Solve Fluid Structure Interaction Problems Research Articles

Numerical Simulation of a Submerged Floating Tunnel: Validation and Analysis

The dynamic response analysis of submerged floating tunnels (SFTs) under seismic action is a complex two-way fluid–structure coupling problem that requires expertise in structural dynamics, fluid mechanics, and advanced computational methods. The coupled Eulerian–Lagrangian (CEL) method is a promising method for solving fluid–structure interaction problems, but its application to SFTs is not well established. Therefore, it is crucial to verify the accuracy and reliability of the CEL method in fluid–structure coupling simulations. This study verified the applicability of the CEL method for simulating one-way and two-way fluid–structure coupling cylindrical flow problems, and then applied the CEL method for the analysis of a shaking table test of a model SFT. A comparison of results obtained with the CEL method with those obtained in a previous indoor model test of an SFT demonstrates the agreement between the results of the CEL method and the overall trend of the experimental results, indicating the reliability of the method for the seismic analysis of SFTs. Moreover, the analysis of the dynamic response characteristics of SFTs under seismic conditions provides data support and a technological means for the seismic design of SFTs.

Coupling of the immersed boundary and Fourier pseudo-spectral methods applied to solve fluid–structure interaction problems

The current manuscript addresses fluid–structure interaction (FSI) problems to the analysis of vortex-induced vibration (VIV), employing the methodology designated as IMERSPEC2D. The approach seamlessly integrates the Fourier pseudo-spectral method (FPSM) and the immersed boundary method (IBM) to solve the Navier–Stokes (NS) and continuity equations. Simultaneously, the effects of cylindrical structure, involving 1 and 2 degrees of freedom (d.o.f.) are simulated, by incorporating structural motion equations into NS via the IBM source term and implementing a two-way FSI algorithm. In the paper are presented the comparison of low and high-order temporal integration methods applied to solve the dynamic behavior of the structure and the dimensionless of the cylinder’s structural motion equations, resulting in an increase in computational time step from 1E(-9\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-9$$\\end{document}) to 1E(-3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-3$$\\end{document}). Validation results to refined mesh simulations include the accurate representation of the lock-in phenomenon to simulations of 1 d.o.f. obtaining the range between reduced velocity 5.456 and 5.568 and the maximal amplitude is 0.352. Notably, the eight-shape pattern of the 2 d.o.f. cylinder displacement is obtained and the formation of C2S wake patterns is achieved, as presented by other authors. In conclusion, the dimensionless approach reduces computational time, while the high-order both of IMERSPEC methodology and time advancement integration to FSI improve the results of the cylinder’s motion and alters distinct vortex shedding patterns in fluid dynamics.

A monolithic, finite element-based strategy for solving fluid structure interaction problems coupled with electrostatics

In this work, we present a monolithic finite-element-based strategy for problems involving the deformation of a hyperelastic solid, an incompressible fluid and electrostatics. We use a two-field hybrid Lagrangian formulation for the structure, and a velocity-based ALE mixed formulation for the fluid with appropriately chosen interpolations for the various field variables to ensure stability of the resulting numerical procedure. The equations of electrostatics are solved on the reference configuration over both the solid and fluid domains, with voltage and electric displacement continuity imposed at the interface. Keeping in view that the thickness of typical MEMS structures is small, a stress-based hybrid formulation is used to prevent locking. The use of a monolithic strategy provides a robust and stable algorithm, and allows the user to take large time steps. The consistent linearization ensures a quadratic rate of convergence of the non-linear iterations at each time step. Detailed expressions for the tangent stiffness and associated matrices for the three-way coupled problem are provided. The robustness and accuracy of the proposed method are demonstrated by solving several benchmark problems from the literature.

Increasing Micro-Rotational Viscosity Results in Large Micro-Rotations: A Study Based on Monolithic Eulerian Cosserat Fluid–Structure Interaction Formulation

In classical continuum mechanics, a monolithic Eulerian formulation is used for numerically solving fluid–structure interaction (FSI) problems in the frame of a physically deformed configuration. This numerical approach is well adapted to large-displacement fluid–structure configurations where velocities of solids and fluids are computed all at once in a single variational equation. In the recent past, a monolithic Eulerian formulation for solving FSI problems of finite deformation to study the different physical features of fluid flow has been employed. Almost all the current studies use a classical framework in their approach. Despite producing decent results, such methods still need to be appropriately configured to generate exceptional results. Recently, a number of researchers have used a non-classical framework in their approach to analyze several physical problems. Therefore, in this paper, a monolithic Eulerian formulation is employed for solving FSI problems in a non-classical framework to study the micro-structural characteristics of fluid flow by validating the results with classical benchmark solutions present in the literature. In this respect, the Cosserat theory of continuum is considered where a continuum of oriented rigid particles has, in addition to the three translational degrees of freedom of classical continuum, three micro-rotational degrees of freedom. The mathematical formulation of model equations is derived from the general laws of continuum mechanics. Based on the variational formulation of the FSI system, we propose the finite element method and semi-implicit scheme for discretizing space and time domains. The results are obtained by computing a well-known classical FSI benchmark test problem FLUSTRUK-FSI-3* with FreeFem++. The results of the study indicate that the increase in micro-rotational viscosity μr leads to significantly large micro-rotations in fluid flow at the micro-structural level. Further, it is found that the amplitude of oscillations is related inversely to the material parameters c1 and μr while the increase in c1 stabilizes the amplitude of oscillations relatively more quickly than increasing μr. The color snapshots of the numerical results at different times during the computer simulations and general conclusions drawn from the results are presented.

An efficient explicit immersed boundary-reconstructed lattice Boltzmann flux solver for isothermal fluid-structure interaction problems with large deformations and complex geometries

In this paper, a novel approach for isothermal fluid-structure interaction (FSI) problems is proposed that not only inherits the advantages of a reconstructed lattice Boltzmann flux solver (RLBFS) in solving the fluid field, but also retains the efficiency found in the explicit boundary condition-enforced immersed boundary method (EIB) for implementation of boundary conditions on the solid wall. Hence, the new approach (EIB-RLBFS) is highly suitable for complex FSI problems such as large deformations and complex geometries. Furthermore, the arbitrary Lagrangian-Eulerian (ALE) approach is integrated with EIB-RLBFS to solve moving boundary problems efficiently. The structural dynamics are solved by a finite difference method for moving objects and flexible structures. The overall framework of EIB-RLBFS is simple yet robust, where a fractional method is applied to split the FSI process into a predictor step and a corrector step. The RLBFS is applied in the predictor step to predict the intermediate flow field, while the EIB is invoked in the corrector step to impose the no-slip boundary conditions within the flow field, thereby, correcting the predicted flow field to satisfy the no-slip boundary conditions. The proposed approach (EIB-RLBFS) has been tested and evaluated extensively in terms of accuracy and efficiency on several benchmark cases such as, a 2D self-propelled unconstrained flapping/undulatory foil, a 2D filament, a 3D streamwise rotating sphere, and a 3D flapping flag. Results obtained using the proposed approach are in good agreement with previous studies, substantiating the capability and flexibility of EIB-RLBFS for solving FSI problems.

Accurate and efficient hydrodynamic analysis of structures with sharp edges by the Extended Finite Element Method (XFEM): 2D studies

Achieving accurate numerical results of hydrodynamic loads based on the potential-flow theory is very challenging for structures with sharp edges, due to the singular behavior of the local-flow velocities. In this paper, we introduce, perhaps the first time in the literature on marine hydrodynamics, the Extended Finite Element Method (XFEM) to solve fluid–structure interaction problems involving sharp edges on structures. Compared with the conventional FEMs, the singular basis functions are introduced in XFEM through the local construction of shape functions of the finite elements. Four different FEM solvers, including conventional linear and quadratic FEMs as well as their corresponding XFEM versions with local enrichment by singular basis functions at sharp edges, are implemented and compared. To demonstrate the accuracy and efficiency of the XFEMs, a thin flat plate in an infinite fluid domain and a forced heaving rectangle at the free surface, both in two dimensions, will be studied. For the flat plate, the mesh convergence studies are carried out for both the velocity potential in the fluid domain and the added mass, and the XFEMs show apparent advantages thanks to their local enhancement at the sharp edges. Three different enrichment strategies are also compared, and suggestions will be made for the practical implementation of the XFEM. For the forced heaving rectangle, the linear and 2nd order mean wave loads are studied. Our results confirm the previous conclusion in the literature that it is not difficult for a conventional numerical model to obtain convergent results for added mass and damping coefficients. However, when the 2nd order mean wave loads requiring the computation of velocity components are calculated via direct pressure integration, the influence of singularity is significant, and it takes a tremendously large number of elements for the conventional FEMs to get convergent results. On the contrary, the numerical results of XFEMs converge rapidly even with very coarse meshes, especially for the quadratic XFEM. Unlike other methods based on domain decomposition when dealing with singularities, the FEM framework is more flexible to include the singular functions in local approximations.

A monolithic arbitrary Lagrangian–Eulerian‐based finite element strategy for fluid–structure interaction problems involving a compressible fluid

AbstractIn this work, we present a new monolithic finite element strategy for solving fluid–structure interaction problems involving a compressible fluid and a hyperelastic structure. In the Lagrangian limit, the time‐stepping strategy that we propose conserves the total energy, and linear and angular momenta. Detailed proofs with numerical validations are provided. We use a displacement‐based Lagrangian formulation for the structure, and a velocity‐based arbitrary Lagrangian–Eulerian mixed formulation with appropriately chosen interpolations for the various field variables to ensure stability of the resulting numerical procedure. A hybrid formulation is used to prevent locking of thin structures. Apart from physical variables such as displacement, velocity, and so forth, no new variables are introduced in the formulation. The use of the exact tangent stiffness matrix ensures that the algorithm converges quadratically within each time step. A number of benchmark examples have been solved to illustrate the good performance of the proposed method.

Adaptive High-Order Fluid-Structure Interaction Simulations with Reduced Mesh-Motion Errors

This paper demonstrates an adaptive approach for solving fluid–structure interaction problems using high-fidelity numerical methods along with a detailed analysis of mesh-motion errors. A high-order partitioned approach is applied to couple the fluid and the structural subsystems, where the fluid subsystem is discretized using a discontinuous Galerkin finite-element method, while the structures solver uses a continuous Galerkin discretization. An explicit mapping is used as the primary mesh deformation algorithm. High-order time-integration schemes are used by the coupled solver to march forward in time, and the space-time mesh of the fluid subsystem is adapted using output-based methods. The error estimates for the unsteady outputs are evaluated by calculating the uncoupled, unsteady adjoint of the fluid subsystem. Adaptive meshing is used to demonstrate the importance of mesh-motion errors on output convergence, and a comprehensive analysis is conducted to control such errors arising from the mesh deformation algorithm. The benefits of adaptive meshing are demonstrated on a cantilevered Euler–Bernoulli beam placed in a low-Reynolds number flow and on a two-dimensional pitching–plunging airfoil in a high-Reynolds number flow.

Verification and application of 2-D DDA-SPH method in solving fluid–structure interaction problems

The study of fluid–structure interaction (FSI) is a challengeable topic, which concerns a coupled system with consideration of not only the behaviors of the fluid and the structure, but also the interaction process between both. In this paper a coupled method is introduced to simulate FSI problems in two-dimensional (2-D) case. In this coupled method (2-D DDA-SPH), the smoothed particle hydrodynamics (SPH) based on kernel approximation and particle approximation is employed to represent the fluid domain governed by Navier–Stokes equations and the discontinuous deformation analysis (DDA) based on the minimum total potential energy principle is used to model the real solid structure (with rigidity or elasticity) through virtual joints. A coupling scheme bridging both methods is used based on a penalty-force method, and an improved contact detection between particle and block is proposed. Several challenging examples, including breaking dam flow through an elastic plate, breaking dam flow on a rigid barrier or an elastic barrier are investigated to demonstrate the capability of the 2-D DDA-SPH method to capture the entire FSI process. Finally, two application examples, failure of gravity dam induced by water pressure, and dynamic response of armor blocks on breakwater under incident wave, are studied by using 2-D DDA-SPH. The simulation results show satisfactory agreements with available experimental, numerical, and analytical results, suggesting the applicability of the 2-D DDA-SPH method to solve FSI problems.

Coupling edge-based smoothed finite element method with smoothed particle hydrodynamics for fluid structure interaction problems

Numerical simulation of fluid structure interaction (FSI) problems is one of the most challenging topics in computational fluid dynamics. In this paper, coupling edge-based smoothed finite element method (ES-FEM) and smoothed particle hydrodynamics (SPH) method (ES-FEM-SPH) is proposed for solving FSI problems, where the edge-based smoothed finite element method is used to model the movement and deformation of structures, and the smoothed particle hydrodynamics is used to model the fluid flow. In ES-FEM, the gradient smoothing technique is applied over the smoothing domain and it can effectively overcome the ‘‘overly-stiff’’ effect in conventional FEM model. Some correction algorithms including density correction, kernel gradient correction and particle shift technique are integrated into the SPH method to improve computational stability and accuracy. A virtual particle coupling scheme is used to implement the coupling of ES-FEM and SPH with complex geometry interface. As ES-FEM is more accurate than conventional FEM, and it is expected that this ES-FEM-SPH coupling approach should be superior than existing FEM-SPH coupling approaches. A number of test examples with FSI are investigated with the presented ES-FEM-SPH, and compared with results from other approaches including FEM-SPH. From the obtained numerical results, we can conclude that the ES-FEM-SPH coupling approach is effective to simulate FSI problems.

An explicit MPS/FEM coupling algorithm for three-dimensional fluid-structure interaction analysis

Currently, accurate simulations of fluid structure interaction (FSI) problems still remain a challenging task in the academic community. The purpose of this work is to develop a three-dimensional (3D) coupling algorithm to achieve the end, where the explicit moving particle simulation method (MPS) and the finite element method (FEM) are respectively employed to account for fluid flows and structural deformation. The developed coupling algorithm inherits the advantages of the aforementioned methods, while also addressing their shortcomings. We start by extending a newly proposed ghost cell boundary (GCB) model, which has proved to be an effective method to deal with the wall boundary of complicated shapes, to three dimensions. For the problems of interest, the finite elements for structural discretization serve as ghost cells for interaction force calculation, thereby providing an easy and natural way for the construction of ghost cells. The interactions between fluids and structures are dealt with using an integral version of the MPS model, and the resultant interaction forces calculated at integration points of a cell are distributed to finite element nodes for the update of nodal kinematics in the context of an explicit time integration scheme. The effectiveness and accuracy of the 3D GCB model are validated via two numerical examples, i.e., the dam break test and the water flow in a rotating gear test. Afterwards, the developed coupling algorithm is applied to two common FSI problems, i.e., the dam break tests with respective an elastic obstacle and an elastic gate. The good agreements between our simulation results and the existing data in literature demonstrate the accuracy and capacity of the developed coupling algorithm in solving FSI problems.

A strong-coupled method combined finite element method and lattice Boltzmann method via an implicit immersed boundary scheme for fluid structure interaction

Fluid structure interaction (FSI) problems are often encountered in ocean science and technology. In this present, an implicit immersed boundary (IB) method combined with Lattice Boltzmann Method (LBM) and finite element method (FEM) is presented for the strong-coupled simulations of fluid structure interaction. Velocity field is solved rapidly by lattice Boltzmann-BGK equations without external force, and the deformation of a flexible structure was computed by FEM. Fluid structure coupling was processed by immersed boundary implicit forced method. The resulting combination gives an easy-to-use, inexpensive and accurate technique to solve FSI problems. Simultaneously, the body force on the immersed boundary can be calculated directly and acts as the load for structure solver, so the displacement of structure can be obtained at the same time, which is avoid the time lag between the fluid solver and solid solver. Several examples including flow over a static and deformable plate, and the flow problems of an oscillating and cantilever flexible plate were simulated and analyzed. The results agree well with the previous experimental and numerical investigations, which indicate the IB-LB-FEM proposed in this paper is an efficient and reliable fluid-structure interaction numerical simulation method.

An Eulerian-Lagrangian-Lagrangian method for solving fluid-structure interaction problems with bulk solids

This paper presents an Eulerian-Lagrangian-Lagrangian (ELL) method to solve the fluid-structure interaction (FSI) problem, in which a bulk solid is immersed in the fluid. The ELL approach uses a small portion of the Lagrangian fluid to wrap the solid body, and they are treated as an enlarged “composite solid”. Then the conventional immersed finite element method (IFEM) is implemented. The velocity condition of the moving interface is explicitly imposed within the unified Lagrangian grids of the composite solid domain, and then smoothly transferred onto the Eulerian fluid nodes nearby the FSI interaction zone. The inaccurate numerical FSI interface in IFEM is hence significantly improved. The idea of warping Lagrangian fluid makes ELL a combination of the body-conforming method and the immersed type method. It is straightforward but offers an excellent physical explanation that makes ELL more realistic. Several numerical examples are computed to demonstrate the superior performance of the proposed approach for solving FSI problems with bulk solids, in comparison with the conventional IFEM.

Fluid-structure interaction analysis of offshore structures based on separation of transferred responses

A new partitioned fluid-structure interaction (FSI) method is proposed for dynamic analysis of offshore structures. The main idea of the developed approach is to provide the separation of different components caused by different contributions (such as transferred conditions and updated loadings). One theoretical development is that separated Laplace-domain responses can be obtained from the previous responses. The other is that the structural responses in time domain can be easily calculated by inverse Laplace transform. Once solutions to the structural responses at the time of interest are obtained, the fluid loadings can be updated to consider the impacts of the responses on the geometry of the fluid domain. More importantly, the proposed method is able to improve the estimation accuracy of the structure responses, and hence, may provide better updating results of fluid loadings when the FSI mechanism is considered. To demonstrate the correctness and accuracy of the approach, three numerical examples are used in this paper. The first example is a single degree-of-freedom (DOF) system subject to an irregular dynamic loading. The computation results show that the system responses at previous time steps can be successfully separated into typical components that correspond to different contributions such as transferred conditions and updated loadings. The system responses at current time, obtained by combining previous responses, are in a good agreement with analytical results and those obtained by the Newmark-β method. Then, the second example of a four-DOF lumped system is explored to indicate the superiority of the proposed method over the Newmark-β method in terms of accuracy. Finally, in the third example of an elastic upright cantilever beam in water, results show that the developed method has the ability to calculate dynamic responses with high precision when solving FSI problems, which implies a potential application in ocean engineering.

Efficient FSI solvers for multiple-degrees-of-freedom flow-induced vibration of a rigid body

Flow-induced vibration (FIV) of a bluff body is a complex fluid-structure interaction (FSI) problem, for which analytical solutions generally don’t exist. Therefore, such problems generally need to be examined with experimental methods or computational simulations. Researchers have developed various numerical methodologies to solve FSI problems using either conforming or non-conforming grid methods. However, these methods are not always ideal for flow-induced vibration problems, as they can be computationally expensive or generate low accuracy solutions, especially for the cases with large body displacements. FIV problems often require long simulation times because, for a given parameter set, the transient flow solution time can be long and generally at least 10 oscillation cycles are required to simulate the representative long term behaviour. Thus, to gain a clear understanding and enhance knowledge of FIV of a bluff body, it is advantageous to have an efficient numerical methodology. We have developed two efficient fully-coupled FSI solvers to accurately predict the FIV of an elastically mounted bluff body and a tethered bluff body. These FSI solvers were developed based on the widely used open-source CFD package OpenFOAM. In these solvers, the fluid flow was modelled in a reference frame attached to the centre of mass of the solid body, so that a non-deforming grid can be employed. A predictor-corrector iterative method was used to enable strong coupling between the solid motion and the fluid flow. Each of the FSI solvers was validated against previously reported investigations. While efficient, the limitation of these FSI solvers is that they can only be used to examine the nature of FIV of a single, rigid bluff body.

Study on the Pressure Characteristics of Shock Wave Propagating across Multilayer Structures during Underwater Explosion

The propagation of the shock wave across multilayer structures during underwater explosion is a very complex physical phenomenon, involving violent fluid-structure interaction (FSI) problems. In this paper, the coupled Eulerian–Lagrangian (CEL) method in AUTODYN is used to simulate the process of shock wave propagation and solve FSI problems. Firstly, the governing equation and the treatment of fluid and structure interface of the CEL method are briefly reviewed. Afterwards, two underwater explosion numerical models are established, and the results are compared with the empirical formula and experimental data, respectively, to verify the reliability of numerical solutions. The results obtained by this method show good agreements with those of the empirical formula and experiment. Furthermore, the model of the multilayer structures composed of two hemispherical shells and the fluid filled between the shells subjected to underwater explosion is established, and the pressure characteristics of the shock wave propagating across the multilayer structures are analyzed regarding the wave reflection and transmission. Finally, the effects of the shell thickness and the filled fluid type among the multilayer structures on the wave reflection and transmission are studied.

An Immersed Boundary Proper Generalized Decomposition (IB-PGD) for Fluid–Structure Interaction Problems

Proper generalized decomposition (PGD), a method looking for solutions in separated forms, was proposed recently for solving highly multidimensional problems. In the PGD, the unknown fields are constructed using separated representations, so that the computational complexity scales linearly with the dimension of the model space instead of exponential scaling as in standard grid-based methods. The PGD was proven to be effective, reliable and robust for some simple benchmark fluid–structure interaction (FSI) problems. However, it is very hard or even impossible for the PGD to find the solution of problems having complex boundary shapes (i.e., problems of fluid flow with arbitrary complex geometry obstacles). The paper hence further extends the PGD to solve FSI problems with arbitrary boundaries by combining the PGD with the immersed boundary method (IBM) to give a so-called immersed boundary proper generalized decomposition (IB-PGD). In the IB-PGD, a forcing term constructed by the IBM is introduced to Navier–Stokes equations to handle the influence of the boundaries and the fluid flow. The IB-PGD is then applied to solve Poisson’s equation to find the fluid pressure distribution for each time step. The numerical results for three problems are presented and compared to those of previous publications to illustrate the robustness and effectiveness of the IB-PGD in solving complex FSI problems.

A moving-grid approach for fluid–structure interaction problems with hybrid lattice Boltzmann method

In this paper, we propose a hybrid lattice Boltzmann method (HLBM) for solving fluid–structure interaction problems. The proposed numerical approach is applied to model the flow induced by a vibrating thin lamina submerged in a viscous quiescent fluid. The hydrodynamic force exerted by the fluid on the solid body is described by means of a complex hydrodynamic function, whose real and imaginary parts are determined via parametric analysis. Numerical results are validated by comparison with those from other numerical as well as experimental works available in the literature. The proposed hybrid approach enhances the capability of lattice Boltzmann methods to solve fluid dynamic problems involving moving geometries.

A continuous energy-based immersed boundary method for elastic shells

The immersed boundary method is a mathematical formulation and numerical method for solving fluid–structure interaction problems. For many biological problems, such as models that include the cell membrane, the immersed structure is a two-dimensional infinitely thin elastic shell immersed in an incompressible viscous fluid. When the shell is modeled as a hyperelastic material, forces can be computed by taking the variational derivative of an energy density functional. A new method for computing a continuous force function on the entire surface of the shell is presented here. The new method is compared to a previous formulation where the surface and energy functional are discretized before forces are computed. For the case of Stokes flow, a method for computing quadrature weights is provided to ensure the integral of the elastic spread force density remains zero throughout a dynamic simulation. Tests on the method are conducted and show that it yields more accurate force computations than previous formulations as well as more accurate geometric information such as mean curvature. The method is then applied to a model of a red blood cell in capillary flow and a 3D model of cellular blebbing.

A Higher-Order Discontinuous Galerkin/Arbitrary Lagrangian Eulerian Partitioned Approach to Solving Fluid–Structure Interaction Problems with Incompressible, Viscous Fluids and Elastic Structures

This manuscript presents a discontinuous Galerkin-based numerical method for solving fluid–structure interaction problems involving incompressible, viscous fluids. The fluid and structure are fully coupled via two sets of coupling conditions. The numerical approach is based on a high-order discontinuous Galerkin (with Interior Penalty) method, which is combined with the Arbitrary Lagrangian–Eulerian approach to deal with the motion of the fluid domain, which is not known a priori. Two strongly coupled partitioned schemes are considered to resolve the interaction between fluid and structure: the Dirichlet–Neumann and the Robin–Neumann schemes. The proposed numerical method is tested on a series of benchmark problems, and is applied to a fluid–structure interaction problem describing the flow of blood in a patient-specific aortic abdominal aneurysm before and after the insertion of a prosthesis known as stent graft. The proposed numerical approach provides sharp resolution of jump discontinuities in the pressure and normal stress across fluid–structure and structure–structure interfaces. It also provides a unified framework for solving fluid–structure interaction problems involving nonlinear structures, which may develop shock wave solutions that can be resolved using a unified discontinuous Galerkin-based approach.