Implicit Coupling Research Articles

SORM‐Enhanced Inverse Reliability Analysis for Geotechnical Multiobjective Reliability‐Based Design Optimization

ABSTRACTThe first‐order reliability method (FORM) is mostly employed in the existing geotechnical reliability‐based design (RBD) methods due to its computational simplicity and efficiency. However, the first‐order Taylor approximation of the limit state surface (LSS) may result in significant errors, especially in cases of highly nonlinear LSS characterized by substantial curvatures. Therefore, FORM‐based RBD methods require a modification of the curvatures to enhance the accuracy of the probabilistic constraints, specifically by converting the target reliability index into a more precise target failure probability. Correspondingly, reliability index‐based design is converted into failure probability‐based design. In this study, the parabolic second‐order reliability method (SORM), which avoids the Hessian calculations, is adopted to improve the accuracy of probabilistic constraints beyond what is achievable with FORM. The proposed SORM‐enhanced RBD method accounts for the curvature information of the nonlinear LSS, modifying the target reliability index to align with the exact target failure probability through the application of SORM. Moreover, by incorporating an implicit coupling function, multiobjective RBD can be effectively implemented without any additional surrogate model. Furthermore, the proposed RBD method is readily extended to reliability‐based design optimization (RBDO) through integration with an optimization strategy. The proposed RBDO method demonstrates a more precise convergence of the probabilistic constraints, surpassing the accuracy of FORM‐based RBDO methods. Notably, the proposed SORM‐enhanced RBDO method not only significantly improves accuracy but also bypasses the necessity for Hessian computation, which remains both the second‐order accuracy and first‐order efficiency. The feasibility of the proposed method is demonstrated through a mathematical example and three practical geotechnical design examples.

Fracture as an Emergent Phenomenon

The mechanics of fracture propagation provides essential knowledge for the risk tolerance design of devices, structures, and vehicles. Techniques of free energy minimization provide guidance, but have limited applicability to material systems evolving away from equilibrium. Experimental evidence shows that the material response depends on driving forces arising from mechanical fields. Recent years have witnessed the development of new methods for modeling complex dynamic and quasistatic fracture. New approaches may differ remarkably from previous ones, as they involve implicit coupling between damaged and undamaged states, allowing fracture to be modeled as emergent phenomena.The focus of this workshop is on the most advanced techniques for modeling fracture, represented by eigenerosion methods, variational approaches, phase field fracture models, and non-local approaches. Technical progress is contingent on the further development of the mathematical framework underlying these techniques. This is necessary for accurate and reliable computational modeling of fracture for multiple freely propagating cracks. The objective of this workshop is to mathematically identify and discuss open issues related to fracture modeling and to highlight recent advances. Addressing fundamental issues will foster exchange between the different communities, essential for advancing the field.

Domain decomposition for physics-data combined neural network based parametric reduced order modelling

This paper proposes a novel domain decomposition (DD) method for the parametric reduced-order model based on the Physics-Data Combined Neural Network (DD-PDCNN). The computational domain is partitioned into a number of subdomains, and a Physics-Data Combined Neural Network (PDCNN) is constructed for each subdomain, which not only represents the dynamics within its region but also considers interactions with neighbouring subdomains. The interface conditions between subdomains are considered by averaging solutions at the neighbourhoods, incorporating averaged solutions, predicted solutions at current and next time levels into reduced governing equations. The implicit coupling among the subdomains ensures global continuity and establishes boundary conditions for each subdomain.The performance of this new DD-PDCNN is compared with that of PDCNN without domain decomposition, data-driven model and traditional Reduced Basis(RB) model. The capability of this model is tested using a number of parametric nonlinear problems, such as the Korteweg-de Vries (KdV) equation, the two-dimensional Kovasznay flow and the two-dimensional incompressible Navier–Stokes equation. The results indicate that the proposed method offers an effective way to construct an accurate reduced order model for parameterised PDEs through machine learning. In particular, in specific parameter ranges where distinct physical phenomenon regions are prominent, the method outperforms the model without domain decomposition, demonstrating excellent performance on several challenging problems.

Leakage detection method based on transient pressure behaviors during pigging process in pipelines

Pipelines are the most common way to transport oil and gas due to its convenience. They are facing many threatens such as leakage, which may cause serious pipeline accidents. This paper proposes a leakage detection method coupled with the transient pressure characteristics to recognize leaks in pipeline. A coupled dynamic mesh method was used to achieve the movement of pigging device. The explicit and implicit coupling method has been developed to simulate transient pressures and leak behaviors. Cases has been conducted through the established experimental pipeline system to validate the proposed leakage detection method. The reasonable agreement between the results from these two methods verify that the proposed leakage detection method is accurate enough to simulate transient pressure behaviors in pipelines during the pigging process. Leak volume and location identification methods have been presented and the calculation accuracy is verified in a reasonable range. The proposed leakage detection method in this paper is a supplement to the field of subsea pipeline detection.

Fluid selection and parametric analysis of organic Rankine cycle applicable to the turboshaft engine with a recuperator

With ever increasing fossil fuel price and growing demands in cutting emissions, waste heat recovery (WHR) appears as a promising pathway to improve propulsion system performance, which can be potentially achieved by incorporating a recuperator. This paper explores the advantages and potentiality of further recovering exhaust heat from recuperated turboshaft engine through the concept of organic Rankine cycle (ORC) to improve fuel economy and thermal efficiency. For the intended application, working fluid selection is conducted after systematic consideration of thermophysical properties, environmental impact, health and safety issues. Furthermore, parametric analysis is carried out from the viewpoint of thermodynamics, and the genetic algorithm is also employed to obtain the maximum net power output. Targeting the implicit coupling between recuperator effectiveness and ORC performance, the potential advantages of the combined engine-ORC system are comprehensively evaluated at different operational regimes. The influence of flight condition is also discussed through sensitivity simulations for different altitudes. Results reveal that the combination of the recuperated engine with ORC cycle operated using acetone generally offers the greatest benefits, significantly reducing specific fuel consumption by 46%–59 % relative to the baseline simple-cycle engine, depending on the availability of heat source. This analytical work contributes to provide valuable insights into WHR technologies in the aviation industry.

A generic approach for modelling hydrogen-methane-air detonation in hydrocode

Hydrogen is pivotal in the transition to a sustainable energy supply. The presence of hydrogen-methane mixtures is increasing as the feasibility of utilizing existing natural gas infrastructure for large-scale hydrogen transportation and distribution. However, recent explosion accidents underscore the need to understand the detonation hazards of hydrogen and methane. Current modelling techniques for hydrogen-methane-air detonations are computationally prohibitive due to extra-fine mesh and time step requirements to solve the chemical reaction coupling within detonation structure. This study presented a generic approach to address these challenges, enabling precise and rapid simulation of hydrogen-methane-air blast profiles within hydrocodes. Modified open-source codes helped bypass the time-consuming implicit coupling of detailed chemical reactions with detonation structure and thermodynamic properties based on Chapman-Jouguet (C-J) theory and equilibrium reactive flow assumption, yielding a 90% reduction in computational time. An empirical model, developed through theoretic calculations, provided C-J parameters for hydrocode input with high accuracy across typical industrial conditions. Then, these C-J parameters were employed in LS-DYNA hydrocode based on modified Jones-Wilkins-Lee (JWL) equation of state (EoS) to simulate the hydrogen-methane-air blast loading. This approach was validated against diverse experimental data, encompassing hydrogen-air, methane-air, and hydrogen-methane-air mixtures, and various fuel concentrations, experimental scales, confinement conditions, and fuel shapes. Although conservative results were observed in unstable detonations near the lower detonable limit, it outperformed traditional CFD methods in both accuracy and efficiency. Furthermore, the use of hydrocodes enables the analysis of blast loading as well as the dynamic behaviour of structures subjected to explosive forces. This approach is easily adaptable to other gaseous detonations beyond hydrogen-methane-air by simply replacing the chemical reaction models, making it a versatile tool across various fields.

Role of minimization entropy generation and heat transfer on the nanofluid peristaltic flow via Reiner-Philippoff model

The primary objective of this study is to explore the effects of minimizing entropy generation in the context of peristaltic flow within an asymmetric tapered channel, using Buongiorno’s nanofluid model to account for pseudoplastic and dilatant behaviors of the nanofluid. To accurately represent the non-Newtonian characteristics of the fluid, we employ the Reiner-Philippoff (RPh) fluid model, known for its intricate nature among non-Newtonian models. In the RPh model, the relationship between shear stress and velocity gradient is nonlinear, and it also accounts for the implicit coupling between stress and deformation rate, presenting a formidable challenge. Our investigation incorporates the effects of thermophoresis motion, the viscosity parameter of the RPh fluid, and Brownian motion into the governing equations. We simplify these equations under the assumptions of low Reynolds numbers and long wavelengths. Subsequently, we numerically solve the resulting nonlinear equations. We thoroughly discuss the significant impact of RPh nanofluid parameters on entropy generation and the Bejan number by presenting graphical representations. Notably, we observe that the fluid transitions from a dilatant behavior to Newtonian behavior and from Newtonian behavior to pseudoplastic behavior as we vary the RPh fluid parameter. Furthermore, we briefly address the influence of thermophoretic diffusion, the Brinkman number, the RPh fluid parameter, Prandtl number, and Brownian motion parameters on entropy production and the Bejan number. It is experimented that the entropy generation is less for dilatants fluid and higher for pseudoplastic fluids. We can also notice that the entropy generation significantly increases by Brinkman number Br for both types of fluid. We also provide a mathematical and graphical examination of the effects of all these significant parameters.

Experimental and Numerical Study of the Flow Around Rigid and Flexible Hydrofoils for Wetted and Cavitating Flow Conditions

Abstract The hydro-elastic response of a flexible NACA 0015 hydrofoil is investigated for both wetted and cavitating flow conditions. Computational fluid dynamics (CFD) analysis are performed using a fully implicit coupling between the ISIS-CFD solver (developed by the METHRIC team at Ecole Centrale de-Nantes) and a modal approach for the structure. The Reynolds-averaged Navier–Stokes (RANS) solver is first validated for wetted and cavitating flow conditions around a similar rigid hydrofoil, with experimental results carried out at the hydrodynamic tunnel of the French Naval Academy, including lift and drag measurements and high speed camera images. Then the numerical predictions for the flexible hydrofoil response are compared with experimental bending shapes and vibrations amplitudes, with a focus on cavitating flow conditions. For wetted flow conditions, numerical results show a good agreement with the experiments, for both rigid and flexible hydrofoils. For cavitating flow conditions, the hydro-elastic response is dominated by vibrations at the hydrofoil modal frequencies and the reentrant jet instability frequency. For the lowest values of the cavitation number, a large amplitude peak is experimentally observed in the frequency response spectra, due to lock-in between the first modal frequency and the reentrant jet frequency. Strong harmonics of this dominant peak also appear in the spectra, revealing a nonlinear response of the hydrofoil. While the amplitudes of vibrations are well predicted by the computations, the frequency lock-in observed in the experiments is not captured by the numerical model.

General Muscle Torque Generator Model for a Two Degree-of-Freedom Shoulder Joint.

Muscle torque generators (MTGs) have been developed as an alternative to muscle-force models, reducing the muscle-force model complexity to a single torque at the joint. Current MTGs can only be applied to single Degree-of-freedom (DoF) joints, leading to complications in modeling joints with multiple-DoFs such as the shoulder. This study aimed to develop an MTG model that accounts for the coupling between 2-DoF at the shoulder joint: shoulder plane of elevation (horizontal abduction/adduction) and shoulder elevation (flexion/extension). Three different 2-DoF MTG equations were developed to model the coupling between these two movements. Net joint torques at the shoulder were determined for 20 participants (10 females and 10 males) in isometric, isokinetic, and passive tests. Curve and surface polynomial fitting were used to find the best general fit for the experimental data in terms of the different degrees of coupling. The models were validated against experimental isokinetic torque data. It was determined that implicit coupling that used interpolation between single-DoF MTGs resulted in the lowest root-mean-square percent error of 8.5%. The work demonstrated that general MTG models can predict torque results that are dependent on multiple-DoFs of the shoulder.

Model based precise register control method for shaft-driven Roll-to-Roll(R2R) systems

Shaft-driven Roll-to-Roll (R2R) printing systems have advantages in keeping the printing rolls synchronously rotating, thereby reducing the register errors of R2R printing systems. However, tension oscillations and propagation are still inevitable due to other factors such as disturbances, which lead to the fluctuation of register errors. In this paper, a new mechanical model is established for the shaft-driven R2R systems. Then, a model-based precise control (MBPC) method is proposed, in which an implicit coupling algorithm is designed for the cooperate actions of the dancer rolls to rapidly suppress the tension oscillations and propagation. The stability of the proposed control system is proved via Lyapunov analysis. Moreover, the effectiveness of the proposed modeling and control method is verified via an industrial example. The results indicate that the proposed model can accurately characterize the dynamics of the R2R systems, and the MBPC can effectively eliminate the register errors caused by the tension oscillations and propagation, through the implicit coupling algorithm. Additionally, the results also demonstrate that the MBPC can increase the register precision of package manufacturing R2R systems into ±40 micrometers, which is superior to the existing control method.

Extension of a sharp-interface immersed-boundary method for simulating parachute inflation

In this work, the sharp-interface immersed boundary (IB) method proposed by Mittal et al. (J Comput Phys 227(10):4825–4852, 2008) is extended to fluid-structure-interaction (FSI) simulation of parachute inflation by utilizing several open-source tools. The method employs a Cartesian-grid ghost-cell methodology to accurately represent the immersed boundary, and it is suitable for solving moving-boundary flows with arbitrarily complex geometries. The finite-element code CalculiX is employed to solve the structural dynamics of the parachute system. The IB flow solver is coupled with CalculiX in a minimally-invasive manner using the multi-physics coupling library preCICE. The implicit fluid-structure coupling together with the Aitken adaptive under-relaxation scheme is considered to improve the numerical accuracy and stability. The developed approach is validated by a benchmark FSI case. Numerical experiments on the inflation process of several typical parachutes are further conducted. The breathing process, flow structure, canopy displacement and drag coefficient are analyzed to demonstrate the applicability of the present approach for simulating parachute inflation.

Numerical investigation of liquid sloshing in 2D flexible tanks subjected to complex external loading

Due to the complexity of fluid–structure interactions (FSI), the majority of studies in the literature dealing with the sloshing problem are restricted to rigid tanks. This paper is devoted to a numerical investigation of the liquid sloshing behavior in a flexible tank subjected to external loading. A numerical methodology is proposed, taking into account the FSI problem by coupling two open-source codes: OpenFOAM for the fluid and FEniCS for the solid, using the preCICE library, a free library for fluid–structure interaction. The Arbitrary Lagrangian–Eulerian formulation is used for the two-phase flow system to solve the Navier–Stokes equations in the fluid domain using the finite volume method. Simultaneously, the linear-elastic equation of the structure is solved using the finite element method. An implicit coupling scheme is considered at the fluid–structure interface. The numerical methodology is validated by the results given in literature for harmonic excitation at different frequencies. Subsequently, an analysis of complex external loading, such as Gabor wavelets and earthquake ground motion, is conducted to highlight the significant impact of the wall flexibility on sloshing, as well as the influence of hydrodynamic forces on the structure’s deformation. The proposed coupling methodology is robust and effective, it can be applied to all types of liquids and materials. A dataset of one of the studied cases is given as a supplement to the paper (Kha et al., 2024).

Flexible and rigorous numerical modelling of multiphysics processes in fractured porous media using PorePy

Multiphysics processes in fractured porous media is a research field of importance for several subsurface applications and has received considerable attention over the last decade. The dynamics are characterized by strong couplings between processes as well as interaction between the processes and the structure of the fractured medium itself. The rich range of behaviour calls for explorative mathematical modelling, such as experimentation with constitutive laws and novel coupling concepts between physical processes. Moreover, efficient simulations of the strong couplings between multiphysics processes and geological structures require the development of tailored numerical methods.We present a modelling framework and its implementation in the open-source simulation toolbox PorePy, which is designed for rapid prototyping of multiphysics processes in fractured porous media. PorePy uses a mixed-dimensional representation of the fracture geometry and generally applies fully implicit couplings between processes. The code design follows the paradigms of modularity and differentiable programming, which together allow for extreme flexibility in experimentation with governing equations with minimal changes to the code base. The code integrity is supported by a multilevel testing framework ensuring the reliability of the code.We present our modelling framework within a context of thermo-poroelasticity in deformable fractured porous media, illustrating the close relation between the governing equations and the source code. We furthermore discuss the design of the testing framework and present simulations showcasing the extendibility of PorePy, as well as the type of results that can be produced by mixed-dimensional simulation tools.

An implicit thermo-mechanical coupling model for heat conduction and thermal cracking in brittle materials

In this paper, an implicit thermo-mechanical coupling model is developed to simulate heat conduction and thermal cracking in brittle materials. In the thermal analysis, an implicit particle heat conduction model (PHCM) is proposed. A linear algebraic system of heat conduction equations is derived based on the temperatures of the particle system and the heat flux among adjacent particles. An analytical expression is introduced for the involved correction coefficient, with which the macroscopic thermal conductivity coefficient can be directly adopted without calibration. Furthermore, a thermal conductivity reduction coefficient is introduced to account for the thermal resistance of the cracks. In the mechanical analysis, particle discontinuous deformation analysis (PDDA), which is an implicit variant of the discrete element method, is employed. The PHCM is first verified against analytical and finite element solutions for transient heat conduction problems. The results show that the PHCM is an effective and accurate heat conduction model that readily reflects the thermal resistance of cracks. Then, the thermo-mechanical coupling model is verified by the expansion of heated specimens under different conditions. Finally, the successful application of the coupling model in the simulation of thermal shock tests demonstrates its effectiveness for thermal cracking problems.

Fully finite volume method on a curvilinear grid-based arbitrary Lagrangian Eulerian approach for computational fluid flexible-structure interaction

For Computational Fluid flexible-Structure Interaction (CFfSI), this paper in on proposition of a unified fluid-dynamic and elastic stresses-based fully Finite Volume Method (FVM)—for both fluid and structural dynamics—on a curvilinear grid for both fluid and structure subdomains. Further, a hybrid method is proposed for the dynamic curvilinear-grid generation in the fluid subdomain. Arbitrary Lagrangian Eulerian (ALE) framework-based governing equations are presented for fluid-flow while those for the structural deformations are presented in the Lagrangian framework; along with the fluid-solid interfacial conditions. Solution methodology is presented, for the ALE method on the curvilinear grid, using a fully implicit pressure projection method for the flow solver and a pseudo-transient time stepping method for the structural solver; along with a fully implicit coupling between the two solvers. For the ALE method-based in-house CFfSI solver, an excellent agreement with the published numerical results is demonstrated (for steady and periodic flow-profiles/structural-deformations) on four different CFfSI problems. Further, a II-order accuracy in space as well as time is demonstrated for the present ALE method. After the validation and order of accuracy studies, a performance study is presented for our CFfSI solver on a dynamic-grid—generated by the proposed hybrid method as compared to a traditional method. The hybrid method resulted in up to 30% reduction in computational time for the four CFfSI problems; used in the validation study. An ALE method, based on a novel fully-FVM and hybrid method for dynamic curvilinear-grid generation, is presented here—for an easy-to-implement, stable, and computationally-efficient CFfSI development.

A comparative study of fully implicit staggered and monolithic solution methods. Part II: Coupled excitation–contraction equations of cardiac electromechanics

A comparative study of fully implicit staggered and monolithic solution algorithms for the coupled bidomain equations of cardiac electrophysiology was discussed in Part I (JCAM 407:114021, 2022). In this follow-up study, we further employ the similar approach and present an extensive comparative analysis between the staggered and monolithic solution techniques for the coupled partial differential equations (PDEs) of cardiac electromechanics both in the monodomain and bidomain setting. For the monolithic solution technique, we adopt the work of Göktepe et al. (CM 45: 227-243, 2010) and Dal et al. (CMAME 253: 353-336, 2013), where the governing PDEs of the excitation–contraction problem are solved simultaneously and all rate equations are treated with an implicit time integration scheme. For the staggered scheme, however, we simply suggest a decoupled solution of the governing PDEs while keeping other aspects of the monolithic algorithm the same, such as utilization of the implicit time integration scheme and coupling of ordinary differential equations, which describe the state variables of cardiac electrophysiology, to the parabolic PDE of the electrophysiology. Both solution algorithms are applied to several problems, where we simulate regular planar wave propagations and scroll waves for different spatial and temporal resolution and material parameters. The comparison between the solution schemes is performed in terms of accuracy, efficiency and stability. We reveal that for regular wave propagation the results of different solution algorithms are identical. The only deviation is observed during scroll wave propagation, if the parameters controlling the mutual interaction between the mechanical and electrical field are relatively large and at the same time if the time increment is big, e.g., Δt=2.0ms. Nevertheless, the suggested staggered solution scheme yields almost identical results even for high coupling if smaller time increments are used. Besides, the staggered scheme provides an enormous gain in computational efficiency, particularly, as the number of degrees of freedom is increased and we do not encounter any stability issue arising specifically from the decoupled solution of the governing PDEs. Similar to the conclusion that was made for cardiac electrophysiology in Part I, we report that the suggested fully implicit staggered solution algorithm has a tremendous application potential for computer simulations of excitation–contraction coupling of the heart both in the monodomain and bidomain setting.

Research on passive deformation and hydrodynamic performance of a biomimetic cownose ray in gliding motion through fluid-structure interaction analysis

This work explores the impact of passive deformation on the hydrodynamic performance of cownose rays gliding at various angles of attack (AoA) and pectoral fin stiffness. We employ a partitioned fluid-structure coupling scheme to resolve the dynamic interaction between the fluid and structure. Specifically, the incompressible Navier–Stokes equations are solved through the finite volume method, while structural deformation is addressed via the finite element method. A co-simulation engine is utilized for communication and coordination between the fluid and structural solver. Furthermore, an implicit coupling scheme is implemented to ensure numerical stability. Our results demonstrate that passive deformation of the pectoral fin would stabilize the gliding motion with increased drag and lift but reduced pitching moment. The lift-to-drag ratio is improved slightly at any angle of attack, with the maximum increase reached at an AoA of ±7.5°. Pectoral fin stiffness can influence passive deformation significantly, and the minimal stiffness leads to the most evident impact on gliding lift enhancement and pitching moment reduction under the parameters considered in this work. This study may provide insight into the control strategy of optimal gliding angle of attack and the selection of material properties of flexible fins in the design of high-performance biomimetic underwater gliders.

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.

Implicit coupling methods for nonlinear interactions between a large‐deformable hyperelastic solid and a viscous acoustic fluid of infinite extent

AbstractThis paper addresses the challenges in studying the interaction between high‐intensity sound waves and large‐deformable hyperelastic solids, which are characterized by nonlinearities of the hyperelastic material, the finite‐amplitude acoustic wave, and the large‐deformable fluid–solid interface. An implicit coupling method is proposed for predicting nonlinear structural‐acoustic responses of the large‐deformable hyperelastic solid submerged in a compressible viscous fluid of infinite extent. An arbitrary Lagrangian–Eulerian (ALE) formulation based on an unsplit complex‐frequency‐shifted perfectly matched layer method is developed for long‐time simulation of the nonlinear acoustic wave propagation without exhibiting long‐time instabilities. The solid and acoustic fluid domains are discretized using the finite element method, and two different options of staggered implicit coupling procedures for nonlinear structural‐acoustic interactions are developed. Theoretical formulations for stability analysis of the implicit methods are provided. The accuracy, robustness, and convergence properties of the proposed methods are evaluated by a benchmark problem, that is, a hyperelastic rod interacting with finite‐amplitude acoustic waves. The numerical results substantiate that the present methods are able to provide long‐time steady‐state solutions for a nonlinear coupled hyperelastic solid and viscous acoustic fluid system without numerical constraints of small time step sizes and long‐time instabilities. The methods are applied to investigate nonlinear dynamic behaviors of coupled hyperelastic elliptical ring and acoustic fluid systems. Physical insights into 2:1 and 4:2:1 internal resonances of the hyperelastic elliptical ring and period‐doubling bifurcations of the structural and acoustic responses of the system are provided.

Stable monolithic immersed boundary projection method for particle sedimentation with heat transfer at density ratios near unity

This study proposes a highly stable and efficient monolithic immersed boundary projection method with staggered time discretization for particle sedimentation with heat transfer at density ratios near unity. To achieve the implicit coupling of fluid and solid motion, the proposed method uses a monolithic approach that incorporates temperature, fluid velocities, particle velocities, momentum forcing, energy forcing, and pressure. Subsequently, a two-step approximate lower–upper decomposition is used to decouple the complex large system. Two-dimensional and three-dimensional (3D) single particle sedimentation at various Grashof numbers and density ratios verifies the ability of the proposed method to handle particle sedimentation at density ratios near unity. Moreover, the proposed method demonstrates its clear advantages by successfully addressing both stability issues and spurious oscillations. Furthermore, simulation with the proposed method was performed for 3D two- and multi-particle sedimentation with heat transfer to demonstrate the robustness of the proposed method. The investigation of the effects of density ratio and Grashof numbers on particle sedimentation reveals a significant influence of buoyancy force, particularly for relatively lighter particles. An increase in the drag coefficient for multi-particle sedimentation is observed, owing to interactions between particles, and the Grashof number exerts a pronounced influence, particularly at low-density ratios.