Pressure Field Research Articles

Real-Time Aerodynamic Load Estimation for Hypersonics via Strain-Based Inverse Maps

This work develops an efficient real-time inverse formulation for inferring the aerodynamic surface pressures on a hypersonic vehicle from sparse measurements of the structural strain. The approach aims to provide real-time estimates of the aerodynamic loads acting on the vehicle for ground and flight testing, as well as guidance, navigation, and control applications. Specifically, the approach targets hypersonic flight conditions where direct measurement of the surface pressures is challenging due to the harsh aerothermal environment. For problems employing a linear elastic structural model, the inference problem can be posed as a least-squares problem with a linear constraint arising from a finite element discretization of the governing elasticity partial differential equation. Due to the linearity of the problem, an explicit solution is given by the normal equations. Precomputation of the resulting inverse map enables rapid evaluation of the surface pressure and corresponding integrated quantities, such as the force and moment coefficients. The inverse approach additionally allows for uncertainty quantification, providing insights for theoretical recoverability and robustness to sensor noise. Numerical studies demonstrate the estimator performance for reconstructing the surface pressure field, as well as the force and moment coefficients, for the Initial Concept 3.X (IC3X) conceptual hypersonic vehicle.

Pressure Monitoring of Disposal Reservoirs in North‐Central Oklahoma: Implications for Seismicity and Geostorage

AbstractDisposal of industrial wastewater and activities such as underground sequestration depend upon pressure conditions within deep geologic reservoirs. Sometimes, injection and storage are associated with induced seismicity, suggested to result from reservoir compartmentalization, leakage into faults, or other mechanisms in the subsurface. To understand subsurface pressure conditions within a major regional disposal reservoir, the Arbuckle Group of Oklahoma, we monitored the water levels in 15 inactive injection wells. The wells were monitored at 30‐s intervals, with eight wells monitored since September 2016, and an additional seven from July 2017. All the wells were monitored until early March 2020. Since 2016, hydraulic head decreased in 13 of the 15 wells, proportional to near‐borehole fluid pressure even considering decreasing regional injection volumes during this period. The well pressures respond to three types of perturbations: (i) gravitational fluctuations (a.k.a. solid‐earth tides) (ii) distal and proximal earthquakes, and (iii) injections into nearby wells. Parameterization of tidal responses illustrates that the near wellbore environments have negative fluid flux (i.e., are leaking). Earthquakes cause differing pressure responses from well to well, with some highly sensitive to proximal events, some to distal events, and some apparently insensitive. Injections have variable impacts in some cases masking tidal and earthquake pressure signals. Collectively, there appears to be a threshold injection rate above which well pressure becomes less sensitive to the volume of injections within 15 km. Multi‐scale geological structure and temporal permeability changes are likely controlling the pressure field, indicating leakage of fluids across the system.

The influence of non-Newtonian behaviors of blood on the hemodynamics past a bileaflet mechanical heart valve

This study employs extensive three-dimensional direct numerical simulations to investigate the hemodynamics around a bileaflet mechanical heart valve. In particular, this study focuses on assessing whether non-Newtonian rheological behaviors of blood, such as shear-thinning and yield stress behaviors, exert an influence on hemodynamics compared to the simplistic Newtonian behavior under both steady inflow and physiologically realistic pulsatile flow conditions. Under steady inflow conditions, the study reveals that blood rheology impacts velocity and pressure field variations, as well as the values of clinically important surface and time-averaged parameters like wall shear stress (WSS) and pressure recovery. Notably, this influence is most pronounced at low Reynolds numbers, gradually diminishing as the Reynolds number increases. For instance, surface-averaged WSS values obtained with the non-Newtonian shear-thinning power-law model exceed those obtained with the Newtonian model. At Re=750, this difference reaches around 67%, reducing to less than 1% at Re=5000. Correspondingly, pressure recovery downstream of the valve leaflets is lower for the shear-thinning blood than the constant viscosity one, with the difference decreasing as the Reynolds number increases. On the other hand, in pulsatile flow conditions, jets formed between the leaflets and the valve housing wall are shorter than steady inflow conditions. Additionally, surface-averaged wall shear stress and blood damage (BD) parameter values are higher (with differences more than 13% and 47%, respectively) during the peak stage of the cardiac cycle, especially for blood exhibiting non-Newtonian yield stress characteristics compared to the shear-thinning or constant viscosity characteristics. Therefore, blood non-Newtonian behaviors, including shear-thinning and yield stress behaviors, exert a considerable influence on the hemodynamics around a mechanical heart valve. All in all, the findings of this study demonstrate the importance of considering non-Newtonian blood behaviors when designing blood-contacting medical devices, such as mechanical heart valves, to enhance functionality and performance.

Hurricane surge and inundation in the Bahamas, part 1: Storm surge model

AbstractA storm surge model has been developed as part of a pilot study for The Commonwealth of the Bahamas. The hydrodynamic model, TELEMAC‐2D, is used to simulate the response of water level to tide and the wind and atmospheric pressure fields of hurricanes and subsequent inundation over land. The model is used by The Bahamas Department of Meteorology to forecast storm surge and flooding over the islands of Grand Bahama and Eleuthera for incoming hurricanes to assist in preparation for and management of hurricane surge events and has been used in a flood risk assessment, reported in a companion paper. The model has been optimised to run quickly while also resolving the bathymetry and topography that affect the development and propagation of storm surge. Wind fields are generated within TELEMAC‐2D based on hurricane warning bulletins. The model has been validated for its representation of water level and against tide gauge measurements during four historical hurricanes: Irene, Sandy, Matthew and Dorian. Factors contributing to uncertainty in forecast predictions are discussed and recommendations are provided to improve the performance in future. The pilot study provides a template for future expansion to cover the other inhabited islands of The Bahamas.

Development and testing of hybrid (PNM–CFD) mathematical model and numerical algorithm for description of fluid flows in three-dimensional digital core models

Numerical simulation of fluid flow in porous and fractured rocks is an important task for many industrial applications. The most common approaches to constructing such models are direct (CFD or lattice Boltzmann) and porous network (PNM) modeling. Each approach has its own advantages and disadvantages. This paper presents a hybrid mathematical PNM–CFD model for describing fluid flows in three-dimensional digital core models, which has the high speed performance of PNM approaches and high accuracy of CFD models. Numerical technique has been developed for describing fluid flows in three-dimensional digital core models using a hybrid PNM–CFD model. The numerical technique links a one-dimensional pore network solver and a three-dimensional CFD solver into a combined model in original way by constructing a single pressure field for the entire computation domain. To validate the model, several tests were performed, including flow in straight channels and numerical simulation of fluid flow in a microfluidic chip. The test results have shown the adequacy of the hybrid model performance. The hybrid model for determining pressure drop in a branched network with three-dimensional chambers has an error of no more than 5 % when compared to experimental data. Similarly, the error in calculating velocity does not exceed 7 % when compared to the full three-dimensional calculation. The hybrid model has shown an almost twofold increase in calculation speed compared to the full three-dimensional model.

Numerical analysis of flow and heat transfer characteristics in Taylor-Couette-Poiseuille flow utilizing Large Eddy Simulation method

The flow and heat transfer characteristics within the Taylor-Couette-Poiseuille configuration induced by supercritical carbon dioxide flowing through the gap between the turbine shaft and the stationary casing were studied using Large Eddy Simulation. Wavelet analysis was used to calculate pressure fluctuations across various frequencies. Computational assessments were carried out to evaluate changes in the field synergy angle and inertial perturbations within the annular gap. A new theory was introduced to seamlessly integrate temperature, pressure, and velocity fields. Additionally, entropy generation in the Taylor-Couette-Poiseuille flow regime was thoroughly examined. The study revealed the emergence of vortices at the rotating wall, indicating a dynamic process in which large-scale vortices dissolve and more minor ones form. As frequency increases, pressure fluctuations grow. Increasing the mass flow rate can reduce the twisting vortex at the rotating wall and delay the onset of temperature fluctuations. Additionally, increasing the mass flow rate enhances the cooling effect on the rotating shaft. In the radial direction, as r increases, the field synergy angle and the inertial disturbance both show a trend of first decreasing and then increasing. The heat transfer performance is best when r = 0.6 and decreases significantly when r = 0.95. The synergy between the temperature gradient field, pressure gradient field, and velocity field shows a trend opposite to the field synergy angle and the inertial disturbance. As one moves from the rotating wall toward the stationary wall, temperature and velocity entropy production rates decrease, with noticeable fluctuations near the rotating wall.

A combined Markov Chain Monte Carlo and Levenberg–Marquardt inversion method for heterogeneous subsurface reservoir modeling

In this study, we systematically investigate an inverse method for heterogeneous porous media to obtain porosity and permeability fields considering only production well data. The forward modeling of the input data, namely pressure and saturation fields, is based on the motion equations of a coupled Darcy flow system involving two phases of isothermal fluid flow. We discretize these equations using a multiscale finite volume simulation technique in the spatial domain, and the backward Euler method in time domain. In the inversion procedure, we combine a global optimization method, the Markov Chain Monte Carlo (MCMC) method, with a local optimization method, the Levenberg–Marquardt (LM) method. The MCMC was implemented as the Random Walk algorithm, and to generate the samples of the porosity and permeability fields, we employed Karhunen–Loève (KL) expansion of second-order stationary fields with Gaussian covariance. The coefficients of the KL expansion are estimated by minimizing the norm of the residual dependent on these fields. At the end of the MCMC iterations, we refine the KL coefficients associated with the porosity and permeability fields using the LM method. We verify in the numerical experiments that the accuracy of the porosity and permeability fields is improved by the LM refinement step.

Ultrasonic multi-frequency piezoelectric transducer for generation different sound pressure field patterns

Ultrasonic multi-frequency piezoelectric transducer for generation different sound pressure field patterns

Mixed material point method formulation, stabilization, and validation for a unified analysis of free-surface and seepage flow

This paper presents a novel stabilized mixed material point method (MPM) designed for the unified modeling of free-surface and seepage flow. The unified formulation integrates the Navier-Stokes equation with the Darcy-Brinkman-Forchheimer equation, effectively capturing flows in both non-porous and porous domains. In contrast to the conventional Eulerian computational fluid dynamics (CFD) solver, which solves the velocity and pressure fields as unknown variables, the proposed method employs a monolithic displacement-pressure formulation adopted from the mixed-form updated-Lagrangian finite element method (FEM). To satisfy the discrete inf-sup stability condition, a stabilization strategy based on the variational multiscale method (VMS) is derived and integrated into the proposed formulation. Another distinctive feature is the implementation of blurred interfaces, which facilitate a seamless and stable transition of flows between free and porous domains, as well as across two distinct porous media. The efficacy of the proposed formulation is verified and validated through several benchmark cases in 1D, 2D, and 3D scenarios. Conducted numerical examples demonstrate enhanced accuracy and stability compared to analytical, experimental, and other numerical solutions.

Magnetomechanical Behaviors of Hard-Magnetic Elastomer Membranes Placed in Uniform Magnetic Field.

This paper aims to develop a theoretical model for a viscoelastic hard-magnetic elastomer membrane (HMEM) actuated by pressure and uniform magnetic field. The HMEM is initially a flat, circular film with a fixed boundary. The HMEM undergoes nonlinear large deformations in the transverse direction. The viscoelastic behaviors are characterized by using a rheological model composed of a spring in parallel with a Maxwell unit. The governing equations for magneto-visco-hyperelastic membrane under the axisymmetric large deformation are constructed. The Zeeman energy, which is related to the magnetization of the HMEM and the magnetic flux density, is employed. The governing equations are solved by the shooting method and the improved Euler method. Several numerical examples are implemented by varying the magnitude of the pre-stretch, pressure, and applied magnetic field. Under different magnetic fields, field variables such as latitudinal stress exhibit distinct curves in the radial direction. It is observed that these varying curves intersect at a point. The position of the intersection point is independent of the applied magnetic field and only controlled by pressure and pre-stretch. On the left side of the intersection point, the field variables increase as magnetic field strength increases. However, on the other side, this trend is reversed. During viscoelastic evolution, one can find that the magnetic field can be used to modulate the instability behaviors of the HMEM. These findings may provide valuable insights into the design of the hard-magnetic elastomer membrane structures and actuators.

Analysis of electroviscous effects in electrolyte liquid flow through a heterogeneously charged uniform microfluidic device

Charge-heterogeneity (i.e., surface charge variation in the axial direction of the device) introduces non-uniformity in flow characteristics in the microfluidic device. Thus, it can be used for controlling practical microfluidic applications, such as mixing, mass, and heat transfer processes. This study has numerically investigated the charge-heterogeneity effects in the electroviscous (EV) flow of symmetric (1:1) electrolyte liquid through a uniform slit microfluidic device. The Poisson’s, Nernst-Planck (N-P), and Navier–Stokes (N-S) equations are numerically solved using the finite element method (FEM) to obtain the flow fields, such as total electrical potential (U), excess charge (n *), induced electric field strength (E x), and pressure (P) fields for following ranges of governing parameters: inverse Debye length (2 ≤ K ≤ 20), surface charge density (4 ≤ S 1 ≤ 16), and surface charge-heterogeneity ratio (0 ≤ S rh ≤ 2). Results have shown that the total potential (∣ΔU∣) and pressure (∣ΔP∣) drop maximally increase by 99.09% (from 0.1413 to 0.2812) (at K = 20, S 1 = 4) and 12.77% (from 5.4132 to 6.1045) (at K = 2, S 1 = 8), respectively with overall charge-heterogeneity (0 ≤ S rh ≤ 2). Electroviscous correction factor (Y, i.e., ratio of effective to physical viscosity) maximally enhances by 12.77% (from 1.2040 to 1.3577) (at K = 2, S 1 = 8), 40.98% (from 1.0026 to 1.4135) (at S 1 = 16, S rh = 1.50), and 41.35% (from 1 to 1.4135) (at K = 2, S rh = 1.50), with the variation of S rh (from 0 to 2), K (from 20 to 2), and S 1 (from 0 to 16), respectively. Further, a simple pseudo-analytical model is developed to estimate the pressure drop in EV flow, accounting for the influence of charge-heterogeneity based on the Poiseuille flow in a uniform channel. This model predicts the pressure drop ± 2%–4% within the numerical results. The robustness and simplicity of this model enable the present numerical results for engineering and design aspects of microfluidic applications.

The effect of stress barriers on unconventional-singularity-driven frictional rupture

Whether or not energy dissipation is localized in the vicinity of the rupture tip, and whether any distal energy dissipation far from the crack tip has a significant influence on rupture dynamics are key questions in the description of frictional ruptures, in particular regarding the application of Linear Elastic Fracture Mechanics (LEFM) to earthquakes. These questions are investigated experimentally using a 40-cm-long experimental frictional interface. Three independent pistons apply a normal load with a fourth piston applying a shear load, enabling the application of a heterogeneous stress state and stress barriers. After loading the frictional interface to a near-critical state, subsequent unloading of one normal-load piston leads to dynamic ruptures which propagate into the heterogeneous stress fields. The ruptures in these experiments are found to be driven by unconventional singularities, characterized by an ever-increasing breakdown work with slip, and as a result do not conform to the assumptions of LEFM. As these experimental stress barriers inhibit slip, they therefore also reduce the breakdown work occurring outside of the cohesive zone. It is shown that this distal weakening, far from the crack tip, must be considered for the accurate prediction of rupture arrest length. These experiments are performed in the context of a proposed stimulation technique for Enhanced Geothermal Systems (EGSs). It has previously been suggested, through theoretical arguments, that stress barriers could be induced through the manipulation of pore pressure such that there is reduced seismic hazard during the shear stimulation of EGSs. This stimulation technique, known as preconditioning, is demonstrated here to reduce the mechanical energy flux to the crack tip, G, while also increasing the fracture energy, Gc. Preconditioning is shown to be capable of arresting seismic rupture and reducing co-seismic slip, slip velocity, and seismic moment at preconditioning stresses which are reasonably achievable in the field. Due to the fully-coupled nature of seismic rupture and fault slip, preconditioning also reduces distal weakening and its contribution to the propagation of induced seismic ruptures. In a similar vein, heterogeneous pore pressure fields associated with some seismic swarms can be used to explain changes in stress drop within the swarm without recourse to material or total-stress heterogeneity.

Catastrophe Information Characteristics and Prevention Measures of Water Inrush in Tunnel Approaching Fault with Different Water Pressure

In order to ensure the safety of the tunnel approaching the fault and prevent water inrush disasters, and then take reasonable protective measures, a fault-tunnel-surrounding rock is established by using a three-dimensional (3D) discrete element numerical analysis method, which takes into account the fluid-structure coupling effect. Based on the method of control variables, the catastrophe information characteristics of displacement and water pressure of the surrounding rock of the tunnel face and the corresponding characteristics of changes before the occurrence of water inrush disasters were studied under different fault water pressures during the excavation of the tunnel approaching the water-rich fault. The results show that, during excavation at the same step, displacement and its magnitude in the surrounding rock escalate as fault water pressure increases. The maximum pressure of the water in the surrounding rock is also constantly increasing. As tunnel excavation progresses, at constant fault water pressure, longer excavation distances result in greater axial displacement of the surrounding rock mass and increased water pressure at corresponding positions within the surrounding rock, leading to higher magnitude increases. As excavation proceeds, the displacement and water pressure in the surrounding rock and the increase of its amplitude continue to increase. Pre-reinforcement grouting techniques and pipe umbrella support systems that are very effective protective measures can be determined by a comprehensive approach integrating advanced geological forecasting methods, real-time water pressure detection, and the analysis of stress-strain and seepage pressure field variations in the surrounding rock mass.

A New 3D reconstruction method for pressure-sensitive paint measurements under limited optical access

Reconstruction of 3D pressure field is crucial for pressure-sensitive paint measurements in turbomachinery experiments. Existing methods impose high requirements on feature points in terms of quantity, spatial distribution, and positional accuracy, and is difficult to apply under limited optical access, such as in planar cascade wind tunnels. We propose a novel direct linear transformation method based on contour matching (CM-DLT). This method leverages model contours captured from a tilted camera perspective, which provides the basis for identifying the projection matrix linking image pixels to 3D spatial points. The subsequent optimization of the projection matrix significantly enhances the accuracy and robustness of 3D pressure field reconstruction. In a benchmark experiment, the efficiency and reprojection accuracy of 3D reconstruction are investigated. Subsequently, the CM-DLT method is successfully applied in the cascade wind tunnel experiment. The obtained 3D pressure fields of two surfaces of adjacent blades are analyzed.

Effective prediction of drug transport in a partially liquefied vitreous humor: Physics-informed neural network modeling for irregular liquefaction geometry

As the medium for intravitreal drug delivery, the vitreous body can significantly influence drug delivery because of various possible liquefaction geometries. This work innovatively proposes a varying-porosity approach that is capable of solving the pressure and velocity fields in the heterogeneous vitreous with randomly-shaped liquefaction geometry, validated with a finite difference model. Doing so enables patient-specific treatment for intravitreal drug delivery and can significantly improve treatment efficacy. A physics-informed neural network (PINN) model is also established for the simulation, and three cases are used for validation. Despite limited information, the PINN model, together with the varying-porosity approach, captured fluid and drug transport in the partially liquefied vitreous. This opens the possibility for optimizing intravitreal drug delivery based on ultrasonography in clinical practice.

Numerical simulations of a low-pressure electrodeless ion source intended for air-breathing electric propulsion

Abstract Air breathing electric propulsion (ABEP) systems offer a promising solution to extend the lifetime of very low earth orbit (VLEO) missions by using residual atmospheric particles as propellants. Such systems would operate in very low-pressure environments where plasma ignition and confinement prove challenging. In this contribution, we present results of a global plasma model (GPM) of a plasma ignited in a very low-pressure air mixture. The results are validated against experimental measurements acquired using a laboratory electrodeless ion source utilizing a resonator for plasma ignition. The device is specifically designed to operate within low-pressure environments as it holds potential applications in ABEP systems for VLEO missions. Parametric studies are carried out via GPM to investigate the resonant behavior and its implications. The potential of the model serving as a predictive tool is assessed through experimental validation against measured data, mainly investigating the extracted ion current dependency on operational pressure and external magnetic field strength. The verified model is further utilized to extrapolate additional information about the resonant plasma such as ion composition or a degree of ionization.

Micronuclear battery based on a coalescent energy transducer.

Micronuclear batteries harness energy from the radioactive decay of radioisotopes to generate electricity on a small scale, typically in the nanowatt or microwatt range1,2. Contrary to chemical batteries, the longevity of a micronuclear battery is tied to the half-life of the used radioisotope, enabling operational lifetimes that can span several decades3. Furthermore, the radioactive decay remains unaffected by environmental factors such as temperature, pressure and magnetic fields, making the micronuclear battery an enduring and reliable power source in scenarios in which conventional batteries prove impractical or challenging to replace4. Common radioisotopes of americium (241Am and 243Am) are α-decay emitters with half-lives longer than hundreds of years. Severe self-adsorption in traditional architectures of micronuclear batteries impedes high-efficiency α-decay energy conversion, making the development of α-radioisotope micronuclear batteries challenging5,6. Here we propose a micronuclear battery architecture that includes a coalescent energy transducer by incorporating 243Am into a luminescent lanthanide coordination polymer. This couples radioisotopes with energy transducers at the molecular level, resulting in an 8,000-fold enhancement in energy conversion efficiency from α decay energy to sustained autoluminescence compared with that of conventional architectures. When implemented in conjunction with a photovoltaic cell that translates autoluminescence into electricity, a new type of radiophotovoltaic micronuclear battery with a total power conversion efficiency of 0.889% and a power per activity of 139 microwatts per curie (μW Ci-1) is obtained.

Hinge Modes of Surface Arcs in a Synthetic Weyl Phononic Crystal.

Chiral bulk Landau levels and surface arcs, as the two distinctive features unique to Weyl semimetals, have each attracted enormous interest. Recent works have revealed that surface-arc modes can support one-sided chiral hinge modes, a hallmark of the three-dimensional quantum Hall effect, as a combined result of chiral Landau levels of bulk states and magnetic response of surface arcs. Here, we exploit a two-dimensional phononic crystal to construct an ideal Weyl semimetal under a pseudomagnetic field, in which a structural parameter is combined to construct a synthetic three-dimensional space. By directly measuring the acoustic pressure fields, we have not only visualized the one-sided chiral hinge modes, but also observed the quantized Landau level modes. The results pave the way to explore the high-dimensional quantum Hall physics in low-dimensional phononic platforms.

Comparative Performance Assessment between Incompressible and Compressible Solvers to Simulate a Cavitating Wake

To study the effects of fluid compressibility on the dynamics of a cavitating vortex street flow in a regime where the vortex shedding frequency increases as a result of the cavitation increase, the cavitating wake behind a wedge was simulated employing both incompressible and compressible solvers. To do this, a compressible cavitation model was implemented, modifying the Zwart-Gerber-Belamri (ZGB) incompressible solver and including a pressure limit and absorbing boundary conditions to prevent a non-physical pressure field. To validate the performance of the compressible model, preliminary simulations were carried out on a 1D Sod cavitating tube and the cavitating vortex shedding behind a circular body at laminar flow conditions. The results of the cavitating wake behind the wedge with the incompressible and the compressible solvers showed similar predictions in terms of pressure, vortex shedding frequency, and instantaneous and average vapor volume fraction profiles. In spite of this, differences were obtained in the energy content of the fluid force fluctuations on the body at higher frequencies, which appear to be better resolved and amplified when the compressibility model is considered. Overall, both solvers provided comparable results in terms of cavitation phenomena that are well aligned with experimental observations.

High-Order Models for Gas Transport in Multiscale Coal Rock.

The coal reservoirs exhibit great heterogeneity and strong anisotropy in multiscale pore/fracture structures. Developing highly accurate multiscale models for real-time prediction of microgaseous flow in complicated porous media with pronounced contrast in transport coefficients is crucial but not yet available, which is time-consuming, expensive, and even computationally impossible. In this study, a multiscale approximate solution of the gas flow and pressure field is derived in this paper for predicting coalbed methane (CBM) transport in macro-microscopic two-scale porous media of typical coal rocks in Guizhou Province, China, and the detailed finite element algorithm is established. The multiscale approximate solutions are constructed from the first- and second-order auxiliary cell functions and low- or high-order derivatives of the homogenized pressure field, which can accurately approximate the solution of the original problem to a certain extent. The numerical accuracy and validity of the multiscale approximate solutions under various working conditions are analyzed in detail by comparing and verifying the results with the direct numerical simulation results of fine-mesh high-precision finite elements. The results show that the homogenized approximate solution can only roughly capture the characteristics of the macroscopic pressure evolution, the first-order approximate solution can partially reproduce the macro-microscopic pressure oscillation phenomenon, and the second-order approximate solution can accurately predict the pressure profile and its evolution law with time in porous media with macro-micro configuration under various complex conditions. The second- and high-order two-scale approximate solutions constructed in this paper exhibit high numerical accuracy and excellent computational efficiency. We also develop multiscale approximate solutions for predicting microgaseous flow at a low reservoir pressure where the slippage effects are very pronounced. Potential applications of our high-order models to the coal reservoirs with a hierarchical matrix and fractures are discussed. The developed multiscale models exhibit excellent applicability to investigating the crossflow effects and coupling mechanisms between the matrix and cleats or fractures with multiple configurations in the CBM and shale gas reservoirs, which is crucial for the effective implementation of hydraulic fracturing technology. This study provides a fundamental understanding of gas transport in multiscale matrix-fracture networks, which helps to improve the optimization design of hydraulic fracturing in tight reservoirs.