Implicit Coupling Research Articles

Oscillation mitigation in subsurface and surface couplings using PID controllers

Simulation coupling subsurface (reservoir) and surface (network) systems is a challenging problem, especially for computationally intensive multi-reservoir models and complex surface network facilities. Integration of petroleum systems can be done using different simulators (explicit coupling) or considering all individual components of the system in one simulator (implicit coupling). The explicit method is more flexible, allowing the integration of commercial-off-the-shelf simulators. However, as a drawback, it can yield oscillatory solutions. In this work, a new framework for mitigating explicit coupling numerical instabilities (oscillations) is developed by recasting the problem in a control setting. Results from this work show that explicit coupling without a mechanism to avoid numerical instabilities presents oscillations that can grow throughout the simulation. In order to mitigate the numerical oscillations we develop a framework based on a feedback control system, namely a PID (Proportional, Integral and Derivative) controller. The PID controller, with parameters (KC, τI, τD) tuned manually for a group of well settings, adjusts the traditional IPR curve generated by the reservoir simulator so that the error between the bottom-hole pressure calculated by the reservoir simulator (BHPRS) and the bottom-hole pressure defined in the operating point (BHPOP) is minimal. In this case, a qOP value representative for the entire time step (next time step) is obtained. The new methodology was tested in a synthetic numerical model (UNISIM-I-D) based on Namorado field (Campos Basin – Brazil), comprised by 20 satellite wells (7 injectors and 13 producers). The PID control reduces the rate and pressure oscillations in the case study, and results converge with base case scenario, which represents the network system of producer wells by proper pressure drop tables.

A semi-implicit approach for the modeling of wells with inflow control completions

In the last two decades, new technologies have been introduced to equip wells with intelligent completions such as Inflow Control Device (ICD) or Inflow Control Valve (ICV) in order to optimize the oil recovery by reducing the undesirable production of gas and water. To optimally define the locations of the packers and the characteristics of the valves, efficient reservoir simulation models are required. This paper is aimed at presenting the specific developments introduced in a multipurpose industrial reservoir simulator to simulate such wells equipped with intelligent completions taking into account the pressure drop and multiphase flow. An explicit coupling or decoupling of a reservoir model and a well flow model with intelligent completion makes usually unstable and non-convergent results, and a fully implicit coupling is CPU time consuming and difficult to be implemented. This paper presents therefore a semi-implicit approach, which links on one side to the reservoir simulation model and on the other side to the well flow model, to integrate ICD and ICV.

Structure learning in coupled dynamical systems and dynamic causal modelling.

Identifying a coupled dynamical system out of many plausible candidates, each of which could serve as the underlying generator of some observed measurements, is a profoundly ill-posed problem that commonly arises when modelling real-world phenomena. In this review, we detail a set of statistical procedures for inferring the structure of nonlinear coupled dynamical systems (structure learning), which has proved useful in neuroscience research. A key focus here is the comparison of competing models of network architectures-and implicit coupling functions-in terms of their Bayesian model evidence. These methods are collectively referred to as dynamic causal modelling. We focus on a relatively new approach that is proving remarkably useful, namely Bayesian model reduction, which enables rapid evaluation and comparison of models that differ in their network architecture. We illustrate the usefulness of these techniques through modelling neurovascular coupling (cellular pathways linking neuronal and vascular systems), whose function is an active focus of research in neurobiology and the imaging of coupled neuronal systems. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

An implicit dual‐based approach to couple peridynamics with classical continuum mechanics

SummaryA general local/nonlocal implicit coupling technique called the dual‐based approach is proposed to couple peridynamics (PD) with classical continuum mechanics. In the present method, physical information is transmitted mutually from local to nonlocal regions through the coupling elements; no transition region is introduced. For different mesh discretizations, two coupling methods are achieved with simplicity and effectivity. To obtain the stiffness matrix of the coupled model, without loss of generality, the implicit dual‐horizon ordinary state‐based peridynamic model is proposed, in which the linearization of dual‐horizon ordinary state‐based PD is derived and the dual assembly algorithm of the peridynamic stiffness matrix is developed. It will be seen that the implicit dual‐based coupling approach provides a new implicit coupling method that is easy to implement and makes full use of the internal connection between PD and classical continuum mechanics. Several numerical examples involving static crack propagation are investigated, and the satisfactory results show both quantitative and qualitative agreement with either the analytic solution or the available experiment.

Level set function–based immersed interface method and benchmark solutions for fluid flexible‐structure interaction

SummaryUsing a hybrid Lagrangian‐Eulerian approach, a level set function–based immersed interface method (LS‐IIM) is proposed for the interaction of a flexible body immersed in a fluid flow. The LS‐IIM involves finite volume method for the fluid solver, Galerkin finite element method for the structural solver, and a block‐iterative partitioned method–based fully implicit coupling between the two solvers. The novelty of the proposed method is a level set function–based direct implementation of fluid‐solid interface boundary conditions in both the solvers. Another novelty is the computation of the level set function from a geometric method instead of differential equations commonly used in level set methods—the novel geometric as compared to the traditional method is found to be more accurate and less time‐consuming. The LS‐IIM is demonstrated as second‐order accurate. Verification study is presented first separately for both the solvers and then together for four fluid‐structure interaction (FSI) problems, with different levels of complexity including lid‐driven flow, channel flow, and free‐stream flow. Benchmark solutions are presented for two class of FSI problems: first, easy to set up and less time‐consuming and, second, a reasonably challenging and complex FSI problem involving sharp edges and forced‐motion of the flexible structure. The benchmark solutions are proposed at steady state for the first problem, after a verification study with two open‐source solvers and, at periodic state, after a validation with published experimental results for the second problem. Our benchmark solutions may be useful for verification study in future.

A domain decomposition method for the non-intrusive reduced order modelling of fluid flow

In this paper we present a new domain decomposition non-intrusive reduced order model (DDNIROM) for the Navier–Stokes equations. The computational domain is partitioned into subdomains and a set of local basis functions is constructed in each subdomain using Proper Orthogonal Decomposition (POD). A radial basis function (RBF) method is then used to generate a set of hypersurfaces for each subdomain. Each local hypersurface represents, not only the fluid dynamics over the subdomain to which it belongs, but also the interactions with the surrounding subdomains. This implicit coupling between the subdomains provides the global coupling necessary to enforce incompressibility and is a means of providing boundary conditions for each subdomain.The performance of this DDNIROM is illustrated numerically by three examples: flow past a cylinder, and air flow over 2D and 3D street canyons. The results show that the DDNIROM exhibits good agreement with the high-fidelity full model while the computational cost is reduced by several orders of magnitude. The domain decomposition (DD) method provides the flexibility to choose different numbers of local basis functions for each subdomain depending on the complexity of the flow therein. The fact that the RBF surface representation takes input only from its current subdomain and the surrounding subdomains, means that, crucially, there is a reduction in the dimensionality of the hypersurface when compared with a more traditional, global NIROM. This comes at the cost of having a larger number of hypersurfaces.

The Interactive Self – A Review on Simulating Social Interactions to Understand the Mechanisms of Social Agency

Abstract The sense of agency is a core element of self-experiences and is defined as the feeling of oneself being the ‘initiator’ of an action. It is thought to depend on an implicit coupling of action-outcome predictions and the sensory perception of the action. This concept is well-studied in the motor-domain, but less is known about agency during social interactions. It is clear that a sense of agency also occurs when we perform a social action (e. g. looking at someone’s eyes) and receiving feedback by another person (e. g. returning eye-contact). Here, we will refer to the experience of agency within a social interaction as the sense of social agency. The main aim of this article is to first, describe the concept of social agency and second review how virtual reality can help to simulate social interactions in order to systematically study self-experiences and social agency. Gaze-contingent eye-tracking paradigms represent a powerful tool in this endeavour, while we emphasise the importance of implementing ecologically valid, interactive stimuli. We furthermore propose a computational approach that can be useful to analyse such data based on the concept of predictive processing. Finally, we highlight the clinical relevance of this account and suggest how this approach can be helpful in providing a mechanistic description of social impairments across various psychiatric disorders. With this article, we attempt to review previous experimental work, suggest new methodological procedures and encourage future empirical research in the field.

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.

An advanced numerical framework for the simulation of flow induced vibration for nuclear applications

In this work, an advanced solver for the simulation of Fluid-Structure Interaction (FSI) problems for nuclear applications is presented. The numerical framework, called as NRG-FSIFOAM, uses a Finite Volume (FV) fluid solver and a Finite Element (FE) structural solver coupled together with a partitioned approach. State-of-the-art implicit coupling algorithms are used in order to increase the accuracy and the stability of the solver for low solid-to-fluid density ratio, i.e. strongly coupled, FSI problems. Furthermore, the solver offers significant advantages with respect to traditional approaches for the solution of turbulent flows because it is equipped with an advanced algorithm to predict pressure fluctuations without the necessity to perform high fidelity simulations. This approach, called as Pressure Fluctuation Model (PFM), uses a stochastic model to generate velocity fluctuations that satisfy the mean turbulent quantities; the corresponding fluctuating pressure field is computed from the Poisson’s equation. The pressure fluctuation field complements the mean pressure field computed with URANS models and it is then used as a part of the external forcing for the structural problem. This solver is first tested against benchmark FSI problems with laminar flows. Subsequently, it is used to simulate flow induced vibrations of cylindrical fuel rods in turbulent water and liquid metal flows and to simulate the vibrations of a cantilever beam in turbulent water flow.

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.

A Generic Framework for Learning Explicit and Implicit User-Item Couplings in Recommendation

The nature of recommendation is Non-IID, which has potential in improving recommendation quality and addressing issues such as sparsity and cold start. However, existing many state-of-the-art methods assume users and items are independent and same distributed while ignoring complex coupling relationships within and between users and items, resulting in limited performance improvement. To solve this issue, this paper proposes a novel neural user-item coupling learning model, short for CoupledCF, based on non-IID learning for collaborative filtering. CoupledCF joint learns explicit coupling with CNN and implicit coupling with deepCF within/between users and items accompanying user/item side information for recommendation tasks. User/item side information contains of attribute-based and feature-based. For different user/item side information, we use different embedding methods to learn embedding representation. We conduct comparative experiments on (1) two datasets from MovieLens1M and Tafeng with attribute-based user/item information for Top-K recommendation. (2) two datasets from MovieLens1M and BookCrossing with attribute-based user/item information for rating prediction. (3) two datasets from Amazon Movies and TV (AMT) and Yelp for feature-based user/item information for Top-K item recommendation and rating prediction tasks. Empirical results on five available real-world large datasets prove our proposed CoupledCF model is able to obtain better recommendation accuracy compared with several mainstream approaches for recommendation: BMF, neural matrix factorization, Google’s Wide&Deep network, DeepFM, convMF, and $A^{3}NCF$ model.

Preliminary Study on Mesh Stiffness Models for Fluid-structure Interaction Problems

One of the challenges in modern computational engineering is the simulation of fluid-structure interaction (FSI) phenomena where one of the crucial issues in the multi-physics simulation is the choice of stiffness model for mesh deformation. This paper focuses on the application of iteratively implicit coupling procedure on two transient FSI cases of vortex induced-vibration (VIV) that manifest oscillating flexible structures. The aim is to study various mesh stiffness models in the Laplace equation of diffusion employed within the arbitrary Lagrangian-Eulerian (ALE) methodology to handle the moving mesh. In the first case where a laminar flow interacted with a flexible splitter, it was demonstrated that a near FSI boundaries increased-stiffness model prevails to manage a large deformation of the moving structure as compared to a near volume increased-stiffness model. However, the potential technique could not be exploited to the second FSI configuration, where the effect of the turbulence of flow was included. It was found that the mesh topology near the FSI interface was collapsed. Instead of utilizing the same approach, a mesh stiffness based on a wall distance was found to be auspicious. Thus, the mesh stiffness model in the FSI simulation is case-dependent.

Numerical models for the prediction of the behavior of a flexible slender shaped membrane in interaction with free surface flow under the influence of a moving flotsam

AbstractThe motivation for this work is the great need of applying light structures for the protection of coastal areas from detrimental effects of rapid water runoff. In case of windy or stormy weather conditions, light structures are extremely vulnerable to be attacked by floating debris and even tree trunks. To meet the safety criteria, speculation of this impulsive force on light structures gains in importance on account of the massive deformation of membrane. This matter provides the incentive to investigate an impact phenomenon numerically. The analysis was first performed within a standalone Abaqus standard environment, where the effect of fluid domain on the flexible structure was executed on structure by user subroutine of DLOAD, which was updated in each iteration based on new deformed shape. This model was extended by a partitioned strategy which makes it possible for fluid and structure domains to be interconnected powerfully. The impact of free surface water flow on the membrane was executed using the finite volume solver of Star CCM+, which behaves in response to displacements of the structures. On account of added mass effects, the implicit coupling algorithm between fluid and solid regions was implemented.

An immersed boundary method for incompressible flows in complex domains

This paper presents an immersed boundary method (IBM) to model the behaviour of solid–fluid interfaces in incompressible flows on non-conforming, unstructured meshes. Based on a smooth-interface direct forcing formulation, the proposed forcing method directly and implicitly uses the discretised momentum equations to evaluate the source terms required to enforce a no-slip condition on the boundary. The IBM is derived for a finite-volume framework with an implicit pressure-velocity coupling and a colocated variable arrangement, to enable application in complex domains. The novel framework is applied to flows with stationary and moving IBs on both Cartesian and tetrahedral meshes, and the results are compared to and validated with findings reported in the literature. The results demonstrate that the proposed formulation results in an accurate enforcement of the no-slip condition on the IB at every time-step, even for flows with strong transient behaviour and high velocity and pressure gradients. The results are similar to or better than those obtained with other methods that can only be applied on Cartesian meshes. The current method is shown to accurately preserve local continuity in the vicinity of the IB, ensuring local and global mass conservation in addition to satisfying the local no-slip condition. Moreover, the proposed forcing framework shows good results for unstructured meshes, with a similar accuracy as obtained on Cartesian meshes.

Analysis of several subcycling schemes in partitioned simulations of a strongly coupled fluid‐structure interaction

SummaryFluid‐structure interaction (FSI) simulations are used extensively to calculate the vibration of structures subjected to an internal or external flow. In the case of partitioned FSI simulations, separate flow and structure solvers are used, which requires some kind of coupling between both. The time step in both solvers is typically taken the same, but this unnecessarily leads to long calculation times when the time step is small due to stability reasons in one of the two solvers. Subcycling, the procedure where the time step of one solver is chosen smaller than the time step used in the other solver, may reduce the computational cost of the FSI simulation. The subcycling procedure can be either explicit or implicit, the latter implying the use of coupling iterations in each time step. Contrary to explicit subcycling, no stability analyses of implicit subcycling schemes are found in the literature. In this paper, the temporal stability of the implicit subcycling procedure is investigated. The one‐dimensional flow in an elastic cylindrical tube is studied analytically. The results of this analysis are subsequently compared to a partitioned two‐dimensional axisymmetric FSI calculation with implicit coupling between the flow and structure solvers.

The Numerics of Physical Parametrization in the ECMWF Model

The numerical aspects of physical parametrization are discussed mainly in the context of the ECMWF Integrated Forecasting System. Two time integration techniques are discussed. With parallel splitting the tendencies of all the parametrized processes are computed independently of each other. With sequential splitting, tendencies of the explicit processes are computed first and are used as input to the subsequent implicit fast process. It is argued that sequential splitting is better than parallel splitting for problems with multiple time scales, because a balance between processes is obtained during the time integration. It is shown that sequential splitting applied to boundary layer diffusion in the ECMWF model leads to much smaller time truncation errors than does parallel splitting. The so called Semi-Lagrangian Averaging of Physical Parametrizations (SLAVEPP), as implemented in the ECMWF model, is explained. The scheme reduces time truncation errors compared to standard first order methods, although a few implementation questions remain. In the scheme fast and slow processes are handled differently and it remains a research topic to find the optimal way of handling convection and clouds. Process specific numerical issues are discussed in the context of the ECMWF parametrization package. Examples are the non-linear stability problems in the vertical diffusion scheme, the stability related mass flux limit in the convection scheme and the fast processes in the cloud microphysics. Vertical resolution in the land surface scheme is inspired by the requirement to represent diurnal to annual time scales. Finally, a new coupling strategy between atmospheric models and land surface schemes is discussed. It allows for fully implicit coupling also for tiled land surface schemes.

Fully Implicit Chebyshev Time-Spectral Method for General Unsteady Flows

An efficient fully implicit Chebyshev time-spectral method (TSM) is developed to solve general unsteady flows with or without periodicity. High accuracy of the Chebyshev time-spectral operator is demonstrated by simulating the one-dimensional shock motion at constant speed. A space-time lower–upper symmetric Gauss–Seidel (LU-SGS) fully implicit scheme with multigrid acceleration is used to efficiently solve the equations resulting from the Chebyshev TSM. The implicit temporal coupling term is properly split so that the LU-SGS sweeps are extended to the time domain. For cases in which the physical time step is small, a modification to the implicit scheme is suggested to enhance numerical stability. Computational results of nonperiodic flows over a pitching airfoil are presented for different physical time steps and various numbers of Chebyshev collocation points. The fully implicit Chebyshev TSM is also tested to predict the natural vortex shedding frequency for a stationary circular cylinder. This efficient approach can be easily applied to the time-accurate computation of general nonperiodic unsteady flows with a given initial condition.

Implicit and explicit cross‐correlations in coupled data assimilation

The European Centre for Medium‐Range Weather Forecasts has recently developed an implicit coupling approach in the coupled atmosphere–ocean assimilation (CERA) system, where atmospheric 4D‐Var and ocean 3D‐Var are synchronized using multiple outer iterations in the incremental variational formulation. Since this original work on outer‐loop coupling, it has been unclear just how closely the CERA system with implicit coupled covariances approximates a strongly coupled data assimilation with ensemble‐based coupled covariances.A series of single‐observation experiments in a perfect twin framework has been conducted to evaluate the effectiveness and efficiency of outer‐loop coupling and the amplitude of the implicit cross‐correlations between atmospheric and ocean temperature. They are compared against a coupled assimilation system that specifies cross‐correlations explicitly from an ensemble of coupled forecasts. We find that both the implicit outer‐loop and explicit ensemble‐based methods produce equally skilful estimates of the coupled state in the middle of a 24 hr assimilation window. Our estimates of the rate of outer‐loop convergence suggest that atmospheric and ocean states synchronize within the first 6–10 hr of the assimilation window. We conclude that outer‐loop coupling is effective when the window is long enough that original imbalances in the atmospheric and ocean increments can synchronize within the length of the assimilation window. On the other hand, we suggest that explicit coupling is preferable for data assimilation systems with short assimilation windows (e.g. 6 hr or less).

Improving EEG Source Localization with a Novel Regularization: Spatiotemporal Graph Total Variation (STGTV) Method.

Electroencephalography (EEG) source Iocalization aims at reconstructing the current density on the brain cortex from scalp EEG recordings. It of ten starts with a generative model that maps brain activity to the EEG recording, and then solves the inverse problem. Previously proposed method graph fractional-order total variation (gFOTV) is based on spatial regularization, and was shown superior to some other existing spatial-regularized methods in simulation tests. However, the gFOTV addresses inverse problem for one time point at a time. The resultant estimated times series of brain activity is a simple concatenation of reconstructions independently performed at each time instance, and risks spurious temporal discontinuity due to overfitting noise in EEG recordings. In addition, the performance is subject to low signal-to-noise ratio (SNR) and small number of electrodes, which happens in realistic EEG recordings. To account for the generally continuous temporal variation in brain activity, but also allow for properly triggering abrupt changes, we propose a novel formulation that incorporates spatiotemporal regularization. Specifically, our method, called spatiotemporal graph total variation (STGTV) adopts graph fractional-order total variation (gFOTV) for spatial regularization and total variation (TV) for temporal regularization. The gFOTV encourages spatially smooth source distributions, and the temporal TV enhances temporal consistency in estimated activity maps. The introduction of implicit temporal coupling by temporal TV also helps with noise cancelation and enhances SNR. In a simulation study, the performance of the proposed method was compared against that from the gFOTV regularization alone. The results showed that the proposed STGTV method significantly improved gFOTV, with lower Iocalization errors and less spuriously discovered sources.

An IB-LBM implementation for fluid-solid interactions with an MLS approximation for implicit coupling

• Extend the implicit velocity correction method to simulate complex fluid solid interaction. • Implicit immersed boundary method to combined IMLS is first presented. • IMLS approximation with the weight orthogonal basis functions for stable solution. This paper presents a combination of the implicit immersed boundary (IB) method and the lattice Boltzmann method (LBM) for a fluid-solid interaction involving an immersed body with moving boundaries and complex geometries. In the implicit IB-LBM method, the flow is computed using LBM. The body force caused by the immersed body is not pre-calculated, but implicitly determined using a corrected velocity field that accurately satisfies the no-slip and no-penetration conditions on the interface between the fluid and solid. The information transfer is not using the traditional Dirac delta function and moving-least-square (MLS). But an improved MLS (IMLS) approximation has been developed to combined the implicit IB-LBM method, where the orthogonal function system with a weight function is used as the basis function and overcome these disadvantages of traditional MLS, in which it may cause numerical instabilities because the matrix inversion must be solved and the final equations system is easily ill-conditioned or singular. Several different flow problems (a two-dimensional flow past a static, rotating and oscillating cylinder, and the vortex-induced vibration of a cylinder as well as the free movement of flapping foil) are simulated to validate the accuracy and efficiency of the present implicit IB-LBM method. The simulation results show good agreement with previous numerical and experimental results. It is found that the present IB-LBM is efficient and reliable in dealing with fluid–solid interaction problems.