Semi-implicit Coupling Research Articles

Validation of a Hybrid Domain Overlapping Coupling Between SAM and CFD Against the TALL-3D Transients

The system thermal-hydraulic (STH) code SAM has been coupled to the computational fluid dynamics (CFD) code Simcenter STARCCM+ utilizing a hybrid domain overlapping coupling method in space and an explicit coupling in time. The coupling aims to extend the STH code’s applicability to scenarios where local momentum and energy transfers are important yet difficult for STH standalone models to capture, such as three-dimensional (3D) mixing and thermal stratification. The coupling method’s numerical stability was previously verified against multiple test cases including two closed-loop configurations, and it was validated against a double T-junction experiment with 3D scalar mixing. In the present work, the method is validated against the TALL-3D STH/CFD coupling benchmark facility. TALL-3D is a liquid-metal facility with a large, pool-type enclosure (test section) that exhibits 3D flow effects to be modeled by a CFD code. The rest of the system exhibits approximately one-dimensional behavior that is well predicted by a STH code. First, a STAR-CCM+ CFD model of the 3D test section is validated against experimental temperature data. Then a SAM-STARCCM+ coupled model is validated against six different TALL-3D steady states and includes SAM standalone results for comparison. Last, the coupled model is validated against two TALL-3D transients: one exhibiting flow reversal in the test section and one exhibiting nonlinear, limit cycle oscillations (LCOs). For the first transient, the SAM-STARCCM+ coupled model properly predicts an increase in the test section’s inlet temperature during flow reversal, and this increase is not predicted by the SAM standalone model. The coupled model also better predicts initial flow recovery and subsequent oscillations as the system approaches a final natural circulation state. For the second transient, no true final steady state is observed due to LCOs. Neither the SAM-STARCCM+ coupled model nor the SAM standalone model can perfectly capture the experiment’s changing oscillation frequency during the transient. Nevertheless, the coupled model does reproduce the general oscillatory feedback observed. This is a significant achievement because the present coupling only uses an explicit coupling in time, as opposed to a tighter, semi-implicit coupling. In comparison, STH/CFD coupling efforts previously performed by other authors required a semi-implicit coupling to obtain similar results to this work. The strengths of the novel coupling scheme validated in the present paper lie in the superior convergence characteristics and the much simpler, nonintrusive implementation.

Coexistence of passive vortex-induced vibrations and active pitch oscillation triggered by a square cylinder attached with a deformable splitter plate

To understand passive vortex-induced vibrations (VIV) coexisting with active structure motions, this paper numerically investigates the use of pure pitch oscillation to control a square cylinder mounted with a deformable splitter plate at the Reynolds number of 333. The oscillation is enforced with an amplitude of 3° and different frequencies from 0 to 6 Hz. Direct numerical simulations using a partitioned method with a semi-implicit coupling algorithm are performed. According to the trajectories of the splitter-plate tip displacement with respect to the lift or drag force coefficient, a specific lock-in regime determined by the frequency of the enforced pitch oscillation is identified. Further spectral analyses of the tip displacement and lift force show that the lock-in frequencies are equal to the enforced frequencies. Next to the lock-in regime, semi-lock-in regimes with narrow bandwidths are distinguished, exhibiting both lock-in and non-lock-in features. In the non-lock-in regimes, the frequencies of the most predominant peaks in the spectra are found near the natural frequency of the splitter plate of 3.236 Hz, and the frequencies of the two secondary peaks are distributed along the characteristic lines following the ratios of these frequencies to the enforced frequency, which are ±1. Thus, the interaction is dependent on the combined effects of the passive VIV and the actively enforced pitch oscillations. Moreover, the intersection points of the characteristic lines are located close to the upper and lower frequency limits of the lock-in regime, inferring the conditions for the lock-in onset.

CBS-Based Partitioned Semi-implicit Coupling Algorithms for Fluid–Structure Interaction: A Decade Review

CBS-Based Partitioned Semi-implicit Coupling Algorithms for Fluid–Structure Interaction: A Decade Review

An edge-based smoothed finite element method for semi-implicit coupling of unsteady viscoelastic fluid–structure interaction

In this paper, a new partitioned semi-implicit coupling algorithm is developed for unsteady viscoelastic fluid–structure interaction in association with an edge-based smoothed finite element method (ESFEM). Stabilization techniques tailored for the viscoelastic fluid subproblem are naturally integrated into the hybrid explicit/implicit coupling framework to achieve the enhanced stability. In particular, a mass source term derived from the modified continuity equation in the finite-element context enables the ESFEM to fulfill the geometric conservation law on variable-node smoothing cells during the subiterations. Moreover, both multi-field equations and interface conditions are easily discretized with the ESFEM which enjoys high flexibility of smoothed Galerkin weak-form integral. Desirable numerical results are given for two benchmark problems.

Off-line vs. semi-implicit TH-TH coupling schemes: A BEPU comparison

Several TH-TH code coupling methods are used in the nuclear industry to model the core thermal–hydraulic conditions and the system behaviour. In some cases, the boundary conditions obtained by system codes are applied to sub-channel codes by table (off-line coupling). Even though this approach is in general considered valid, some boundary parameters will present inconsistencies. Alternatively, system and sub-channel codes are coupled using different coupling methods (semi-implicit coupling). Recent studies have shown a strong influence of the boundary conditions uncertainty on the sub-channel code results. The present study aims to evaluate the differences produced by the coupling methods by performing a best-estimate plus uncertainties (BEPU) comparison to the following cases: a complete loss of forced flow and a pressurizer relief valve opening. Results show that BEPU analysis presents good agreement with some discrepancies that can be explained and correlated to the boundary conditions deviations between codes.

A Computational Model for Nonlinear Biomechanics Problems of FGA Biological Soft Tissues

The principal objective of this work was to develop a semi-implicit hybrid boundary element method (HBEM) to describe the nonlinear fractional biomechanical interactions in functionally graded anisotropic (FGA) soft tissues. The local radial basis function collocation method (LRBFCM) and general boundary element method (GBEM) were used to solve the nonlinear fractional dual-phase-lag bioheat governing equation. The boundary element method (BEM) was then used to solve the poroelastic governing equation. To solve equations arising from boundary element discretization, an efficient partitioned semi-implicit coupling algorithm was implemented with the generalized modified shift-splitting (GMSS) preconditioners. The computational findings are presented graphically to display the influences of the graded parameter, fractional parameter, and anisotropic property on the bio-thermal stress. Different bioheat transfer models are presented to show the significant differences between the nonlinear bio-thermal stress distributions in functionally graded anisotropic biological tissues. Numerical findings verified the validity, accuracy, and efficiency of the proposed method.

Splitting schemes for a Lagrange multiplier formulation of FSI with immersed thin-walled structure: stability and convergence analysis

AbstractThe numerical approximation of incompressible fluid–structure interaction problems with Lagrange multiplier is generally based on strongly coupled schemes. This delivers unconditional stability, but at the expense of solving a computationally demanding coupled system at each time step. For the case of the coupling with immersed thin-walled solids, we introduce a class of semi-implicit coupling schemes that avoids strongly coupling without compromising stability and accuracy. A priori energy and error estimates are derived. The theoretical results are illustrated through numerical experiments in an academic benchmark.

Efficient semi-implicit coupling fluid-structure interaction analysis via model-order reduction of dynamic grids

In this paper, a fluid-structure interaction (FSI) using the model-order reduction (MOR) of dynamic grids is proposed. Within the interface problem between the fluid and the structure, the grid deformation is based on the spring analogy, and it is further extended in order for the efficient computation. In this procedure, the projection-based MOR technique is employed. The relevant MOR technique is realized by using the proper orthogonal decomposition and the discrete empirical interpolation method (POD/DEIM). The resulting FSI framework is based on a semi-implicit coupling approach. In order to achieve this, a characteristic-based split (CBS) scheme is used for an arbitrary Lagrangian–Eulerian (ALE) formulation of the two-dimensional Navier-Stokes equation. Also, a structural analysis is based on the co-rotational (CR) formulation in order to simulate the geometrically nonlinear behavior. Both the fluid and structural analyses are combined with the semi-implicit coupling approach, and the relevant algorithm is embedded in the ALE/CBS scheme. Then, the present FSI analysis is verified using three examples, and the computational efficiency is evaluated. The resulting numerical data demonstrated the validity of the present analysis, and it is found that a significant reduction in the computational cost is possibly achieved with the proposed approach.

Stabilization of a smoothed finite element semi-implicit coupling scheme for viscoelastic fluid–structure interaction

We propose in this work a stabilization approach for semi-implicit coupling of viscoelastic fluid–structure interaction (VFSI) using the cell-based smoothed finite element method (CS-FEM). The viscoelastic fluid and nonlinear solid equations are spatially discretized by the CS-FEM and then are semi-implicitly coupled via a partitioned solution strategy. The current semi-implicit coupling framework depends on a second-order characteristic-based split (CBS(B)) scheme that solves the Navier–Stokes equations together with the Oldroyd-B constitutive model in the fractional-step manner. To enhance the stability of the semi-implicit coupling algorithm, the discrete elastic-viscous split stress-gradient (DEVSS-G) procedure is introduced into the explicit stage while the stabilized pressure gradient projection (SPGP) is earmarked for the implicit stage. Moreover, the iterated end-of-step velocity begins with the intermediate velocity during the subiterations. The DEVSS-G/CBS(B)-SPGP technique is readily applied to the CBS-based partitioned semi-implicit coupling algorithm for VFSI. Visible improvements in stabilization and efficiency are revealed in a benchmark test. • A semi-implicit coupling scheme is proposed for viscoelastic fluid–structure interaction. • DEVSS-G/CBS(B)-SPGP stabilization is presented for the semi-implicit scheme. • VFSI system is entirely formulated by cell-based smoothed finite element method. • The developed technique boosts the stability and efficiency considerably.

An Assessment of Coupling Algorithms in HTR Simulator TINTE

This paper evaluates the performance of neutronic and thermal-hydraulic coupling algorithms in transient problems based on the high-temperature gas-cooled reactor simulator TINTE. In particular, the operator splitting semi-implicit (OSSI), Picard iteration, and Jacobian-free Newton-Krylov (JFNK) methods are compared by a practical engineering model. The OSSI method is employed in the original TINTE. The fully implicit algorithms TINTE-Picard and TINTE-JFNK are implemented in this study. Several special numerical technologies are discussed to improve the performance of JFNK. First, a novel JFNK variant is employed to deal with the multiscale coupling between local fuel sphere temperature and global solid porous media temperature. Second, the preconditioning strategy is determined by making a balance between performance and code burden. Finally, the scaling modifications of the Jacobian matrix and perturbation size are investigated to solve the ill-posed problem. What is more, the framework of TINTE-Picard and TINTE-JFNK is presented, and the key points of implementation are discussed. Numerical results indicate that the advanced coupling algorithms Picard and JFNK can achieve higher computational performance than the original semi-implicit coupling algorithm in TINTE due to the accuracy and stability advantage.

A semi-implicit coupling technique for fluid–structure interaction problems with strong added-mass effect

This paper is concerned with the numerical simulation of fluid–structure interaction problems involving an incompressible viscous flow and an elastic structure. A semi-implicit coupling technique is presented which strongly couples the added-mass term of the fluid (pressure stress) to the structure, while the remaining terms are only loosely coupled. A thorough numerical analysis is carried out to verify the accuracy of the proposed method by comparing its results to experimental data and other numerical results from the literature. The performance and accuracy of the proposed method are also compared against a fully implicit coupling technique. Numerical tests show that semi-implicit coupling significantly reduces the computational cost of the simulations without undermining either the stability or the accuracy of the results. The question of implicit or explicit coupling of the dynamic mesh step is addressed by evaluating its effect on the overall accuracy and performance of the semi-implicit method. The implicit coupling of the dynamic mesh step is found to slightly improve the accuracy, while significantly increasing the computational cost. Moreover a comparison is made on the performance of the semi-implicit method with different interface solvers.

The sea ice model component of HadGEM3-GC3.1

Abstract. A new sea ice configuration, GSI8.1, is implemented in the Met Office global coupled configuration HadGEM3-GC3.1 which will be used for all CMIP6 (Coupled Model Intercomparison Project Phase 6) simulations. The inclusion of multi-layer thermodynamics has required a semi-implicit coupling scheme between atmosphere and sea ice to ensure the stability of the solver. Here we describe the sea ice model component and show that the Arctic thickness and extent compare well with observationally based data.

The use of artificial compressibility to improve partitioned semi-implicit FSI coupling within the classical Chorin–Témam projection framework

Over the last decade the classical Chorin–Témam projection method has been utilized to address fluid-structure interaction in a semi-implicit manner. In previous studies the fluid projection step is fully coupled with the structural motion due to the divergence-free constraint. A set of simultaneous equations thus have to be iteratively solved. To overcome this difficulty, a simple and accurate partitioned semi-implicit coupling method is proposed based on the artificial compressibility (AC) in this paper. The iterated AC parameter decouples the pressure, end-of-step velocity and structural motion within the characteristic-based split scheme. The present approach is completely matrix-free and has unlimited access to the finite elements. Its performance is demonstrated for an oscillating bluff body subjected to uniform flows.

AC-CBS-Based Partitioned Semi-Implicit Coupling Algorithm for Fluid-Structure Interaction Using Stabilized Second-Order Pressure Scheme

AbstractWe analyze in this paper the pressure splitting scheme of a partitioned semi-implicit coupling algorithm for fluid-structure interaction (FSI) simulation. The semi-implicit coupling algorithm is developed on the ground of the artificial compressibility characteristic-based split (AC-CBS) scheme that serves not only for the fluid subsystem but also for the global FSI system. As the dual-time stepping procedure recommended for quasi-incompressible flows is incorporated into the implicit coupling stage, the fluctuating pressure may be unusually susceptible to the AC coefficient. Moreover, it is not trivial to devise an optimal AC formulation for pressure estimation. Instead, we consider a stabilized second-order pressure splitting scheme in the AC-CBS-based partitioned semi-implicit coupling algorithm. Computer simulation of a benchmark FSI experiment demonstrates that good agreement is exposed between the available and present data.

A natural framework for isogeometric fluid–structure interaction based on BEM–shell coupling

The interaction between thin structures and incompressible Newtonian fluids is ubiquitous both in nature and in industrial applications. In this paper we present an isogeometric formulation of such problems which exploits a boundary integral formulation of Stokes equations to model the surrounding flow, and a non linear Kirchhoff–Love shell theory to model the elastic behavior of the structure. We propose three different coupling strategies: a monolithic, fully implicit coupling, a staggered, elasticity driven coupling, and a novel semi-implicit coupling, where the effect of the surrounding flow is incorporated in the non-linear terms of the solid solver through its damping characteristics. The novel semi-implicit approach is then used to demonstrate the power and robustness of our method, which fits ideally in the isogeometric paradigm, by exploiting only the boundary representation (B-Rep) of the thin structure middle surface.

A CBS-based partitioned semi-implicit coupling algorithm for fluid–structure interaction using MCIBC method

Abstract The characteristic-based split (CBS) scheme has been extensively utilized to address the fluid subproblem within fluid–structure interaction (FSI) analyses over the past decade. To cope with FSI, this article develops a CBS-based partitioned semi-implicit coupling algorithm where the CBS scheme serves not only for the fluid component but also for the entire coupling algorithm. At each time instant, the first step of the CBS scheme is explicitly treated together with the fluid mesh movement, while the remaining two steps are implicitly coupled with the structural motion on the fluid mesh frozen temporarily. To retrieve the semi-implicit coupling style, a mass source term is iteratively updated in the pressure Poisson equation for elements adhering to the fluid–structure interface. The present algorithm provides the stabilized solution of the Navier–Stokes equations and the computational reduction without stability drop, thus inheriting the virtues of the CBS scheme and the projection-based semi-implicit coupling method. Within our coupling algorithm, FSI is achieved by the modified combined interface boundary condition (MCIBC) method which is re-derived in a more concise fashion. A weak implementation of the MCIBC method is proposed to avoid deteriorating the numerical results. The MCIBC method rectifies the limitations of its original counterpart, making itself applicable to fluid–rigid/flexible body interaction. Flow-induced vibrations of various bluff bodies are analyzed to test the feasibility of the proposed methodology. The overall numerical results agree well with the existing data, demonstrating the validity and the applicability of the present approach.

Semi-Implicit Coupling of CS-FEM and FEM for the Interaction Between a Geometrically Nonlinear Solid and an Incompressible Fluid

A semi-implicit coupling strategy under the arbitrary Lagrangian–Eulerian description is presented for the incompressible fluid flow past a geometrically nonlinear solid in this paper. The incompressible fluid is solved by means of the characteristic-based split (CBS) finite element method while the cell-based smoothed finite element method is employed to settle the governing equation of the geometrically nonlinear solid. Because of the CBS fluid solver, the present coupling strategy is performed in a semi-implicit fashion. In particular, the first step of the CBS scheme is explicitly treated whereas the others are implicitly coupled with the structural motion. The computational cost is hence reduced because no subiterations are included in the explicit coupling step and the fluid mesh is frozen in the implicit coupling step. A classic cantilever problem is dealt with to validate the structural solver, and then flow-induced vibrations of a restrictor flap in a uniform channel flow is analyzed in detail. The obtained results agree well with the existing data.

Combined interface boundary condition method for fluid–structure interaction: Some improvements and extensions

The combined interface boundary condition (CIBC) method devises the increments to correct traditional interface conditions for partitioned computation of fluid–structure interaction. However, the restricted use of the CIBC method has been realized recently. In this paper we present some improvements and extensions of the CIBC method as follows: (1) the method is reformulated in the general situation by using the complete fluid stress tensor; (2) the structural traction rate, which results in the inconsistency in the interfacial traction and may cause the loss of numerical accuracy, is totally removed from the CIBC formulation via a simple revision; (3) we analyze the instability source due to the CIBC compensation and propose an approach to recover the two-sided corrections for Dirichlet and Neumann interface conditions; (4) the CIBC method is extended to the generalized planar rigid-body motion. A novel CBS-based partitioned semi-implicit coupling approach is adopted to couple different fields within the nondimensional ALE finite element framework. The interaction between incompressible flows and a rigid/flexible body is numerically simulated to demonstrate the validity of the developed method. The reasonable agreement is disclosed between the present and available data.

A Semi-Implicit Approach for Integrated Reservoir and Surface-Network Simulation

SummaryConventionally, methods of coupling reservoirs and surface networks are categorized into implicit and explicit approaches. The term "implicit coupling" indicates that the two simulators solve unknowns together, simultaneously, or iteratively, whereas "explicit coupling" indicates that the two simulators solve unknowns sequentially and exchange their boundary conditions at the last coupled time tn.The explicit approach is straightforward to implement in existing reservoir and surface-network models and is widely used. Explicit coupling does have drawbacks, however, because well rate and pressure oscillations are often observed.In this paper, a new semi-implicit method for coupled simulation is presented. This technique stabilizes and improves the accuracy of the coupled model. The "semi-implicit coupling" overcomes the problems found in explicit-coupling methods without requiring the complexity of a fully implicit coupled model.The new approach predicts inflow-performance-relationship (IPR) curves at the next coupled time tn+1 by simultaneously conducting well tests for all wells in the reservoir before actually taking the required timestep. All wells first flow simultaneously to the next coupled time tn+1 with the well rates unchanged from the last coupled timestep. The timestep is rewound, and all well rates are reduced by a uniform fraction and then simultaneously flow again to tn+1. By extrapolating the resulting well pressures, the well's shut-in pressures at time tn+1 are determined, and thus, straight-line IPRs are produced. The new IPR curves approximate better each well's drainage region at tn+1 and each well's shut-in pressure at tn+1 which helps to stabilize the explicitly coupled model.The new coupling technique normally does not require iteration between the reservoir and surface network and normally has the stability and accuracy characteristics of an implicitly coupled approach. Because the well tests already account for individual well-drainage regions, an explicit knowledge of the well-drainage region is not required. Because of the stabilized IPR, the approach also was found to reduce the overall computational time compared with explicit coupling.Applications of the new approach are presented that show significant improvements surpassing explicit coupling in both stability and accuracy.

Coupled simulation of multibody and finite element systems: an efficient and robust semi-implicit coupling approach

Standard coupling approaches for simulating coupled MBS/FEM systems may entail enormous CPU times in order to achieve a stable and accurate solution. To stabilize and speed up the solution process, semi-implicit coupling approaches can be applied successfully. In literature, semi-implicit coupling approaches have been introduced, where Jacobian information is exchanged between the subsystems using partial derivatives with respect to the state vectors of the subsystems. The drawback of these methods is that the numerical calculation of the Jacobians with respect to the whole state vector of the subsystems is very time-consuming. The key idea of the semi-implicit coupling technique presented here is to reduce the computational effort by using Jacobian information only with respect to the coupling variables.