with the proposed analytical solution, facilitated conducting sensitivity analyses on permeability variations and compressive storage capacity effects. These simulations validated the findings of the proposed analytical solution, which accounts for both pressure difference and absolute pressure values, and explains the discrepancies observed in lower pressure scenarios using conventional methods.Overall, this study presents a comprehensive framework integrating experimental, analytical, and numerical approaches to enhance our understanding and better analysis of transient PPD test results for compressible gas flows. The findings also offer a more robust approach for analysing gas flow behaviour in porous media.

A three-level model for integration of hydrogen refuelling stations in interconnected power-gas networks considering vehicle-to-infrastructure (V2I) technology

The coupling with natural gas networks creates an excellent opportunity for renewable-rich power systems to facilitate the utilisation of renewable energy resources; on the other hand, with the increase in employment of fuel cell vehicles (FCVs), the number of hydrogen refuelling stations (HRSs) is increasing. The integration of HRSs in electric distribution systems may impact the operation of electric distribution systems. Through vehicle-to-infrastructure (V2I) technology, vehicles may exchange information with HRSs and know hydrogen prices. The operation of the coupled power and natural gas networks with integration of green HRSs, considering the model of FCVs has not been investigated in the literature, so, it has been set as the goal of this paper. To avoid the challenges of nonlinear gas flow model, they are linearized through piecewise linearisation. The case study is a 33-bus electric distribution system, coupled with a 14-node gas distribution network; each HRS includes a battery, a hydrogen tank, an electrolyzer, a PV and a wind turbine. MILP models have been used for FCVs, HRSs and power-gas networks. CPLEX solver is used for solving the developed MILP models. The results show that the total cost of the coupled electricity-gas network is $760.37 and the refuelling cost of each FCV is $17.30. The results indicate that both electric and hydrogen storage systems enhance the flexibility of HRSs, enabling efficient utilisation of PV modules and wind turbines, so, only in few hours, HRSs need to purchase electricity from electric distribution system; that is why each HRS makes a considerable profit of $519 per day. The achieved results also indicate that the pressure of all gas nodes and gas flow of all pipelines fall within their prespecified range.

Experimental research on gas flow and aerosol scrubbing characteristics under low Weber number pool scrubbing conditions

Radioactive aerosol may be released from the molten core during a severe accident in a nuclear power plant. Pool scrubbing, a representative aerosol scrubbing process incorporated in several severe accident scenarios, has been modeled in MELCOR. Under gas injection conditions with a low Weber number, gas flow regimes above the nozzle are globule and swarm. Based on visual scrubbing experiments, we investigated the gas flow and aerosol scrubbing characteristics under low-Weber-number injection conditions. We systematically analyzed the relationship between scrubbing efficiency and gas flow behavior through experiments and the applicability of the aerosol scrubbing model in MELCOR to different pool scrubbing conditions. Also, the variation of the globule and swarm shapes with the inlet pressure was obtained to evaluate the applicability of the gas flow model in MELCOR. Additionally, the bubble size distribution and Sauter average diameter were used to characterize the swarm flow characteristics based on the image processing results. Finally, we used a modified scrubbing model to compare the experimental results and evaluate the most suitable swarm characterization parameters.

Bayesian learning of gas transport in three-dimensional fracture networks

Modeling gas flow through fractures of subsurface rock is a particularly challenging problem because of the heterogeneous nature of the material. High-fidelity simulations using discrete fracture network (DFN) models are one methodology for predicting gas particle breakthrough times at the surface but are computationally demanding. We propose a Bayesian machine learning method that serves as an efficient surrogate model, or emulator, for these three-dimensional DFN simulations. Our model trains on a small quantity of simulation data with given statistical properties and, using a graph/path-based decomposition of the fracture network, rapidly predicts quantiles of the breakthrough time distribution on DFNs with those statistical properties. The approach, based on Gaussian Process Regression (GPR), outputs predictions that are within 20%–30% of high-fidelity DFN simulation results. Unlike previously proposed methods, it also provides uncertainty quantification, outputting confidence intervals that are essential given the uncertainty inherent in subsurface modeling. Our trained model runs within a fraction of a second, considerably faster than reduced-order models yielding comparable accuracy (Hyman et al., 2017; Karra et al., 2018) and multiple orders of magnitude faster than high-fidelity simulations.

A Coupled Model of Multiscaled Creep Deformation and Gas Flow for Predicting Gas Depletion Characteristics of Shale Reservoir at the Field Scale

The viscoelastic behavior of shale reservoirs indeed impacts permeability evolution and further gas flow characteristics, which have been experimentally and numerically investigated. However, its impact on the gas depletion profile at the field scale has seldom been addressed. To compensate for this deficiency, we propose a multiscaled viscoelasticity constitutive model, and furthermore, a full reservoir deformation–fluid flow coupled model is formed under the frame of the classical triple-porosity approach. In the proposed approach, a novel friction-based creep model comprising two distinct series of parameters is developed to generate the strain–time profiles for hydraulic fracture and natural fracture systems. Specifically, an equation considering the long-term deformation of hydraulic fracture, represented by the softness of Young’s modulus, is proposed to describe the conductivity evolution of hydraulic fractures. In addition, an effective strain permeability model is employed to replicate the permeability evolution of a natural fracture system considering viscoelasticity. The coupled model was implemented and solved within the framework of COMSOL Multiphysics (Version 5.4). The proposed model was first verified using a series of gas production data collected from the Barnett shale, resulting in good fitting results. Subsequently, a numerical analysis was conducted to investigate the impacts of the newly proposed parameters on the production process. The transient creep stage significantly affects the initial permeability, and its contribution to the permeability evolution remains invariable. Conversely, the second stage controls the long-term permeability evolution, with its dominant role increasing over time. Creep deformation lowers the gas flow rate, and hydraulic fracturing plays a predominant role in the early term, as the viscoelastic behavior of the natural fracture system substantially impacts the long-term gas flow rate. A higher in situ stress and greater formation depth result in significant creep deformation and, therefore, a lower gas flow rate. This work provides a new tool for estimating long-term gas flow rates at the field scale.

A second-order particle Fokker-Planck model for rarefied gas flows

The direct simulation Monte Carlo (DSMC) method has become a powerful tool for studying rarefied gas flows. However, for the DSMC method to be effective, the cell size must be smaller than the mean free path, and the time step smaller than the mean collision time. These constraints make it difficult to use the DSMC method in multiscale rarefied gas flows. Over the past decade, the particle Fokker-Planck (FP) method has been studied to address computational cost issues in the near-continuum regime. To capture the main features of the Boltzmann equation, various FP models have been proposed, such as the quadratic entropic FP (Quad-EFP) and the ellipsoidal statistical FP (ESFP). Nevertheless, few studies have clearly demonstrated that the FP method offers a computational advantage over the DSMC method without sacrificing accuracy. This is because conventional particle FP methods have employed first-order accuracy schemes. The present study proposes a unified stochastic particle ESFP (USP-ESFP) model. This model improves the accuracy of shear stress and heat flux predictions. Additionally, a spatial interpolation scheme is introduced to the particle FP method. The numerical test cases include relaxation problem, Couette flows, Poiseuille flows, velocity perturbation, and hypersonic flows around a cylinder. The results show that the USP-ESFP model agrees well with both analytical and DSMC results. Furthermore, the USP-ESFP model is found to be less sensitive to cell size and time step than the DSMC method, resulting in a factor of four speed-up for the considered hypersonic flow around a cylinder.

Additively manufactured, long, serpentine submillimeter channels by combining binder jet printing and liquid-phase sintering

Metallic microfluidic devices made from powder-bed additive manufacturing systems have received increasing attention, but their feasible channel geometry and complexity are often limited by lack of an effective approach to removing trapped powder particles within the channels or conduits of the sintered parts. Here, we present an innovative approach to fabricating long serpentine, high-aspect-ratio submillimeter channels made of stainless steel 316L (SS) by binder jet printing (BJP) and liquid-phase sintering. We leverage the unique nature of the BJP process, that is printing and consolidation steps are decoupled, enabling us to join two or more parts during the sintering step. Instead of constructing the channel device as a single part, we print multiple parts for easy powder removal and later join them to form enclosed channels. The key innovation lies in adding sintering additives like boron nitrides (BN) to the SS stock powder—at the SS/BN interfaces, liquid phase is locally generated at temperature much lower than the SS melting temperature, facilitating the bonding of the multiple parts as well as the consolidation of parts for near-full density. We systematically vary the sintering temperature to show how it affects the joining quality and the channel shape distortion. The joining quality such as the fracture strengths of the joined samples is measured by a pull test while the shape distortion is characterized by various imaging techniques. The feasibility of the proposed approach is demonstrated by fabricating a 400-mm-long, fully enclosed serpentine channel with a rectangular cross-section of 0.5 mm in width and 1.8 mm in height. The pressure drop across this 3D-printed SS serpentine channels is measured for air flow and compared to a standard gas flow model, showing that the device is free of leakage or clogs.

Distributionally robust risk-resistant synergistic restoration strategy for integrated electricity and gas system with high-fidelity gas dynamic modeling

A synergistic restoration strategy offers a promising solution for expediting restoration of integrated electricity and gas system (IEGS) following blackouts, particularly under the increasing energy interdependence between these two subsystems. However, achieving synergistic restoration is challenging in 1) distinct operational characteristics between electric and gas flow rates, leading to difficulties in accurately modeling the restoration processes with significantly varying system states; 2) potential risks posed by uncertainties, such as fluctuating renewable energy and random contingencies, undermining the effectiveness of restoration strategy. To address these challenges, this paper proposes a novel distributionally robust risk-resistant synergistic restoration strategy for IEGS. Firstly, to accurately capture the dynamics of slow gas flow relative to instantaneous power flow, we propose a high-fidelity linear dynamic gas flow model with multiparametric disaggregation technique, demonstrating satisfactory accuracy in restoration scenarios. Then, the risks by uncertainties of renewable energy and contingencies are handled within distributionally robust framework. Moreover, the IEGS restoration problem is reformulated as a two-stage robust optimization problem by convex conservative approximation and strong duality theory, which is solved by a nested column-and-constraint generation algorithm. Finally, simulation results validate the effectiveness of the proposed restoration strategy, showing the improved restoration efficiency, security, and risk-resistant performance.

A fluid–solid coupling model for hydraulic fracture of deep coal seam based on finite element method

The fluid–solid coupling effect is more pronounced in the process of deep coal seam development compared to shallow coalbed methane, exerting a greater influence on production, and cannot be disregarded. Throughout the extraction process, the interaction between effective stress and gas desorption triggers deformation within the coal seam, leading to dynamic changes in both porosity and permeability. This paper has developed a fully coupled gas flow and deformation model that contains the coal matrix and discrete fractures to describe the dynamic gas seepage behavior and deformation of deep coal seams within a coupled wellbore–hydraulic fractures–matrix system. The model's validity is corroborated through the examination of fracture aperture, employing the finite element numerical simulation capabilities of COMSOL Multiphysics. Subsequent to the model's validation, an in-depth investigation into the permeability and production variations under diverse parametric conditions is conducted. This analysis also encompasses the assessment of hydraulic fracture geometry's impact. The simulation outcomes reveal that the permeability alterations during coal seam development are subject to the counteracting influences of gas desorption and effective stress. Moreover, it is observed that an increase in the Langmuir volume strain constant and initial porosity correlates with enhanced production, whereas a diminution in the hydraulic fracture compression coefficient leads to increased cumulative production. Notably, the optimal production is attained when hydraulic fractures are oriented vertically yet asymmetrically relative to the horizontal well.

Evolution of collisional condensation of biodiesel combustion particulate matter in engine exhaust pipe

To investigate the evolution of biodiesel combustion particulate matter (PM) within the engine exhaust system, PM samples were analyzed from diesel fuel, soybean oil methyl ester (SME), catering waste oil methyl ester (WME) and palm oil methyl ester (PME) at various locations along the engine exhaust pipe, and a gas-solid two-phase flow model of exhaust gas and PM was developed using the coupled computational fluid dynamics-discrete element method (CFD-DEM). The results indicate that the average primary particle diameter of biodiesel PM is smaller than that of diesel PM at the same position within the exhaust pipe, and it exhibits an increasing trend with respect to the iodine value of biodiesel. The adhesion forces of diesel, SME, WME, and PME PM at 0 m downstream from the exhaust pipe were measured as 9.83 nN, 16.74 nN, 26.54 nN, and 34.31 nN, respectively. The biodiesel PM with higher mass density readily formed structurally stable particulate agglomerates at the inlet of the exhaust pipe. With an increase in exhaust flow velocity, there was a corresponding rise in particle collision frequency. The initial agglomeration probability of particles exhibited an increase followed by a subsequent decrease. The normal overlap of particle collisions decreased with an increase in the Young's modulus of the particles, thereby reducing the likelihood of adsorption and adhesion during particle collision and hindering the formation of a greater number of particle aggregates.

Взаимосвязь окружной скорости и потерь энергии в проточной части центростремительной турбины с частичным облопачиванием рабочего колеса

Low-consumption turbomachines are devices that play an important role in the drive of various units in the field of shipbuilding, aircraft engineering and other branches of heavy engineering. They have some advantages over a high-average power turbine. The largest number of low-consumption turbomachines are made partial, i.e. with partial intake. The principle of a turbine with partial flapping of the impeller is considered as one of the types of partial turbomachines. The influence of the main velocity characteristic of the turbine stage on the loss of kinetic energy in the stage is investigated. The simulation of gas dynamic processes occurring in the turbine stage was carried out using the ANSYS Workbench software package. With the help of this complex, a three-dimensional geometric model of the turbine stage with varying degrees of impeller damping was created. By applying the finite element method, a computational grid, a computational model are generated, and boundary conditions of a numerical experiment are set. The result of the numerical experiment is graphs of the dependence of kinetic energy loss on the circumferential velocity (speed characteristics of the turbine stage). This dependence can be represented not only graphically, but also with the help of mathematical apparatus. An example of such an apparatus is the polynomial dependence. The considered mathematical design can be used in order to optimize mathematical models of gas flow in the flow part of a low-flow turbine. Cubic two-parameter polynomials of kinetic energy losses in the flow part of the nozzle and impeller are obtained, and an assessment of its applicability in the current mathematical model is given.

Mesoscopic lattice Boltzmann modeling of dense gas flows in curvilinear geometries

Mesoscopic lattice Boltzmann modeling of dense gas flows in curvilinear geometries