Boundary Method Research Articles

The Nexus between Carbon Emissions and Per Capita Income of Households: Evidence from Japanese Prefectures

Household consumption is significantly influenced by various factors. Despite this, the intricate nature of consumption behaviors and the lack of comprehensive data from the supply chain have led to an incomplete recognition of the attributes contributing to home emissions at the city level. Through the analysis of city-level household consumption in relation to energy demand, utilizing a city-scale input-output model and urban residential consumption inventories, this study considers the environmental responsibility inherent in residential consumption for Japanese’s Prefectures, this study reveals that variations in this responsibility based on household type and season. The study period is 2013-2022. Various factors are taken into account when examining emissions by age and month, including emission type, source, fuel variety, and consumption items. These assertions stem from emissions data computed using the system boundary method. Our hypothesis is supported by a range of statistical findings, encompassing summary statistics and regression analysis. The connection between residential emissions and GDP is also explored through regression analysis. We uncover evidence indicating that carbon emissions in Japan fluctuate with the seasons and across diverse categories. These statistics illustrate a notable discrepancy in the regional distribution of carbon emissions, owing to evident variations in consumption rates and patterns.

Gravitational settling of two impermeable semi-torus particles

This research aimed to numerically investigate the dynamics of two semi-torus particles using the Immersed Boundary (IB) method. Various initial configurations were considered: vertically aligned along the centre of the fluid channel (Case A), vertically aligned in an asymmetric location (Case B), and horizontally aligned symmetrically to the channel centreline (Case C). Additionally, the impact of different starting alignments on particle dynamics was explored. When the particles were dropped along the middle of the channel, their dynamics depended on the fluid viscosity. Higher viscosities led to drafting and kissing phases, while lower viscosities resulted in multiple cycles of drafting, kissing, and tumbling (DKT). Similarly, the dynamics of particles dropped from an asymmetric location were also influenced by viscosity. For horizontally aligned particles along the centreline, the obtained results agreed well with previous studies. Notably, the initial orientation of the particles had a significant effect on their behaviour, particularly in less viscous fluid conditions.

Numerical Solution to a Free Boundary Problem for the Stokes Equation Using the Coupled Complex Boundary Method in Shape Optimization Setting

Numerical Solution to a Free Boundary Problem for the Stokes Equation Using the Coupled Complex Boundary Method in Shape Optimization Setting

An efficient Cartesian mesh generation strategy for complex geometries

Cartesian meshes based on the immersed boundary method are widely adopted for their convenience in implementing automated mesh generation. The performance of Cartesian mesh generation, particularly for complex geometries, is a crucial factor that directly impacts the efficiency of computational fluid dynamics solutions. In this study, we present an innovative strategy for efficient Cartesian mesh generation. Our methodology centers around the inner product test (IPT), enabling precise and efficient interior/exterior determination for intersected Cartesian cells. For this purpose, we enhance the k-d tree based intersection determination process to provide essential information of surface mesh for IPT, while concurrently improving the efficiency of the determination process. Our new methods offer automatic generation capabilities for arbitrary complex geometries. Through a series of tests, the new methods illustrate the notable performance improvements with the generation time of less than 4 min for the Cartesian mesh with 108 cells. Overall, our work optimizes Cartesian mesh generation for complex geometries, presenting significant potential for addressing the challenges of moving boundary problems.

Three-Dimensional Variational Multi-Doppler Wind Retrieval over Complex Terrain

Abstract The interaction of airflow with complex terrain has the potential to significantly amplify extreme precipitation events and modify the structure and intensity of precipitating cloud systems. However, understanding and forecasting such events is challenging, in part due to the scarcity of direct in situ measurements. Doppler radar can provide the capability to monitor extreme rainfall events over land, but our understanding of airflow modulated by orographic interactions remains limited. The SAMURAI software is a three-dimensional variational data assimilation (3DVAR) technique that uses the finite element approach to retrieve kinematic and thermodynamic fields. The analysis has high fidelity to observations when retrieving flows over a flat surface, but the capability of imposing topography as a boundary constraint is not previously implemented. Here, we implement the immersed boundary method (IBM) as pseudo-observations at their native coordinates in SAMURAI to represent the topographic forcing and surface impermeability. In this technique, neither data interpolation onto a Cartesian grid nor explicit physical constraint integration during the cost function minimization is needed. Furthermore, the physical constraints are treated as pseudo-observations, offering the flexibility to adjust the strength of the boundary condition. A series of observing simulation sensitivity experiments (OSSEs) using a full-physics model and radar emulator simulating rainfall from Typhoon Chanthu (2021) over Taiwan are conducted to evaluate the retrieval accuracy and parameter settings. The OSSE results show that the strength of the IBM constraints can impact the overall wind retrievals. Analysis from real radar observations further demonstrates that the improved retrieval technique can advance scientific analyses for the underlying dynamics of orographic precipitation using radar observations.

Simulation of flow over a fixed and oscillating circular cylinder with different surface roughness patterns using a multi-block-multi-mesh framework immersed boundary method

The effect of surface roughness on forces over a cylinder and the resulting vortex patterns at low Reynolds numbers are not well reported in the literature. This paper investigates flow over fixed and transversely oscillating two-dimensional rough cylinders with different roughness heights and spacing. A novel multi-block-multi-mesh framework-based immersed boundary method is developed to resolve the roughness elements over the cylinder surface, using a relatively coarser mesh at the outer domain. Small re-circulation zones trapped inside the roughness elements are captured. A drastic reduction in skin-friction drag is observed due to these vortices for both fixed and oscillating cylinders. Higher roughness height resulted in better lock-in phenomena at lower oscillation frequencies. However, the vortex shedding modes did not show much sensitivity to surface roughness.

Numerical study on vortex-induced vibration of four circular cylinders at low Reynolds number

Vortex-Induced Vibration (VIV) of multiple cylinders has received increasing attention in the ocean engineering field in recent years. In this paper, a two-dimensional numerical model for studying VIV of multiple cylinders is developed. Based on a fixed Cartesian grid with local mesh refinement adopted, the immersed boundary method is utilized to account for the existence of cylinders. Two-degree-of-freedom VIV of a single circular cylinder is simulated to validate the model, and then the model is utilized in the VIV of a four circular-cylinder group with square arrangement. The mass ratio is m* = 2.0, and the spacing ratio L/D is 5.0, where L is the central displacement of two adjacent cylinders and D is the diameter of the cylinders. Reynolds number ranging from 45 to 210 is considered, and the variation of which is achieved by changing the inflow velocity. The corresponding reduced velocity varies from 3 to 14. The influences of Reynolds number on the vibrating frequencies, the response amplitudes, the X–Y trajectories, the vorticity field distribution, and the hydrodynamic coefficients are analyzed in detail. A critical Reynolds number of 105 is observed, at which the X–Y trajectories and the vorticity field distribution change their patterns.

Determination of line heating conditions for plate forming using the strain directed boundary method based on deformation superposition

Determination of line heating conditions for plate forming using the strain directed boundary method based on deformation superposition

Numerical Investigation of a Pitching NACA 0012 Wing with Plasma-Based Flow Control Using Prediction–Correction Direct-Forcing Immersed Boundary Method

Numerical Investigation of a Pitching NACA 0012 Wing with Plasma-Based Flow Control Using Prediction–Correction Direct-Forcing Immersed Boundary Method

High-order moving immersed boundary and its application to a resolved CFD-DEM model

The sharp interface immersed boundary method (IBM) is a powerful tool to simulate the flow around moving objects. This paper extends this method to simulate the motion of particles immersed in a fluid. We introduce a new implicit coupling scheme between the solid and fluid phases, verify the high–order of convergence of the scheme, and validate it using four cases. The fluid dynamics is simulated using a streamline upwind Petrov–Galerkin and pressure-stabilizing Petrov–Galerkin (SUPG/PSPG) stabilizations. The particles’ dynamics and contact are solved using Newton’s second law of motion and a soft sphere contact model derived from the discrete element method. The first validation case is the sedimentation of a lone particle with a Reynolds number smaller than 32. The second validation case is the rise of a positively buoyant particle at a high Reynolds number (2500). The third validation case demonstrates the stability of the scheme when particles are in contact and exhibit the classical drafting, kissing, and tumbling (DKT) behavior. Finally, we use the scheme to study the Boycott effect with a larger number of particles (64) to show the stability of the scheme in cases with numerous particle–particle and particle–wall contacts.

Performance analysis and material distribution optimization for sound barriers using a semianalytical meshless method

AbstractWith the increase in car ownership, traffic noise pollution has increased considerably and is one of the most severe types of noise pollution that affects living standards. Noise reduction by sound barriers is a common protective measure used in this country and abroad. The acoustic performance of a sound barrier is highly dependent on its shape and material. In this paper, a semianalytical meshless Burton–Miller‐type singular boundary method is proposed to analyze the acoustic performance of various shapes of sound barriers, and the distribution of sound‐absorbing materials on the surface of sound barriers is optimized by combining a solid isotropic material with a penalization method. The acoustic effect of the sound‐absorbing material is simplified as the acoustical impedance boundary condition. The objective of optimization is to minimize the sound pressure in a given reference plane. The volume of the sound‐absorbing material is used as a constraint. The density of the nodes covered with the sound‐absorbing material is used as the design variable. The method of moving asymptotes was used to update the design variables. This model completely avoids the mesh discretization process in the finite element method and requires only boundary nodes. In addition, the approach also does not require the singular integral calculation in the boundary element method. The method is illustrated and validated using numerical examples to demonstrate its accuracy and efficiency.

Pore-scale resolved simulation of quenching, acceleration, and transition to detonation of hydrogen explosions by metal foams

Pore-scale simulations of quenching, acceleration, and transition to detonation of gaseous hydrogen explosions by metal foams were performed. The model solves the three dimensional compressible reactive Navier-Stokes equations with detailed chemistry in a closed square channel with a metal foam placed inside. The structures of the foam were fully resolved using an immersed boundary method. Stoichiometric mixtures of hydrogen-oxygen and hydrogen-air were considered. An explosion in the channel was initiated with a high-pressure and high-temperature spark. The simulation results show that the explosion can be quenched, accelerate, or transition to detonation depending on the foam pores-per-inch (PPI). Hydrogen-air explosions were quenched with foams of ∼39 PPI or higher due to heat losses from the flame, which is consistent with experimental observations. The explosion was not quenched by foams with low PPI. Instead the low PPI foams exacerbated the explosion by causing flame acceleration. Worse, a 78 PPI foam caused a stoichiometric H2 and O2 mixture to transition to detonation. Hydraulic resistance due to products venting away from the flame surface was found to produce strong pressure gradients within the foam. This causes a self-pressurizing effect that grows as the flame propagates further into the foam. The pressure within the foam grows and steepens into a shock. The shock initiated the detonation by a Mach reflection, which is similar to deflagration-to-detonation transition mechanisms in traditional obstacle-laden channels. Statement of SignificanceMetal foam structures are often used as devices to inhibit flames in scenarios where explosion hazards are a concern. Direct numerical simulations were performed to increase understanding of how flames and explosions interact with metal foams. The simulation results show that high pores-per-inch (PPI) foams quench the explosion by removing heat from the flame. Lower PPI foams can have the opposite effect and exacerbate the explosion by promoting flame acceleration or even transition to detonation. Flames self-pressurize as they propagate through low PPI foams due to hydrodynamic friction and gas-dynamic effects from flowing product gases. In extreme cases, the pressure waves near the flame can steepen into a shock and initiate a detonation. These results indicate that improperly selected metal foam flame arresters can exacerbate the explosion.

Porous-media model based particle-resolved simulation of a fixed bed with olefin catalytic cracking reaction

Understanding the interstitial reacting flow in particle packing structure and its relation with the reaction performance is crucial to designing a highly efficient fixed bed reactor. This study uses a particle-resolved approach with a porous-media model-based immersed boundary method to simulate an olefin catalytic cracking (OCC) fixed bed with 150 cylindrical particles by combining a six-lump kinetic model and mass transfer model. The effects of weight hourly space velocity (WHSV) and particle shape are further investigated in analyzing conversion, concentration variation, flow structure and pressure drop. The study reveals a three-stage pattern in variation of product concentration along the packing structure height with different WHSVs, providing the basis for determining the optimal packing height. It also finds that the hollow-cylindrical particle manifests the best reaction performance while the cylindrical particle the worst. The coordination of surface area and pressure drop of the packing structure determines the OCC reaction effectiveness.

Investigation of saturation levitation force and optimization of permanent magnet guideway based on multi-seeded superconducting bulks model

After more than 20 years of research, the superconducting maglev has advanced to the engineering research stage. In engineering applications, multi-seeded superconducting bulks have been widely used in high-temperature superconducting (HTS) maglev systems, but there remains a deficiency in terms of the theoretical model description of multi-seeded superconducting bulks. In this paper, the fully coupled, partially coupled, and uncoupled models of the multi-seeded superconductor are presented to simulate HTS multi-seeded bulk. Then, the levitation performance and trapped field of three kinds of HTS bulks were experimentally tested, revealing a saturation levitation performance on the permanent magnet guideway (PMG). Therefore, the levitation force and trapped field of HTS bulks with different critical current density are further studied by 3D simulation. Taking the 90% and 95% of the maximum levitation force as the benchmarks, the corresponding critical current density of HTS bulks are respectively 4.6 × 108 A m−2 and 6.1 × 108 A m−2. Further, a mapping coupled boundary method was adopted to automatic optimize the PMG to increase the levitation force above the PMG. After optimization, the levitation force under a unit of the permanent magnet is increased by 19%, while the maximum levitation force above multi-period Halbach PMG is increased by 9.23%. This study provides a general multi-seeded superconducting bulk simulation model and levitation force optimization method, which can serve as a reference for selecting suitable superconducting bulk.

Simulation of an Elastic Rod Whirling Instabilities by Using the Lattice Boltzmann Method Combined with an Immersed Boundary Method

Mathematical modeling and analysis of biologically inspired systems has been a fascinating research topic in recent years. In this work, we present the results obtained from the simulation of an elastic rod (that mimics a flagellum axoneme) rotational motion in a viscous fluid by using the lattice Boltzmann method (LBM) combined with an immersed boundary method (IBM). A finite element model consists of a set of beam and truss elements used to discretize the flagellum axoneme while the fluid flow is solved by the well-known LBM. The hydrodynamic coupling to maintain the no-slip boundary condition between the fluid and the elastic rod is conducted with the IBM. The rod is actuated with a torque applied at its base cross-section that acts as a driving motor of the axoneme. We simulated the rotational dynamics of the rod for three different rotational frequencies (low, medium, and high) of the motor. To compare with previous publication results, we chose the sperm number Sp=L(4πμω)/(EI)1/4 as the validation parameter. We found that at the low rotational frequency, f = 1.5 Hz, the rod performs stable twirling motion after attaining an equilibrium state (the rod undergoes rigid rotation about its axis). At the medium frequency, f = 2.65 Hz, the rod undergoes whirling motion, where the tip of the rod rotates about the central rotational axis of the driving motor. When the frequency increases further, i.e., when it reaches the critical value, fc ≈ 2.7 Hz, the whirling motion becomes over-whirling, where the tip of the filament falls back to the base and performs a steady crank-shafting motion. All three rotational dynamics, twirling, whirling, and over-whirling, and the critical value of rotational frequency are in good agreement with the previously published results. We also observed that our present simulation technique is computationally more efficient than previous works.

Acoustic simulation using singular boundary method based on loop subdivision surfaces: A seamless integration of CAD and CAE

This paper firstly combines the Burton-Miller-type singular boundary method (BMSBM) with the Loop subdivision surfaces (LSS) for the acoustic simulation of 3D complicated structures. As a modern modeling technique, the LSS provides a flexible and simple means to represent model surfaces by controlling meshes and subdivision rules. Thus, it can achieve arbitrary topology and multi-resolution structures. As a semi-analytical and boundary-type meshless technique, the BMSBM using the fundamental solutions is simple, accurate, and straightforward for solving acoustic radiation and scattering problems. The new approach constructs a geometry model using a subdivision scheme, and therefore can create a multi-resolution hierarchical model meeting various accuracy requirements without a repetitive meshing procedure. The proposed method effectively breaks through the technical bottleneck that the BMSBM makes it difficult to collate boundary nodes of complex structures and achieves a seamless integration between CAD and CAE. The numerical results of three examples demonstrated the effectiveness and accuracy of the proposed method for acoustic simulation. The present study provides an innovative idea for the subsequent optimization of materials and shapes of acoustic structures, which has the potential to enhance precision and efficiency significantly.

Differentiable hybrid neural modeling for fluid-structure interaction

Solving complex fluid-structure interaction (FSI) problems, which are described by nonlinear partial differential equations, is crucial in various scientific and engineering applications. Traditional computational fluid dynamics based solvers are inadequate to handle the increasing demand for large-scale and long-period simulations. The ever-increasing availability of data and rapid advancement in deep learning (DL) have opened new avenues to tackle these challenges through data-enabled modeling. The seamless integration of DL and classic numerical techniques through the differentiable programming framework can significantly improve data-driven modeling performance. In this study, we propose a differentiable hybrid neural modeling framework for efficient simulation of FSI problems, where the numerically discretized FSI physics based on the immersed boundary method is seamlessly integrated with sequential neural networks using differentiable programming. All modules are programmed in JAX, where automatic differentiation enables gradient back-propagation over the entire model rollout trajectory, allowing the hybrid neural FSI model to be trained as a whole in an end-to-end, sequence-to-sequence manner. Through several FSI benchmark cases, we demonstrate the merit and capability of the proposed method in modeling FSI dynamics for both rigid and flexible bodies. The proposed model has also demonstrated its superiority over baseline purely data-driven neural models, weakly-coupled hybrid neural models, and purely numerical FSI solvers in terms of accuracy, robustness, and generalizability.

An efficient hybrid collocation scheme for vibro-acoustic analysis of the underwater functionally graded structures in the shallow ocean

In this paper, a novel hybrid collocation scheme based on the generalized finite difference method (GFDM) and the Burton–Miller singular boundary method (BMSBM) is developed to study the vibration and acoustic radiation characteristics of an underwater functionally graded (FG) structure immersed in the shallow ocean. By utilizing the individual strengths of both methods, the GFDM is adopted for the vibration analysis of the FG structures, while the BMSBM is applied for the acoustic wave radiation analysis. Numerical examples verify the accuracy and efficiency of the proposed hybrid collocation scheme for the natural frequency and acoustic radiation behavior of the underwater structures consisting of the functionally graded materials (FGMs). The influences of the material parameters, structural geometries and shallow ocean environment on the natural frequencies of the structural vibration and the underwater acoustic wave radiation field are investigated in detail. Numerical study shows that the variation trend of the natural frequencies of the structural vibration is consistent with that of the resonance peak frequencies of the underwater acoustic radiation field. The present results may provide valuable references for the design and application of underwater marine structures consisting of the FGMs.

Synergistic effect of ribs and particles on flow and heat transfer in channels using the CFD-DEM-IBM method

To investigate the synergistic effect of the surface structure and particles on flow and heat transfer during forced convection, a model for two-phase flow and heat transfer was established using the computational fluid dynamics-discrete element method-immersed boundary method (CFD-DEM-IBM). The effects of rib size and particle physical properties on the flow and heat transfer were studied. The results showed that large-scale vortices rolling forward were formed in the particle-laden flow, and heat transfer in the rib gaps was intermittently enhanced. Convective heat flux was weakened, and conductive heat flux was strengthened when the height of the ribs was too high or the spacing was too small. Particles with high thermal conductivity promoted conductive and convective heat transfer. Small particles easily entered the rib gaps to strengthen the heat transfer, but this inhibited heat conduction at flat surface. Fluid laden with a mixture of particle sizes enhanced the convective heat transfer.

A regularized projection immersed boundary method for smooth boundary forces

The projection immersed boundary method calculates boundary forces (i.e., surface stresses) from velocity constraints without introducing additional timestep restrictions. However, the projection method generally fails to produce boundary forces that converge to the actual physical surface stresses when the grid is refined. In most cases, the boundary forces show spurious oscillation. This spurious oscillation is particularly violent when the Lagrangian-to-Eulerian grid spacing ratio is small. As a result, the traditional projection method may encounter problems in fluid-structural interaction (FSI) simulations where accurate boundary forces are needed. To address these challenges, we propose a regularized projection method using (generalized) Tikhonov regularization techniques. The regularized projection method yields smoother boundary force solutions that closely approximate the actual boundary force distributions for a wider range of Lagrangian-to-Eulerian grid spacing ratios. The boundary force shows first order convergence with properly chosen parameters. We demonstrate the effectiveness and accuracy of our approach through various test cases.