Implicit Coupling Scheme Research Articles

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).

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.

Modular Framework for the Solution of Boundary-coupled Multiphysics Problems

This paper presents a modular multiphysics framework developed for OpenFOAM. The framework is built around an iterative implicit coupling scheme based on a multi-region partitioned approach. This scheme allows the implementation of formal implicit time-marching schemes, which improves the stability of strongly interacting coupled problems. This methodology allows physical interactions to be handled through specifically designed interface boundary conditions. It also allows region-specific solvers to be implemented as modular class solvers. The coupling methodology is handled with a main program that manages solver-specific actions. The aim of this framework is to facilitate the implementation and testing of new multiphysics coupling problems in an integrated code structure. To show the capabilities of the framework to integrate new physics, solvers and boundary conditions requirements are discussed. Also, three validated examples involving fluid-structure interactions, conjugate heat transfer, and fluid-structure-thermal interactions are presented. Although all these problems are boundary-coupled multiphysics problems, the framework is conceptually not limited to this kind of problems. The benefit of this work to the OpenFOAM community is a general and modular framework that facilitates the setup and solution of diversified multiphysics problems, and that illustrates the implementation of modular interface boundary conditions between physics regions.

Semi-implicit fluid–structure interaction in biomedical applications

Fluid–structure interaction (FSI) incorporates effects of fluid flows on deformable solids and vice versa. Complex biomedical problems in clinical applications continue to challenge numerical algorithms, as incorporating the underlying mathematical methods can impair the solvers’ performance drastically. In this regard, we extend a semi-implicit, pressure Poisson-based FSI scheme for non-Newtonian fluids to incorporate several models crucial for biomechanical applications. We consider Windkessel outlets to account for neglected downstream flow regions, realistic material fibre orientation and stressed reference geometries reconstructed from medical image data. Additionally, we incorporate vital numerical aspects, namely, stabilisations to counteract dominant convective effects and instabilities triggered by re-entrant flow, while a major contribution of this work is combining interface quasi-Newton methods with Robin coupling conditions to accelerate the partitioned (semi-)implicit coupling scheme. The numerical examples presented herein aim to finally bridge the gap to real-world applications, considering state-of-the-art modelling aspects and physiological parameters. FSI simulations of blood flow in an iliac bifurcation derived from medical images and vocal folds deforming in the process of human phonation demonstrate the versatility of the framework.

A CFD-FEM based partitioned fluid structure interaction model to investigate surface cracks in elastohydrodynamic lubricated line contacts

This paper presents a partitioned, two-dimensional fluid structure interaction (FSI) model developed to investigate the effects of surface cracks in rolling/sliding line contacts operating under elastohydrodynamic lubrication (EHL). The lubricant behavior as it flows over and through the crack is determined by solving the Navier-Stokes equations using the Ansys Fluent computational fluid dynamics (CFD) solver. The structural response of the solid body is governed via an elastic-plastic constitutive relationship and solved using the Ansys Mechanical finite element solver. The exchange of (i) forces due to fluid pressure, and (ii) displacements due to solid deformation across the fluid-solid interface (including the crack faces) is facilitated by an iterative implicit coupling scheme. A smoothing based dynamic meshing technique is utilized to capture the deformation of the fluid region. The FSI model developed for this investigation is capable of modeling surface cracks with inclined geometries, overcoming the limitations of the classical Reynolds based approach. The fluid pressure results are presented for different loads, speeds and slide-to-roll ratios. The effects of crack geometry (i.e. location, dimension, inclination, crack tip radius, etc.) on fluid pressure and structural response are investigated. The FSI model presents the details of pressure distribution, fluid streamlines and stress concentration in the solid simultaneously. The model results can be used to provide accurate boundary conditions on the crack faces for crack propagation modeling in rolling contact fatigue. The results of this investigation identify the crack geometries that affect fatigue life of rolling elements in EHL contact by predicting the location and severity of stress concentrations in the material.

CSPACE for a simulation of core damage progression during severe accidents

CSPACE (Core meltdown, Safety and Performance Analysis CodE for nuclear power plants) for a simulation of severe accident progression in a Pressurized Water Reactor (PWR) is developed by coupling of verified system thermal hydraulic code of SPACE (Safety and Performance Analysis CodE for nuclear power plants) and core damage progression code of COMPASS (Core Meltdown Progression Accident Simulation Software). SPACE is responsible for the description of fluid state in nuclear system nodes, while COMPASS is responsible for the prediction of thermal and mechanical responses of core fuels and reactor vessel heat structures. New heat transfer models to each phase of the fluid, flow blockage, corium behavior in the lower head are added to COMPASS. Then, an interface module for the data transfer between two codes was developed to enable coupling. An implicit coupling scheme of wall heat transfer was applied to prevent fluid temperature oscillation. To validate the performance of newly developed code CSPACE, we analyzed typical severe accident scenarios for OPR1000 (Optimized Power Reactor 1000), which were initiated from large break loss of coolant accident, small break loss of coolant accident, and station black out accident. The results including thermal hydraulic behavior of RCS, core damage progression, hydrogen generation, corium behavior in the lower head, reactor vessel failure were reasonable and consistent. We demonstrate that CSPACE provides a good platform for the prediction of severe accident progression by detailed review of analysis results and a qualitative comparison with the results of previous MELCOR analysis.

Fluid-structure interaction effects on the deformable and pitching plate dynamics in a fluid flow

This study presents a numerical investigation of a 2D flexible flat plate dynamics, immersed in a fluid flow with a Reynolds number, based on its chord, of 2000. The plate is animated by a forced sinusoidal pitching movement, whose amplitude is 10∘ from its leading edge. Various materials are considered for the structure, from rigid materials to more flexible ones. The Fluid-Structure Interaction (FSI) effects are taken into account using a partitioned implicit coupling scheme. The Arbitrary Lagrangian-Eulerian (ALE) formulation of the Navier-Stokes equations is applied and the anisotropic diffusion equation is solved to determine the displacements of the fluid domain mesh. The numerical results are validated with experimental ones. A good agreement with the experimental results is obtained. Afterwards, it is shown that under the considered dynamics of the plate, the flexibility of the structure tends to increase the lift and the drag but decrease the thrust. In addition, this produces an acceleration of the fluid flow in the wake of the plate.

Fluid–Structure Interaction Modeling of Elastohydrodynamically Lubricated Line Contacts

Abstract This paper presents a partitioned fluid–structure interaction (FSI) solver to model elastohydrodynamic lubrication (EHL) of line contacts. The FSI model was constructed using the multiphysics simulation software ansys, wherein an iterative implicit coupling scheme is implemented to facilitate the interaction between fluid and solid components. The model uses a finite volume method (FVM) based computational fluid dynamics (CFD) solver to determine the lubricant flow behavior using the Navier–Stokes equations. Additionally, the finite element method (FEM) is utilized to model the structural response of the solid. Fluid cavitation, compressibility, non-Newtonian lubricant rheology, load balance algorithm, and dynamic meshing were incorporated in the FSI model. The pressure and film thickness results obtained from the model are presented for a wide range of loads, speeds, slide to roll ratios (SRR), surface dent, material properties (elastic plastic), etc. The model presents a detailed understanding of EHL contacts by removing any assumptions relative to the Reynolds equation. It provides the (i) two-dimensional variation of pressure, viscosity, etc., in the fluid and (ii) stress, elastic/plastic strain in the solid, simultaneously. The FSI model is robust, easy to implement, and computationally efficient. It provides an effective approach to solve sophisticated EHL problems. The FSI model was used to investigate the effects of surface dents, plasticity and material inclusions under heavily loaded lubricated line contacts as can be found in gears and rolling element bearings. The results from the model exhibit excellent corroboration with published results based on the Reynolds equation solvers.

Development of a coupling between a system thermal–hydraulic code and a reduced order CFD model

The nuclear community has coupled several three-dimensional Computational Fluid Dynamics (CFD) solvers with one-dimensional system thermal–hydraulic (STH) codes. This work proposes to replace the CFD solver by a reduced order model (ROM) to reduce the computational cost. The system code RELAP5-MOD3.3 and a ROM of the finite volume CFD solver OpenFOAM are coupled by a partitioned domain decomposition coupling algorithm using an implicit coupling scheme. The velocity transported over a coupling boundary interface is imposed in the ROM using a penalty method. The coupled models are evaluated on open and closed pipe flow configurations. The results of the coupled simulations with the ROM are close to those with the CFD solver. Also for new parameter sets, the coupled RELAP5/ROM models are capable of predicting the coupled RELAP5/CFD results with good accuracy. Finally, coupling with the ROM is 3–5 times faster than coupling with the CFD solver.

Extensive 3D analysis for fluid–structure interaction of spanwise flexible plunging wing 3D FSI Analysis for Spanwise Flexible Plunging Wing

ABSTRACTIn this study, an improved fluid–structure interaction (FSI) analysis method is developed for a flapping wing. A co-rotational (CR) shell element is developed for its structural analysis. Further, a relevant non-linear dynamic formulation is developed based on the CR framework. Three-dimensional preconditioned Navier–Stokes equations are employed for its fluid analysis. An implicit coupling scheme is employed to combine the structural and fluid analyses. An explicit investigation of a 3D plunging wing is conducted using this FSI analysis method. A further investigation of this plunging wing is performed in relation to its operating condition. In addition, the relation between the wing’s aerodynamic performance and plunging motion is investigated.

Application of CFD and FEA coupling to predict dynamic behaviour of a flexible barge in regular head waves

The ever increasing size of ships and offshore platforms has resulted in ‘softer’ hull which require hydroelastic effects to be taken into account when predicting fluid-structure interactions. The majority of such investigations are carried out numerically using potential flow solvers. Although nonlinear potential flow methods are also used, RANS/CFD (Reynolds-averaged Navier-Stokes equations) can fully take into account of nonlinearities. It is important, therefore, to verify and validate the results from such numerical predictions. This paper aims to investigate the symmetric motions and responses of flexible barge in regular waves by coupling RANS/CFD and Finite Element software. The two-way interaction between a fluid solver, Star-CCM+, and a structural solver, Abaqus, is applied by exchanging pressures and nodal displacements more than once every time step, namely implicit coupling scheme. A combination of overset and mesh morphing approaches and finite volume solution to allow for the motions of a body at the free surface is used. The computational results compared with experimental measurements and 2-D linear hydroelastic predictions show good agreement. The discrepancies between the 2-D and CFD/FEA cosimulation arise due to the strong influence of bow and stern radiated waves and the agreement between them improves when the nonlinearities are not as dominant.

Towards straightforward use of cell-based smoothed finite element method in fluid–structure interaction

This paper presents a straightforward implementation of cell-based smoothed finite element method (CS-FEM) into fluid-structure interaction from the arbitrary Lagriangian-Eulerian perspective. Identical to the practice in solid mechanics, CS-FEM is directly applied to viscous stress and pressure Poisson equation in fluid problem. Minimum programming efforts are thus required to modify existing in-house codes. Following an efficient grid moving strategy, partitioned implicit coupling scheme based upon fixed-point iterations is adopted to interconnect individual fields. The proposed approach is validated against previously published data for several benchmarks. Visible improvements are exposed in predicted results along with flow-induced phenomena.

Extension and application on a pool-type test facility of a system thermal-hydraulic/CFD coupling method for transient flow analyses

The development of multi-scale modeling capabilities through the use of coupled system thermal-hydraulic and CFD codes is addressed in this paper, which presents the extension and application of a partitioned, domain decomposition computational method coupling the 1D code RELAP5-3D and the CFD code FLUENT. An implicit coupling scheme for the solution of the flow field, based on a Quasi-Newton algorithm, is developed and tested on a case with multiple coupling interfaces. Moreover, modeling capabilities of the tool are enhanced through the implementation of thermal coupling to compute conjugate heat transfer phenomena. In this work, a coupled model has been developed for the analysis of the pool-type test facility E-SCAPE, currently under commissioning at the Belgian Nuclear Research Centre SCK•CEN. The installation represents a thermal-hydraulic scaled model of the MYRRHA reactor, with an electrical core simulator, cooled by Lead-Bismuth Eutectic (LBE). The coupling tool is applied on the analysis of a total loss of flow (LOF) transient, involving the complex transition from forced to natural circulation flow in the primary system. The simulation results, compared against stand-alone system thermal-hydraulics (STH) simulation data, highlighted that the transient behavior of a pool-type system in natural circulation is characterized by complex multi-dimensional flow and temperature fields, difficult to predict by 1D STH codes. The study also confirmed the capability of the developed tool to predict the impact of such phenomena on the system behavior, and to capture the development of thermal stratification in a plenum at low flow condition. The planned experimental tests will be used for the validation of the tool, in the view of its use for design and licensing activities.

SOLVING COUPLED PROBLEMS OF LUMPED PARAMETER MODELS IN A PLATFORM FOR SEVERE ACCIDENTS IN NUCLEAR REACTORS

This paper focuses on solving coupled problems of lumped parameter models. Such problems are of interest for the simulation of severe accidents in nuclear reactors~: these coarse-grained models allow for fast calculations for statistical analysis used for risk assessment and solutions of large problems when considering the whole severe accident scenario. However, this modeling approach has several numerical flaws. Besides, in this industrial context, computational efficiency is of great importance leading to various numerical constraints. The objective of this research is to analyze the applicability of explicit coupling strategies to solve such coupled problems and to design implicit coupling schemes allowing stable and accurate computations. The proposed schemes are theoretically analyzed and tested within CEA's procor platform on a problem of heat conduction solved with coupled lumped parameter models and coupled 1D models. Numerical results are discussed and allow us to emphasize the benefits of using the designed coupling schemes instead of the usual explicit coupling schemes.

Implicit co‐simulation methods: Stability and convergence analysis for solver coupling approaches with algebraic constraints

The analysis of the numerical stability of co‐simulation methods with algebraic constraints is subject of this manuscript. Three different implicit coupling schemes are investigated. The first method is based on the well‐known Baumgarte stabilization technique. Basis of the second coupling method is a weighted multiplier approach. Within the third method, a classical projection technique is applied. The three methods are discussed for different approximation orders. Concerning the decomposition of the overall system into subsystems, we consider all three possible approaches, i.e. force/force‐, force/displacement‐ and displacement/displacement‐decomposition. The stability analysis of co‐simulation methods with algebraic constraints is inherently related to the definition of a test model. Bearing in mind the stability definition for numerical time integration schemes, i.e. Dahlquist's stability theory based on the linear single‐mass oscillator, a linear two‐mass oscillator is used here for analyzing the stability of co‐simulation methods. The two‐mass co‐simulation test model may be regarded as two Dahlquist equations, coupled by an algebraic constraint equation. By discretizing the co‐simulation test model with a linear co‐simulation approach, a linear system of recurrence equations is obtained. The stability of the recurrence system, which reflects the stability of the underlying coupling method, can simply be determined by an eigenvalue analysis.

Explicit and Implicit Cosimulation Methods: Stability and Convergence Analysis for Different Solver Coupling Approaches

The numerical stability and the convergence behavior of cosimulation methods are analyzed in this manuscript. We investigate explicit and implicit coupling schemes with different approximation orders and discuss three decomposition techniques, namely, force/force-, force/displacement-, and displacement/displacement-decomposition. Here, we only consider cosimulation methods where the coupling is realized by applied forces/torques, i.e., the case that the coupling between the subsystems is described by constitutive laws. Solver coupling with algebraic constraint equations is not investigated. For the stability analysis, a test model has to be defined. Following the stability definition for numerical time integration schemes (Dahlquist's stability theory), a linear test model is used. The cosimulation test model applied here is a two-mass oscillator, which may be interpreted as two Dahlquist equations coupled by a linear spring/damper system. Discretizing the test model with a cosimulation method, recurrence equations can be derived, which describe the time discrete cosimulation solution. The stability of the recurrence equations system represents the numerical stability of the cosimulation approach and can easily be determined by an eigenvalue analysis.

Partitioned coupling strategies for fluid-structure interaction with large displacement: Explicit, implicit and semi-implicit schemes

In this paper the unsteady fluid-structure interaction (FSI) problems with large structural displacement are solved by partitioned solution approaches in the arbitrary Lagrangian-Eulerian finite element framework. The incompressible Navier-Stokes equations are solved by the characteristic-based split (CBS) scheme. Both a rigid body and a geometrically nonlinear solid are considered as the structural models. The latter is solved by Newton-Raphson procedure. The equation governing the structural motion is advanced by Newmark-<TEX>${\beta}$</TEX> method in time. The dynamic mesh is updated by using moving submesh approach that cooperates with the ortho-semi-torsional spring analogy method. A mass source term (MST) is introduced into the CBS scheme to satisfy geometric conservation law. Three partitioned coupling strategies are developed to take FSI into account, involving the explicit, implicit and semi-implicit schemes. The semi-implicit scheme is a mixture of the explicit and implicit coupling schemes due to the fluid projection splitting. In this scheme MST is renewed for interfacial elements. Fixed-point algorithm with Aitken's <TEX>${\Delta}^2$</TEX> method is carried out to couple different solvers within the implicit and semi-implicit schemes. Flow-induced vibrations of a bridge deck and a flexible cantilever behind an obstacle are analyzed to test the performance of the proposed methods. The overall numerical results agree well with the existing data, demonstrating the validity and applicability of the present approaches.

Acceleration of a fixed point algorithm for fluid-structure interaction using transpiration conditions

In this work, we address the numerical solution of fluid-structure interaction problems. This issue is particularly difficulty to tackle when the fluid and the solid densities are of the same order, for instance as it happens in hemodynamic applications, since fully implicit coupling schemes are required to ensure stability of the resulting method. Thus, at each time step, we have to solve a highly non-linear coupled system, since the fluid domain depends on the unknown displacement of the structure. Standard strategies for solving this non-linear problems, are fixed point based methods such as Block-Gauss-Seidel (BGS) iterations. Unfortunately, these methods are very CPU time consuming and usually show slow convergence. We propose a modified fixed-point algorithm which combines the standard BGS iterations with a transpiration formulation. Numerical experiments show the great improvement in computing time with respect to the standard BGS method.