How to Solve Fluid-Structure Interaction Issues

Fluids are influenced by solid materials, walls or obstacles (see the example of opening a window to let a current of fresh air into a room or filling a glass with water). However, a solid can also be affected by a fluid when it is a deformable structure. Thus, while our "structures" feel a limited impact from fluids in our daily lives, there are all sorts of "reciprocal" situations where the interaction between general fluid flows and structure can cause changes in both. The article is dedicated to fluid-structure interactions, i.e. phenomena occurring on both fluid and solid when fluid flows interact with solid structures.

What are the physics and mathematics behind this interaction? A flow field characterizes laminar and turbulent fluid flows, while deformation and stress fields characterize the solid structure. Thus, solid deformation and stress fields can affect a fluid flow, and the flow field can affect a solid.

How to quantify these changes? And from a practical point of view, what is the relevance of fluid-structure interaction problems for various industries? Follow us in this article to know more! We will start with the description of engineering disasters, fortunately (as far as we know) without victims. We will move on to aerospace examples and delve into the physics and simulation software to conclude with the potentially revolutionary impact of AI on fluid-structure interaction simulation.

Fluid-Structure Interaction - Case Histories

A dramatic example of fluid-structure interaction, shown several times in TV documentaries, is the Tacoma bridge collapse. However, to dispel the idea that FSI is associated with disasters, let us first see how FSI can save your life: the case study is a parachute.

Parachutes

In the case of a parachute, FSI plays a crucial role in its functioning.

When a parachute is deployed, it opens up and exposes a large surface area to the air. As the parachute descends, the air interacts with the fabric, cords, and shape of the parachute. The air resistance or drag force exerted on the parachute opposes its downward motion, resulting from the fluid-structure interaction.

The fabric of the parachute, its shape, and the lines or cords that attach it to the person or payload create a complex interaction with the surrounding air. The airflow around the parachute can be turbulent, and various forces, including drag, lift, and gravity, come into play. These forces are influenced by the FSI and determine the descent rate, stability, and control of the parachute.

Tacoma Bridge Story

The Tacoma Narrows Bridge disaster served as a reminder of the consequences of overlooking fluid-structure interaction. This famous case paved the way for safer and more resilient infrastructure worldwide. Today, skyscrapers, bridges, and other civil structures are meticulously designed to consider their interaction with the surrounding environment, making them more resistant to natural forces and ensuring citizen safety.

On November 7, 1940, the first Tacoma bridge experienced a horrifying phenomenon. It was not an earthquake, as one might assume, but rather a destructive dance between wind and structure, known as fluid-structure interaction. The bridge, designed with a simple truss system and relatively narrow width, was in the grips of strong winds that triggered its downfall. As the wind passed through, it created a series of powerful vortex-shedding effects. These vortices interacted with the bridge's natural frequency, causing oscillations that gradually increased amplitude. The bridge started to sway and bend with ever-increasing intensity.

The vibrations became so extreme that they surpassed the bridge's ability to dissipate the energy efficiently. With each wind pass, the oscillations grew larger and more violent until the bridge reached a point of no return. Finally, on that fateful day, the once-solid Tacoma Narrows Bridge succumbed to the forces of nature. It collapsed dramatically into the waters below, earning it the infamous "Galloping Gertie." The Tacoma Narrows Bridge disaster became a landmark event in engineering, highlighting the importance of understanding fluid-structure interaction in large structures exposed to wind. The lessons learned from this tragedy led to significant advancements in bridge design and the implementation of measures to prevent similar incidents in the future. The new Tacoma bridge is a testament to the progress made in engineering practices. Robust computer simulations, wind tunnel tests, and cutting-edge materials have been employed to ensure that the bridge can withstand the most powerful forces of nature, including extreme wind events.

Sears (Willis Tower) Story

Willis Tower was the first example of fluid-structure interaction personally experienced by the author when the tower was called Sears Tower.

The Willis Tower, previously known as the Sears Tower, is a renowned skyscraper in Chicago, Illinois, constructed in 1973. It remains one of the tallest buildings in the United States, standing at an impressive height of 1,450 feet (443 meters), attracting millions of visitors annually. However, erecting a building of this magnitude was no easy feat. The engineering and architectural teams behind the Willis Tower had to overcome numerous challenges, including severe fluid-structure interactions, to ensure the safety and comfort of its occupants.

One of the most significant challenges in constructing a skyscraper is dealing with wind loads. Wind loads are forces exerted on a building by wind, which can cause structural issues such as excessive sway and vibrations. This is particularly true for a tall building as the Willis Tower, situated in an area with high wind speeds. Engineers adopted a bundled tube construction method to ensure stability and prevent excessive sway. The bundled tube construction technique involves grouping smaller tubes to form larger ones. The Willis Tower has nine bundled tubes, each 23 meters wide and 5 meters deep, arranged in a 3x3 grid. Steel beams connect each tube to the other tubes, and the tubes act as a giant cantilever, distributing the building's weight evenly and providing strength against wind loads. This construction technique also allows for more significant windows and natural light, as the building's weight is distributed more evenly across its perimeter.

Another challenge faced by the engineers was fluid-structure interactions. This phenomenon occurs when wind flows around a building, creating pressure differences on its different sides. These pressure differences can cause a vortex-shedding effect, resulting in the building vibrating and swaying. This can be particularly problematic in a tall building, making occupants uncomfortable or nauseous.

To address this issue, engineers used a combination of design features to minimize the impact of fluid-structure interaction on the Willis Tower. For example, the building's square shape reduces the effects of wind fluid flow, and its corners are rounded to minimize the vortex-shedding effect. The building's tapering shape also reduces wind loads on the upper floors.

Finally, to ensure the comfort of occupants on the highest floors, engineers installed several features to dampen vibrations and reduce noise levels. For instance, they installed a tuned mass damper system on the 99th floor. This system comprises a large, weighted mass suspended from the roof. When the building sways, the mass counteracts the movement, reducing vibrations and stabilizing the building. The engineers also used a combination of insulation, double-paned windows, and sound-absorbing materials to lower noise levels and guarantee a comfortable environment for occupants.

Fluid-Structure Interaction - Beyond Civil Engineering

Not only civil engineering is affected. In aerospace and automotive engineering, as well as biomedical engineering, fluid-structure interaction plays a critical role. It is pretty tricky, for example, to image a helicopter rotor without FSI.

Other important examples are airplane wings, automotive body panels, components in the HVAC system, and engine components.

Thus, FSI analysis has become an important area of investigation for engineers. Engineers have struggled to develop methodologies that could help them in their daily design tasks for years with the help of numerical analysis. Although challenging, several numerical simulation methods approaches allow a designer to simulate a "standalone" flow field with software. "Standalone" solid deformation and stress are even more available for engineers. Both computational fluid dynamics and solid simulation are parts of CAE (Computer-Aided Engineering), known as Computational Fluid Dynamics, or CFD, and Finite Element Analysis, or FEA.

Next, we will discuss the physics of FSI using examples from aerospace and automotive engineering. Finally, we will expose traditional and more recent methods for simulating FSI.

What Is Fluid-Structure Interaction: Physics

The interaction between a fluid and a solid structure is a complex phenomenon that involves structural interactions and several physical processes, such as fluid dynamics, solid mechanics, and thermodynamics. In fluid-structure interactions, the flow and the solid structure's deformation are coupled, and the behavior of each component affects the other. This coupling can result in various phenomena, such as fluid-induced vibration, aeroelasticity, and fluid-structure instability. The physics of fluid-structure interaction can be studied at different scales, from the macroscopic level, where the entire fluid-structure system is considered a single entity, to the microscopic level, where the interaction between individual fluid particles and solid particles is studied.

At the macroscopic level, fluid-structure interaction (FSI) is described by a set of partial differential equations that govern the fluid's motion and the solid object or structure's deformation. These equations are solved using numerical methods, such as finite element analysis or computational fluid dynamics. The interaction between individual fluid particles and solid particles is studied at the microscopic level using molecular dynamics simulations. In these simulations, the motion of each particle is governed by the laws of mechanics and thermodynamics, and intermolecular potentials describe the interaction between particles.

Fluid-Structure Interaction Problems in Aerospace and Automotive Engineering

Fluid-structure interactions are critical in designing and optimizing complex systems such as aircraft wings, helicopter rotors, automotive body panels, and engine components. These systems' fluid and solid interactions can significantly impact performance, safety, and durability.

Aerospace Fluid-Structure Interaction Problems

In aerospace engineering, fluid-structure interaction is significant for the design of wings and rotor blades. The deformation of the wing or rotor blade due to aerodynamic loads can affect the flow of air around the structure, which can, in turn, affect the lift and drag forces acting on the structure. FSI simulations can help designers optimize the shape and stiffness of the wing or rotor blade to improve aerodynamic performance and reduce the risk of structural failure.

Automotive Fluid-Structure Interaction Problems

In automotive engineering, fluid-structure interaction is important for the design of body panels and engine components. The interaction between the fluid and the structure can affect the vehicle's aerodynamics, thermal performance, and the engine components' durability. FSI simulations can help designers optimize the shape and stiffness of body panels to reduce drag, improve fuel efficiency, and optimize the engine's cooling system to prevent overheating and premature failure.

Biomedical Engineering Fluid-Structure Interaction Problems

Biomedical Engineering Fluid-Structure Interaction (FSI) studies are crucial in advancing our knowledge of heart valve dynamics, leading to better-designed heart valve replacements and improved patient outcomes. These models continue to be at the forefront of cardiovascular research, contributing to the development of innovative medical devices and therapeutic approaches. Heart valve dynamics play a critical role in maintaining proper blood flow within the cardiovascular system. Understanding the advantages and limitations of each type of heart valve (rigid vs flexible) through FSI models enables researchers to design more effective prosthetic valves and make informed decisions when choosing the most suitable valve replacement for patients. Additionally, FSI simulations aid in optimizing the design of transcatheter heart valves, which have become an increasingly popular alternative to traditional open-heart surgeries.

FSI models are useful for predicting blood flow and kinetics in cellular native valves. Similarly, mechanical valves and bioprosthetic valves can benefit from FSI simulations to assess their functionality and performance within the dynamic cardiovascular environment. These models allow researchers and engineers to study the interactions between the fluid (blood) and the structure (valve), providing valuable insights into valve functionality, efficiency, and potential failure modes. In the context of heart valve research, the distinction between rigid and flexible valves is of significant importance. Rigid valves, often made from materials like metal or ceramics, offer excellent durability and longevity but may cause issues related to blood turbulence and potential damage to blood cells. On the other hand, flexible valves, typically made from polymers or biological tissues, mimic the natural behavior of native valves more closely, leading to reduced turbulence and improved hemodynamics.

How to Simulate Fluid-Structure Interaction: Early CAE Methods

A fluid-structure interaction numerical simulation involves computer-aided engineering (CAE) methods, which have evolved significantly over the past few decades. Traditional CAE numerical methods for simulating FSI were based on simplified assumptions and empirical models, making them less accurate and unreliable than recent methods. In the 1980s and 1990s, FSI simulations were typically based on one-way coupling, where the fluid and the structure were treated as separate systems. Computational methods for simulating fluid-structure interaction have evolved over the past few decades.

Partitioned FSI Coupling

Traditional methods, used from the 1980s to the early 2000s, involved solving the fluid and structural equations separately and then coupling the two solutions. This approach, called partitioned coupling, has limitations because it assumes that the fluid and structure are stationary during the coupling process. This assumption can lead to errors in predicting the behavior of the coupled system afterwards.

Let us examine the partitioned procedure versus its advantages and challenges. FSI coupling offers computational advantages and flexibility due to its reduced computational effort and modularity. However, it suffers from certain drawbacks, including cumbersomeness in information exchange, reduced precision in predicting dynamic behavior, and stability challenges. As computational methods and hardware advance, researchers and engineers have developed more advanced and accurate fully-coupled FSI techniques to overcome the limitations of partitioned coupling and obtain more reliable and precise numerical simulations of fluid-structure interaction problems.

Partitioned Fluid-Structure Coupling - Advantages and Challenges

Advantages

• One of the primary advantages of a partitioned approach to FSI coupling is its reduced computational effort. By solving the fluid and structural equations separately, the complexity of the problem is significantly reduced compared to fully-coupled methods. This makes it computationally more efficient and allows the use of different specialized solvers for fluid and structural domains.
• Partitioned FSI allows for greater flexibility and modularity in the simulation setup. Engineers and researchers can use well-established, mature solvers for fluid and structural problems independently without the need to develop an integrated solver. This flexibility is beneficial in complex simulations where existing solvers may be optimized for specific tasks.

Challenges

• The main drawback of partitioned FSI is the cumbersomeness of information transfer data exchange between the fluid and structural solvers at each time step. Data transfer and synchronization can lead to additional overhead and may introduce errors in the coupling process. Moreover, the time step sizes of fluid and structural solvers must be appropriately matched to ensure stability and accuracy, adding to the complexity.
• Partitioned coupling assumes that the fluid and structure remain stationary during the coupling process, leading to certain inaccuracies in predicting the behavior of the coupled system afterwards. In reality, fluid-structure interactions can induce dynamic changes and deformations, which the partitioned approach may not entirely capture. As a result, the method might provide less accurate predictions compared to fully-coupled approaches.
• The choice of time step sizes in partitioned FSI coupling is critical for stability. The time step of the fluid solver must be small enough to capture fast fluid dynamics, while the structural solver's time step should be fine enough to account for rapid structural deformations. Balancing these time steps to achieve both stability and accuracy can be challenging, especially in scenarios with disparate time scales between fluid and structural responses.

MpCCI Coupling

Another approach used in traditional methods is monolithic coupling, which involves solving the fluid and structural equations simultaneously. MpCCI stands for "Mesh-based parallel Code Coupling Interface." It is a software framework that facilitates coupling different simulation codes to perform multi-physics and multi-scale simulations efficiently. MpCCI acts as an interface that enables the exchange of data and information between different simulation solvers, allowing them to work together seamlessly in a monolithic manner.

Monolithic coupling, as mentioned, involves solving the fluid and structural equations simultaneously within a single integrated solver. This approach offers several advantages. The first one is superior accuracy in fluid-structure interaction simulations compared to partitioned methods. Solving fluid and structural equations together accounts for the dynamic interactions and feedback between the fluid and structure more comprehensively, leading to more precise predictions of system behavior.

Another advantage is that monolithic coupling avoids data transfers and synchronization between separate solvers; thus, it reduces numerical errors arising from information exchange. The coupling process is more tightly integrated, leading to improved numerical stability and convergence. However, the monolithic procedure also has some drawbacks. As monolithic coupling requires solving both fluid and structural equations simultaneously, it demands significant computational resources. The simultaneous solution of complex fluid and solid mechanics can be computationally intensive, making it prohibitive for large-scale problems or when using high-fidelity models.

Also, monolithic coupling does not allow for easy modularity, unlike partitioned coupling. Integrating different solvers into a monolithic framework can be more challenging, especially when dealing with proprietary or specialized codes. This lack of modularity can hinder simulation setup flexibility and restrict the solver's choices.

How to Simulate FSI: Contemporary CAE Methods

Several computational methods have been developed to simulate FSI in recent years, including fully coupled solvers, immersed boundary methods, and reduced-order modelling techniques. This essay will discuss these more recent computational methods for simulating FSI and their advantages.

Rigid Body Motion with Arbitrary DoFs in CFD

In the computational fluid dynamic approach, the study of rigid body motion with arbitrary Degrees of Freedom (DoFs) holds significant importance in simulating and analyzing complex fluid-structure interaction problems such as valves or yachts. Rigid body motion refers to the movement of solid objects through a fluid domain without undergoing any deformation or internal strain. When analyzing fluid flows around rigid bodies, it is essential to consider all possible degrees of freedom of the moving structure to capture their movement and interaction with the surrounding fluid accurately. Traditional CFD simulations often assume restricted degrees of freedom, such as translational and rotational motions along predefined axes.

However, in many real-world scenarios, rigid bodies can have arbitrary DoFs, such as six-degree-of-freedom ("6-DoF") motion that includes linear translations along x, y, and z axes and rotations about these axes. Simulating the motion of rigid bodies with arbitrary DoFs in CFD requires advanced numerical techniques and robust algorithms. One approach is to incorporate overset grids or moving mesh methods to accommodate the motion of rigid bodies while maintaining grid connectivity. Another method involves coupling the CFD solver with a rigid body dynamics solver, where the forces and moments acting on the body due to fluid interactions are computed and used to update the body's motion in the subsequent time step.

Applications of CFD simulations with arbitrary DoFs are diverse, ranging from analyzing aircraft maneuvering in turbulent flows to studying underwater vehicles' behavior and even understanding the impact of floating structures on ocean currents. These simulations provide valuable insights into the fluid forces and moments acting on rigid bodies, aiding in designing and optimizing various mechanical engineering systems subjected to fluid flow.

Immersed Boundary Method

The immersed boundary method ("ibm") is a computational method class that simulates FSI. These methods use a fixed Cartesian grid to solve the fluid equations, while the structure is represented by an immersed boundary embedded in the grid. The immersed boundary is discretized using Lagrangian elements, such as springs or beams, which interact with the fluid grid points through a force term.

The governing equations for IBM are the Navier-Stokes equations, augmented by a force term that accounts for the interaction between material properties of the fluid and structure: ρ f ∂u/∂t + ρ f(u⋅∇) u = −∇ p + f + μ f ∇²u + f_ibm where f_ibm is the force term that accounts for the interaction between the fluid and structure. The structural equations are given by: ρ s ∂²u/∂t² = ∇⋅σ + f_ibm where σ is the stress tensor.

One advantage of ibm is its flexibility in handling complex geometries. The immersed boundary can be arbitrarily shaped for complex structure simulation and mathematical modelling. Additionally, ibm is computationally efficient, as the fixed Cartesian grid simplifies the computational mesh.

Fully Coupled Solvers

Fully coupled solvers are a class of computational methods that simulate fluid-structure interaction. These methods solve the fluid and structural equations simultaneously without partitioning the system.

This approach provides a more accurate and efficient method for simulating fluid response than FSI. The governing equations for fluid and structure are given by:

• Navier-Stokes Equation: ρf ∂u/∂t + ρ f (u⋅∇)u=−∇p + F+ μ ∇²u where "ρf" is the fluid density, "u" is the fluid velocity, "p" is pressure, "F" is the body force, and "μ" is the fluid viscosity
• Elasticity Equation: ρs ∂²u/∂t² = ∇⋅σ + F where "ρs" is the structural density, "u" is the displacement, "σ" is the stress tensor, and "F" is the body force

The coupling between the fluid and structural equations is accomplished through the boundary conditions. The fluid velocity at the structure equals the structural velocity, and the fluid pressure balances the normal stress at the structure interface at the boundary. These boundary conditions provide information exchange between the fluid domain and structural domains.

One disadvantage of fully coupled solvers is their high computational cost. The simultaneous solution of the fluid and structural equations can be computationally intensive, particularly for large-scale fluid and structural simulations together. However, recent computational hardware and algorithms advancements have made fully coupled solvers more practical for complex FSI simulations.

How to Simulate Fluid-Structure Interaction With Model-Order Reduction and Proper Orthogonal Decomposition

Model order reduction techniques aim to reduce the order of the governing equations for fluid-structure interaction by projecting the original equations onto a lower-dimensional subspace. The reduced set of equations can then be solved simultaneously and more efficiently than the original equations, leading to significant computational savings. This projection into the lower-dimensional subspace is achieved using "basis functions" spanning the solution space. The reduced set of equations obtained using Model order reduction techniques can be written as follows: M(q) ∂²φ/∂t² + K(q) φ = F(q) where M and K are the mass and stiffness matrices, respectively, and q is the vector of input parameters that govern the FSI problem, the vector φ represents the reduced-order solution, and F is the forcing vector.

The basis functions used in model order reduction can be obtained using techniques such as Galerkin projection, Petrov-Galerkin projection, and least-squares projection. These basis functions are typically obtained from a set of high-fidelity simulations, either using fully coupled solvers or immersed boundary methods. One advantage of model order reduction techniques is their computational efficiency. By reducing the order of the governing equations, the computational cost of FSI simulations can be significantly reduced. Additionally, numerical model order reduction techniques can be used to obtain a reduced-order model that captures the essential dynamics of the FSI problem, making them useful for real-time control and optimization applications.

Proper Orthogonal Decomposition

Proper orthogonal decomposition (POD) is a technique used to extract the dominant modes of the FSI solution from a set of high-fidelity simulations. POD involves decomposing the FSI solution into a set of orthogonal modes that capture the dominant dynamics of the problem. These modes can be used to construct a reduced-order model approximating the FSI solution.

The POD technique involves solving the following eigenvalue problem: C ϕ = λ ϕ where C is the covariance matrix of the FSI solution, ϕ is the POD mode, and λ is the corresponding eigenvalue. The POD modes are obtained by solving the eigenvalue problem and sorting the eigenvalues in descending order.

The reduced-order model obtained using POD can be written as φ = Φ a where Φ is the matrix of POD modes, and a is the vector of coefficients that determines the amplitude of each mode. The Φ matrix is constructed from the set of POD modes, and the "a" vector is obtained by projecting the high-fidelity solution onto the POD modes.

One advantage of POD techniques is their ability to capture the dominant dynamics of the FSI problem. By extracting the dominant modes of the FSI solution, POD techniques can provide a low-dimensional representation of the FSI problem, reducing the computational cost of simulations. Additionally, POD techniques can identify the most influential parameters governing the FSI problem, making them useful for design optimization and uncertainty quantification applications.

How to Simulate FSI with Deep Learning

Let us summarize what we have learnt so far on FSI and simulation. Fluid-Structure Interaction simulations involve coupling the mechanics of fluids and solids to analyze the complex interaction between fluids and solid structures. These simulations play a critical role in understanding and predicting the behavior of systems where fluid mechanics affects the deformation and dynamics of the surrounding structures. Traditionally, FSI simulations have relied on computationally expensive CFD and FEA solvers to obtain accurate results. However, recent advancements in deep learning have opened up exciting possibilities for using neural networks as surrogate models to approximate the behavior of the coupled system. This raises the question: Could deep learning replace CFD, FEA, or both in FSI simulations?

In this final section, we explore the concept of using deep learning surrogates in FSI and discuss the potential benefits and challenges associated with this approach.

The Emergence of Deep Learning Surrogates

Deep learning has revolutionized various fields thanks to its ability to extract complex patterns and relationships from large amounts of data. Deep learning has shown promise in surrogate modelling in engineering and scientific domains, where it can approximate complex functions or processes based on input-output data. In the context of FSI, deep learning surrogates have the potential to provide a faster and computationally efficient alternative to traditional CFD and FEA solvers, thus providing a complementary approach to purely physics-based numerical methods leading to finite volume and finite element developments.

Replacing Computational Fluid Dynamics with Deep Learning for Fluid Flow Predictions

CFD simulations involve solving the Navier-Stokes equations to model flow around structures. These simulations can be computationally intensive, especially for large-scale problems or when high-fidelity resolution is required.

Deep learning surrogates offer an appealing option to replace CFD in FSI for certain applications, with several advantages and some challenges. Neural networks, once trained, can perform predictions much faster than traditional CFD solvers. This speed-up can be particularly advantageous in real-time or interactive simulations. Deep learning surrogates can significantly reduce computational expenses associated with running CFD simulations. This opens up the possibility of exploring design spaces and sensitivity analyses with less computational overhead. Well-trained neural networks can generalize from a diverse dataset and approximate complex flow patterns even beyond the training data, making them suitable for a wide range of FSI scenarios. However, training a deep learning surrogate requires a large and representative dataset. Generating such datasets, especially for highly dynamic and complex flow phenomena, can be challenging and time-consuming. Ensuring that the surrogate model accurately captures the fluid dynamics under varying conditions, especially in unexplored regions of the input space, is crucial for reliable predictions. Generalization capability is a key challenge in deep learning surrogate modelling. This is why it is quite important to get out of the "parametrization constraints" of traditional AI methods based on reduced-order models.

Enter Deep Learning for Fluid-Structure Interactions

With a trained deep-learning surrogate in place, the fluid-structure FSI simulation can be set up to perform a coupled analysis of fluid dynamics and structural mechanics more efficiently.

In a wing FSI case, the FEA structural solver simulates the structural deformation of a wing using traditional methods based on the aerodynamic loads provided by the deep learning surrogate for CFD. At each time step, the structural deformation data from the FEA solver is fed into the deep learning model, which then predicts the corresponding fluid forces acting on the wing. These fluid forces are then used as boundary conditions for the structural solver for the next time step. The process of exchanging information between the structural solver (FEA) and the deep learning surrogate for CFD continues iteratively, allowing the simulation to capture the dynamic interactions between the fluid and structure with accuracy since, whereas the deep learning prediction is a surrogate, it reacts in real-time to the FEA solver.

The advantages are evident in terms of computational burden and ease of use.

The use of a deep learning surrogate for CFD significantly reduces the computational burden associated with traditional CFD simulations.

The surrogate model, once trained, performs very fast predictions based on the new deformed shape of the solid domain (considered as a CFD boundary), and it can in fact, provide rapid predictions of fluid forces, leading to faster overall FSI simulations. Also, a deep learning surrogate eliminates the need for creating and managing complex computational grids commonly required in CFD simulations to represent fluid domains. This simplifies the simulation setup and reduces preprocessing efforts.

Conclusion - Future Scenarios

The integration of FEA with a Deep Learning surrogate for CFD in Fluid-Structure Interaction simulations offers a compelling solution to enhance efficiency and reduce computational costs. By leveraging the strengths of both methodologies, engineers are gaining more accurate and more rapid insights into complex fluid-structure interaction problems, paving the way for advancements in various engineering applications, such as aerospace design, automotive engineering, biomedical engineering and civil infrastructures. Addressing the challenges associated with data quality, generalization, and model interpretability will be crucial to fully harness the potential of this hybrid approach and realize its benefits in practical engineering scenarios.

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