Institute of Mechanics,
Chinese Academy of Sciences
2026 Vol.16(3)
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Theoretical and Applied Mechanics Letters 16 (2026) 100645.
doi: 10.1016/j.taml.2025.100645
Abstract:
Unconventional reservoirs such as shale and tight sandstone exhibit low porosity and low permeability. By applying horizontal wellbore fracturing techniques, a fracture network with a certain degree of complexity can be created within the reservoir to enhance oil and gas recovery. The interaction between hydraulic fracture(HF) and natural fracture(NF) plays a crucial role in determining the complexity of the fracture network. This study examines the interaction process between HF and NF, using the unified strength theory as the fracture initiation criterion for the fracture on the opposite side of natural fractures, and considering the influence of T-stress on the radius of the nonlinear zone. An interaction criterion that accounts for both intermediate principal stress and T-stress effects is proposed, and the predictions are highly consistent with experimental results. The results of the sensitivity analysis indicate that T-stress influences the critical radius of the nonlinear zone, thereby causing disturbances in the magnitude of induced stress. With T-stress taken into account, the extent of the penetration zone increases, and the extent of the opening zone decreases. However, at high approach angles, the influence of T-stress diminishes. As the Poisson’s ratio, cohesion, and fracture toughness increase, the tensile strength decreases, making HF more likely to penetrate NF, resulting in a single fracture morphology. A lower stress differential and a lower tensile-to-compressive ratio promote the opening of natural fractures. Additionally, as the intermediate principal stress coefficient increases, the ranges of the opening and slip zones expand, while the penetration zone shrinks.
Unconventional reservoirs such as shale and tight sandstone exhibit low porosity and low permeability. By applying horizontal wellbore fracturing techniques, a fracture network with a certain degree of complexity can be created within the reservoir to enhance oil and gas recovery. The interaction between hydraulic fracture(HF) and natural fracture(NF) plays a crucial role in determining the complexity of the fracture network. This study examines the interaction process between HF and NF, using the unified strength theory as the fracture initiation criterion for the fracture on the opposite side of natural fractures, and considering the influence of T-stress on the radius of the nonlinear zone. An interaction criterion that accounts for both intermediate principal stress and T-stress effects is proposed, and the predictions are highly consistent with experimental results. The results of the sensitivity analysis indicate that T-stress influences the critical radius of the nonlinear zone, thereby causing disturbances in the magnitude of induced stress. With T-stress taken into account, the extent of the penetration zone increases, and the extent of the opening zone decreases. However, at high approach angles, the influence of T-stress diminishes. As the Poisson’s ratio, cohesion, and fracture toughness increase, the tensile strength decreases, making HF more likely to penetrate NF, resulting in a single fracture morphology. A lower stress differential and a lower tensile-to-compressive ratio promote the opening of natural fractures. Additionally, as the intermediate principal stress coefficient increases, the ranges of the opening and slip zones expand, while the penetration zone shrinks.
Theoretical and Applied Mechanics Letters 16 (2026) 100646.
doi: 10.1016/j.taml.2025.100646
Abstract:
This study employed a dynamic caustics system integrated with a Hopkinson pressure bar, Schlieren optics, and a high-speed camera to investigate how joint span and shape affect crack initiation and propagation. First, crack penetration into joints with different spans (10 mm, 30 mm, 50 mm) and different shapes (“u” and “n”) was visualized. Then, crack-tip stress intensity factors and propagation velocity were measured by high-speed caustics patterns. Finally, fractal dimensions of crack trajectories were obtained to quantitatively evaluate the complexity of the crack layout. Based on loading time, the crack behavior is divided into 4 phases: first precrack initiation, propagation toward the joint, secondary initiation from the joint and final propagation toward the boundary. Since the phase 1 duration increases with span, crack initiation from precracks clearly depends on span length. In phases 2 and 3, reflected waves occur from the joint interface; furthermore, they are confirmed to be Rayleigh waves through wave velocity. Meanwhile, the reflected Rayleigh waves from the “n”-shaped joint have a significant effect on crack propagation in phase 2. In phase 4, crack trajectories initiating from joint ends are heavily influenced by joint span, which is associated with crack interaction. Furthermore, different opening orientations (“u” and “n”) of arc-shaped joints have different effects on crack behavior. The “u”-shaped joint exhibits crack behavior similar to that of same-span line-shaped joints. The “n”-shaped joint demonstrates a strong fracture resistance. This work advances the understanding of fracture resistance as influenced by joint span and shape variations.
This study employed a dynamic caustics system integrated with a Hopkinson pressure bar, Schlieren optics, and a high-speed camera to investigate how joint span and shape affect crack initiation and propagation. First, crack penetration into joints with different spans (10 mm, 30 mm, 50 mm) and different shapes (“u” and “n”) was visualized. Then, crack-tip stress intensity factors and propagation velocity were measured by high-speed caustics patterns. Finally, fractal dimensions of crack trajectories were obtained to quantitatively evaluate the complexity of the crack layout. Based on loading time, the crack behavior is divided into 4 phases: first precrack initiation, propagation toward the joint, secondary initiation from the joint and final propagation toward the boundary. Since the phase 1 duration increases with span, crack initiation from precracks clearly depends on span length. In phases 2 and 3, reflected waves occur from the joint interface; furthermore, they are confirmed to be Rayleigh waves through wave velocity. Meanwhile, the reflected Rayleigh waves from the “n”-shaped joint have a significant effect on crack propagation in phase 2. In phase 4, crack trajectories initiating from joint ends are heavily influenced by joint span, which is associated with crack interaction. Furthermore, different opening orientations (“u” and “n”) of arc-shaped joints have different effects on crack behavior. The “u”-shaped joint exhibits crack behavior similar to that of same-span line-shaped joints. The “n”-shaped joint demonstrates a strong fracture resistance. This work advances the understanding of fracture resistance as influenced by joint span and shape variations.
Theoretical and Applied Mechanics Letters 16 (2026) 100648.
doi: 10.1016/j.taml.2025.100648
Abstract:
In the numerical solution of wave propagation problems, spurious oscillations occur in the exact time integration of the related equation of motion. This is due to the high frequencies introduced by the spatial discretization, given the small size of the mesh elements and the integration step required to capture the wave phenomena. Currently, an answer to this problem is given by the use of the smoothing properties, intrinsic to the scheme or obtained through artificial viscosity, of dissipative time integration methods. More recently, in an alternative approach to the problem, the solution has been regularized via a post processing smoothing technique. In particular, on the basis of an initial nondissipative scheme, at a fixed observation time a series of steps of an appropriate dissipative time integration method achieves the desired smoothing. However, in both approaches, as the dissipative steps are performed, the noise progressively decreases, but the important values related to the peak regions of the solution degrade significantly. Here we describe a regularization process that automatically returns a solution where the noise has been eliminated but does not affect the significant regions of the solution. The presented technique recognizes the flat or peak shapes of the original solution among the oscillating components representing the noise. Operationally, the presented algorithm, starting from a nondissipative step-by-step scheme for time integration, iteratively smooths the related kinematic quantities and finally recovers the regularized solution as a suitable composition of smoothed and unsmoothed subdomains.
In the numerical solution of wave propagation problems, spurious oscillations occur in the exact time integration of the related equation of motion. This is due to the high frequencies introduced by the spatial discretization, given the small size of the mesh elements and the integration step required to capture the wave phenomena. Currently, an answer to this problem is given by the use of the smoothing properties, intrinsic to the scheme or obtained through artificial viscosity, of dissipative time integration methods. More recently, in an alternative approach to the problem, the solution has been regularized via a post processing smoothing technique. In particular, on the basis of an initial nondissipative scheme, at a fixed observation time a series of steps of an appropriate dissipative time integration method achieves the desired smoothing. However, in both approaches, as the dissipative steps are performed, the noise progressively decreases, but the important values related to the peak regions of the solution degrade significantly. Here we describe a regularization process that automatically returns a solution where the noise has been eliminated but does not affect the significant regions of the solution. The presented technique recognizes the flat or peak shapes of the original solution among the oscillating components representing the noise. Operationally, the presented algorithm, starting from a nondissipative step-by-step scheme for time integration, iteratively smooths the related kinematic quantities and finally recovers the regularized solution as a suitable composition of smoothed and unsmoothed subdomains.
Theoretical and Applied Mechanics Letters 16 (2026) 100649.
doi: 10.1016/j.taml.2025.100649
Abstract:
Inspired by natural bird nests, nest-like structures consist of randomly packed slender particles confined within a container. This study investigates the dynamic behavior of nest-like structures by finite element simulation and a shock model. Under dynamic impact conditions, the nest-like structures exhibit distinct mechanisms compared to quasistatic loading. A confined deformation zone with nearly uniform stress forms near the loading end. This zone propagates steadily into the undeformed region at a constant velocity. Notably, the expansion speed exceeds the loading rate but remains significantly slower than the stress wave speed in solid material. We proposed a rigid-perfectly plastic-locking shock model to quantitatively establish how initial conditions govern two critical dynamic responses: the stress in the confined zone and the expansion velocity of the confined zone. These dynamic characteristics of nest-like structures demonstrate their potential for impact resistance.
Inspired by natural bird nests, nest-like structures consist of randomly packed slender particles confined within a container. This study investigates the dynamic behavior of nest-like structures by finite element simulation and a shock model. Under dynamic impact conditions, the nest-like structures exhibit distinct mechanisms compared to quasistatic loading. A confined deformation zone with nearly uniform stress forms near the loading end. This zone propagates steadily into the undeformed region at a constant velocity. Notably, the expansion speed exceeds the loading rate but remains significantly slower than the stress wave speed in solid material. We proposed a rigid-perfectly plastic-locking shock model to quantitatively establish how initial conditions govern two critical dynamic responses: the stress in the confined zone and the expansion velocity of the confined zone. These dynamic characteristics of nest-like structures demonstrate their potential for impact resistance.
Theoretical and Applied Mechanics Letters 16 (2026) 100651.
doi: 10.1016/j.taml.2025.100651
Abstract:
We employ the principle of a minimum pressure gradient to transform problems in unsteady computational fluid dynamics (CFD) into a convex optimization framework subject to linear constraints. This formulation permits solving, for the first time, CFD problems efficiently via well-established quadratic programming tools. The proposed approach is demonstrated via three benchmark examples. In particular, through comparison with traditional CFD tools, the proposed framework is capable of predicting the flow field in a lid-driven cavity, in a uniform pipe (Poiseuille flow), and that past a backward facing step. The results highlight the potential of the method as a simple, robust, and potentially transformative alternative to traditional CFD approaches.
We employ the principle of a minimum pressure gradient to transform problems in unsteady computational fluid dynamics (CFD) into a convex optimization framework subject to linear constraints. This formulation permits solving, for the first time, CFD problems efficiently via well-established quadratic programming tools. The proposed approach is demonstrated via three benchmark examples. In particular, through comparison with traditional CFD tools, the proposed framework is capable of predicting the flow field in a lid-driven cavity, in a uniform pipe (Poiseuille flow), and that past a backward facing step. The results highlight the potential of the method as a simple, robust, and potentially transformative alternative to traditional CFD approaches.
Theoretical and Applied Mechanics Letters 16 (2026) 100652.
doi: 10.1016/j.taml.2025.100652
Abstract:
After more than forty years of development, the accuracy of digital image correlation (DIC) methods has reached an extremely high level. However, the interpolation bias of DIC has not been resolved. With the flourishing of deep learning in the field of image superresolution, it has become possible to use deep learning-based image superresolution methods to reduce DIC interpolation bias. To achieve this goal, this paper improves the local implicit image function (LIIF) method based on the characteristics of speckle images to obtain LIIF-S, achieving continuous image representation and arbitrary resolution interpolation. Subsequently, LIIF-S is used as the interpolation algorithm of the inverse compositional-Gaussian Newton (IC-GN) method to reduce the interpolation bias. The simulation experiment results show that LIIF-S not only improves the accuracy by more than one order of magnitude compared to traditional interpolation algorithms but also that the interpolation bias does not have sinusoidal characteristics. In addition, the effectiveness and generalization of the LIIF-S method in unseen real-world scenarios have also been demonstrated through physical experiments. The code and dataset are publicly available athttps://github.com/LianpoWang/SLIIF .
After more than forty years of development, the accuracy of digital image correlation (DIC) methods has reached an extremely high level. However, the interpolation bias of DIC has not been resolved. With the flourishing of deep learning in the field of image superresolution, it has become possible to use deep learning-based image superresolution methods to reduce DIC interpolation bias. To achieve this goal, this paper improves the local implicit image function (LIIF) method based on the characteristics of speckle images to obtain LIIF-S, achieving continuous image representation and arbitrary resolution interpolation. Subsequently, LIIF-S is used as the interpolation algorithm of the inverse compositional-Gaussian Newton (IC-GN) method to reduce the interpolation bias. The simulation experiment results show that LIIF-S not only improves the accuracy by more than one order of magnitude compared to traditional interpolation algorithms but also that the interpolation bias does not have sinusoidal characteristics. In addition, the effectiveness and generalization of the LIIF-S method in unseen real-world scenarios have also been demonstrated through physical experiments. The code and dataset are publicly available at
Theoretical and Applied Mechanics Letters 16 (2026) 100653.
doi: 10.1016/j.taml.2026.100653
Abstract:
Projectile-borne electronics are essential components for precision-guided munitions. However, they are subjected to a complex overload environment characterized by high-frequency vibrations, high temperatures, and high pressures during launch. Evaluating overload damage presents a significant challenge. Consequently, this study aims to establish a damage tolerance criterion for projectile-borne electronics in high-g extreme environments using impact overload tests and high-precision numerical simulations. Initially, an impact overload test device was designed and implemented, considering the guidance segment and chamber firing characteristics, to ascertain the overload damage characteristics of projectile-borne electronics. Subsequently, a simulation model incorporating projectile-borne electronics was established and validated to identify the most vulnerable regions and critical overload responses under various conditions. Based on the simulation data, the overload damage tolerance curve was established using a power function regression fitting method. Leveraging the concept of impulse equivalence, the damage tolerance criterion for the high-g extreme environment was formulated. The criterion’s accuracy and practicality were further verified through experimental damage results of electronic components. This study provides a practical design foundation for the anti-high-overload design of projectile-borne electronics.
Projectile-borne electronics are essential components for precision-guided munitions. However, they are subjected to a complex overload environment characterized by high-frequency vibrations, high temperatures, and high pressures during launch. Evaluating overload damage presents a significant challenge. Consequently, this study aims to establish a damage tolerance criterion for projectile-borne electronics in high-g extreme environments using impact overload tests and high-precision numerical simulations. Initially, an impact overload test device was designed and implemented, considering the guidance segment and chamber firing characteristics, to ascertain the overload damage characteristics of projectile-borne electronics. Subsequently, a simulation model incorporating projectile-borne electronics was established and validated to identify the most vulnerable regions and critical overload responses under various conditions. Based on the simulation data, the overload damage tolerance curve was established using a power function regression fitting method. Leveraging the concept of impulse equivalence, the damage tolerance criterion for the high-g extreme environment was formulated. The criterion’s accuracy and practicality were further verified through experimental damage results of electronic components. This study provides a practical design foundation for the anti-high-overload design of projectile-borne electronics.
Theoretical and Applied Mechanics Letters 16 (2026) 100655.
doi: 10.1016/j.taml.2026.100655
Abstract:
Shale formations contain many pores 2–50 nm in size. These pores can make up more than 20% of the total pore volume. In such small pores, interactions between the pore walls and fluids cannot be ignored. This leads to significant confinement effects on the fluids. Alkanes are the main components of shale oil and gas. Their thermodynamic properties are key to understanding the distribution, efficient extraction, and industrial application of shale reserves. In this study, we used molecular simulations to study the phase behavior of methane, n-dodecane and n-eicosane in shale nanopores. We compared how chain length affects their phase behavior. First, we optimized the critical exponent values to improve the calculation accuracy of the critical parameters. To quantitatively evaluate confinement effects, we investigated the vapor-liquid equilibrium and critical properties of n-alkanes in nanopores with different pore sizes and geometries. The results show that in water-wet hydroxylated silica pores, the shifts in confined critical properties of n-alkanes do not exhibit a clear carbon chain length dependence. Based on the simulation results, we established predictive models for the critical properties of pure fluid. Finally, using a multicomponent shale oil reservoir as an example, we explored the influence of confinement effects on phase diagrams and the evolution of fluid component distribution during the pressure depletion process.
Shale formations contain many pores 2–50 nm in size. These pores can make up more than 20% of the total pore volume. In such small pores, interactions between the pore walls and fluids cannot be ignored. This leads to significant confinement effects on the fluids. Alkanes are the main components of shale oil and gas. Their thermodynamic properties are key to understanding the distribution, efficient extraction, and industrial application of shale reserves. In this study, we used molecular simulations to study the phase behavior of methane, n-dodecane and n-eicosane in shale nanopores. We compared how chain length affects their phase behavior. First, we optimized the critical exponent values to improve the calculation accuracy of the critical parameters. To quantitatively evaluate confinement effects, we investigated the vapor-liquid equilibrium and critical properties of n-alkanes in nanopores with different pore sizes and geometries. The results show that in water-wet hydroxylated silica pores, the shifts in confined critical properties of n-alkanes do not exhibit a clear carbon chain length dependence. Based on the simulation results, we established predictive models for the critical properties of pure fluid. Finally, using a multicomponent shale oil reservoir as an example, we explored the influence of confinement effects on phase diagrams and the evolution of fluid component distribution during the pressure depletion process.
Theoretical and Applied Mechanics Letters 16 (2026) 100656.
doi: 10.1016/j.taml.2026.100656
Abstract:
HighlightA numerical framework is developed for dust transport by coupling the regularized lattice Boltzmann method (RLBM) with large eddy simulation (LES) in an Eulerian–Eulerian formulation. The model incorporates wall-modeled LES through a wall shear stress treatment and adopts a recursive regularization strategy to enhance numerical stability for high Reynolds turbulence. Dust transport is modeled using an additional distribution function governed by an eddy-diffusion-based paradigm. The model is validated using two benchmark cases: the inviscid Taylor-Green vortex with dust and a high-Reynolds-number turbulent channel flow. It is then applied to simulate dust transport in the atmospheric boundary layer, where large-scale coherent structures drive lateral dispersion and influence vertical transport and particle residence time. The effects of particle size are systematically examined, showing that larger particles exhibit stronger settling due to inertia, while smaller particles remain suspended through enhanced coupling with turbulence. A negative correlation between streamwise velocity and particle concentration is also identified, highlighting the interaction between turbulent flow structures and particulate transport.
HighlightA numerical framework is developed for dust transport by coupling the regularized lattice Boltzmann method (RLBM) with large eddy simulation (LES) in an Eulerian–Eulerian formulation. The model incorporates wall-modeled LES through a wall shear stress treatment and adopts a recursive regularization strategy to enhance numerical stability for high Reynolds turbulence. Dust transport is modeled using an additional distribution function governed by an eddy-diffusion-based paradigm. The model is validated using two benchmark cases: the inviscid Taylor-Green vortex with dust and a high-Reynolds-number turbulent channel flow. It is then applied to simulate dust transport in the atmospheric boundary layer, where large-scale coherent structures drive lateral dispersion and influence vertical transport and particle residence time. The effects of particle size are systematically examined, showing that larger particles exhibit stronger settling due to inertia, while smaller particles remain suspended through enhanced coupling with turbulence. A negative correlation between streamwise velocity and particle concentration is also identified, highlighting the interaction between turbulent flow structures and particulate transport.
Theoretical and Applied Mechanics Letters 16 (2026) 100658.
doi: 10.1016/j.taml.2026.100658
Abstract:
To address the challenges and difficulties in predicting the relative permeability of reservoirs using traditional physics-driven and data-driven approaches, this paper proposes a collaborative analysis intelligent agent for the relative permeability of oil and gas reservoirs based on a large model. By constructing a multiagent collaborative workflow, integrated collaboration of data, models, and analysis results is achieved. The intelligent agent automatically completes data preprocessing, feature extraction, parameter calibration, small model calling, and output and evaluation of prediction results based on preset task dependencies. At the same time, by introducing deep learning-based embedding of physical information, the analysis efficiency and accuracy are significantly improved. The results show that compared with traditional physical analysis methods, this method improves the accuracy of reservoir relative permeability prediction by 10%, has a computational efficiency 10 times higher than traditional deep learning algorithms, and a computational speed 100–1,000 times higher than conventional physical models. This study further enhances the efficiency and intelligence of physical property analysis of oil and gas reservoirs, providing a new research direction for the intelligent development of oil and gas digitization.
To address the challenges and difficulties in predicting the relative permeability of reservoirs using traditional physics-driven and data-driven approaches, this paper proposes a collaborative analysis intelligent agent for the relative permeability of oil and gas reservoirs based on a large model. By constructing a multiagent collaborative workflow, integrated collaboration of data, models, and analysis results is achieved. The intelligent agent automatically completes data preprocessing, feature extraction, parameter calibration, small model calling, and output and evaluation of prediction results based on preset task dependencies. At the same time, by introducing deep learning-based embedding of physical information, the analysis efficiency and accuracy are significantly improved. The results show that compared with traditional physical analysis methods, this method improves the accuracy of reservoir relative permeability prediction by 10%, has a computational efficiency 10 times higher than traditional deep learning algorithms, and a computational speed 100–1,000 times higher than conventional physical models. This study further enhances the efficiency and intelligence of physical property analysis of oil and gas reservoirs, providing a new research direction for the intelligent development of oil and gas digitization.
Theoretical and Applied Mechanics Letters 16 (2026) 100667.
doi: 10.1016/j.taml.2026.100667
Abstract:
The turbulent flow in internal combustion engines is inherently complex due to moving geometries and time-varying topologies. This complexity is reflected in the wall-bounded regions, where experimental and numerical studies have reported velocity profiles that deviate substantially from classical turbulent boundary-layer behavior, often lacking a distinct logarithmic region. However, a systematic assessment of the applicability of established mean-velocity scaling methods under such conditions has not yet been performed. Here, we investigate the mean velocity within the boundary layer developing on the piston surface of a motored internal combustion research engine, for which experimental and numerical high-resolution near-wall boundary layer data have recently become available. Several scaling and transformation approaches are examined in terms of their ability to provide universal mean-velocity profiles relative to the classical logarithmic wall law. The results show that none of the tested transformations achieves a universal collapse of the velocity profiles across different piston locations and crank-angle positions. At the piston center, however, the semi-local scaling and the Trettel-Larsson (TL) transformation yield an effective collapse of the mean profiles. Nevertheless, none of the transformations fully aligns the profiles with the classical logarithmic law, with the TL transformation performing best in this regard. These findings confirm and quantify that the absence of a distinct logarithmic region is an inherent feature of the engine boundary layer.
The turbulent flow in internal combustion engines is inherently complex due to moving geometries and time-varying topologies. This complexity is reflected in the wall-bounded regions, where experimental and numerical studies have reported velocity profiles that deviate substantially from classical turbulent boundary-layer behavior, often lacking a distinct logarithmic region. However, a systematic assessment of the applicability of established mean-velocity scaling methods under such conditions has not yet been performed. Here, we investigate the mean velocity within the boundary layer developing on the piston surface of a motored internal combustion research engine, for which experimental and numerical high-resolution near-wall boundary layer data have recently become available. Several scaling and transformation approaches are examined in terms of their ability to provide universal mean-velocity profiles relative to the classical logarithmic wall law. The results show that none of the tested transformations achieves a universal collapse of the velocity profiles across different piston locations and crank-angle positions. At the piston center, however, the semi-local scaling and the Trettel-Larsson (TL) transformation yield an effective collapse of the mean profiles. Nevertheless, none of the transformations fully aligns the profiles with the classical logarithmic law, with the TL transformation performing best in this regard. These findings confirm and quantify that the absence of a distinct logarithmic region is an inherent feature of the engine boundary layer.
Theoretical and Applied Mechanics Letters 16 (2026) 100678.
doi: 10.1016/j.taml.2026.100678
Abstract:
This paper employs a new lifting-body model investigated through a cavitation tunnel, in which high-speed photography is combined with large eddy simulation to analyze flow characteristics under different cavitation numbers. The simulated cavity structures agree well with the experimental observations. Particular attention is given to the evolutionary characteristics of leading-edge vortex cavitation. The results demonstrate that the spiral vortex structure formed at the leading edge develops without periodic vortex shedding. Through analysis of vortex structures and surface pressure distribution, it is revealed that the secondary vortex induced by flow separation exhibits significant correlation with surface pressure, while increasing the cavitation number does not alter the established separation pattern.
This paper employs a new lifting-body model investigated through a cavitation tunnel, in which high-speed photography is combined with large eddy simulation to analyze flow characteristics under different cavitation numbers. The simulated cavity structures agree well with the experimental observations. Particular attention is given to the evolutionary characteristics of leading-edge vortex cavitation. The results demonstrate that the spiral vortex structure formed at the leading edge develops without periodic vortex shedding. Through analysis of vortex structures and surface pressure distribution, it is revealed that the secondary vortex induced by flow separation exhibits significant correlation with surface pressure, while increasing the cavitation number does not alter the established separation pattern.
Theoretical and Applied Mechanics Letters 16 (2026) 100654.
doi: 10.1016/j.taml.2026.100654
Abstract:
This paper introduces an improved scheme based on the discrete velocity method. Specifically, the reconstruction of the velocity distribution function and numerical flux at the interface is founded on the solution of the Bhatnagar-Gross-Krook equation along the characteristic line. The proposed method accurately considers molecular transport and collision effects at the interface, thereby enabling accurate modeling from rarefied to continuum flow regimes. Additionally, the implicit discretization of the microscopic equations and incorporation of macroscopic equations result in accelerated convergence properties for steady-state problems. The proposed numerical approach is validated through several cases, including Rayleigh flow, lid-driven cavity flow, flow past an NACA0012 airfoil, and supersonic flow around a sphere. Numerical results demonstrate that the proposed method can efficiently and accurately obtain multiscale flow properties.
This paper introduces an improved scheme based on the discrete velocity method. Specifically, the reconstruction of the velocity distribution function and numerical flux at the interface is founded on the solution of the Bhatnagar-Gross-Krook equation along the characteristic line. The proposed method accurately considers molecular transport and collision effects at the interface, thereby enabling accurate modeling from rarefied to continuum flow regimes. Additionally, the implicit discretization of the microscopic equations and incorporation of macroscopic equations result in accelerated convergence properties for steady-state problems. The proposed numerical approach is validated through several cases, including Rayleigh flow, lid-driven cavity flow, flow past an NACA0012 airfoil, and supersonic flow around a sphere. Numerical results demonstrate that the proposed method can efficiently and accurately obtain multiscale flow properties.
Theoretical and Applied Mechanics Letters 16 (2026) 100662.
doi: 10.1016/j.taml.2026.100662
Abstract:
This paper presents a comparative study of the solid weighting functions within the text of the modified partially saturated method (MPSM), which is an effective fluid-solid boundary condition in the lattice Boltzmann-discrete element coupling method (LBM-DEM). In its original form, the solid weighting function is τ-dependent. Past studies have shown that the computational drag is viscosity-dependent when using the τ-dependent solid weighting function to solve fluid-particle interactions. To address this issue, two modified solid weighting functions, namely, the higher-order function and the solid-coverage function, are proposed. Nevertheless, the literature lacks a comparison of these functions, especially for viscosity dependence. In this study, the solid weighting functions are implemented and tested through two benchmark multiphase configurations, i.e., a sphere settling between two parallel plates and the ‘drafting, kissing and tumbling’ of two settling spheres. The computational accuracy, viscosity dependence and convergence of the two modified functions are validated and compared against the original τ-dependent function. The LBM-DEM-MPSM formulation is then applied to study the settling behavior of a particle pack with varying solid fractions in a narrow fracture, which highlights the potential of employing the LBM-DEM-MPSM approach to a broader range of fluid-particle systems.
This paper presents a comparative study of the solid weighting functions within the text of the modified partially saturated method (MPSM), which is an effective fluid-solid boundary condition in the lattice Boltzmann-discrete element coupling method (LBM-DEM). In its original form, the solid weighting function is τ-dependent. Past studies have shown that the computational drag is viscosity-dependent when using the τ-dependent solid weighting function to solve fluid-particle interactions. To address this issue, two modified solid weighting functions, namely, the higher-order function and the solid-coverage function, are proposed. Nevertheless, the literature lacks a comparison of these functions, especially for viscosity dependence. In this study, the solid weighting functions are implemented and tested through two benchmark multiphase configurations, i.e., a sphere settling between two parallel plates and the ‘drafting, kissing and tumbling’ of two settling spheres. The computational accuracy, viscosity dependence and convergence of the two modified functions are validated and compared against the original τ-dependent function. The LBM-DEM-MPSM formulation is then applied to study the settling behavior of a particle pack with varying solid fractions in a narrow fracture, which highlights the potential of employing the LBM-DEM-MPSM approach to a broader range of fluid-particle systems.
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