Frontiers in Computational Fluid-Structure Interaction and Flow Simulation

We present a novel formulation based on an immersed coupling of Isogeometric Analysis (IGA) and Peridynamics (PD) for the simulation of fluid–structure interaction (FSI) phenomena for air blast. We aim to develop a practical computational framework that is capable of capturing the mechanics of air blast coupled to solids and structures that undergo large, inelastic deformations with damage and fragmentation. The interaction between fluid and solid is modeled in two different ways, i.e., using strong and weak (penalty-based) coupling. It is shown that using a simple volumetric penalty technique enables effective handling of the solid fracture and fragmentation. Several numerical examples of ductile and brittle solids under blast loading scenarios, including point-charge detonation on 3D concrete slabs using an M7 Microplane constitutive material model, are provided to clearly illustrate the power and robustness of the proposed air-blast FSI framework.

This chapter presents three applications of computational fluid-structure interaction (CFSI) in the field of turbomachinery. We explore novel designs for morphing blades that adapt to changes in flow direction, focusing on small-size reversible fans and turbines. The model framework is based on the finite element formulations of fluid dynamics, structural mechanics, and mesh moving equations, while a block-iterative approach is used for the FSI coupling. We conduct first a 2D study of a reversible fan cascade made of low-stiffness material. The goal is to achieve a stable passive change in airfoil curvature in response to the aerodynamic forces. A similar design solution is then investigated for a Wells type turbine. A 2D cascade study verifies the feasibility of the concept and explores the use of different material layouts. Then, we test the 3D blade under time-dependent flow rate conditions, simulating operation of the turbine in an oscillating water column facility for sea wave energy conversion. In all cases, the results show that using CFSI provides useful insight into the functioning of these devices.

We show that the second-order accurate generalized-\(\alpha \) method on a uniform temporal mesh may be viewed as an implicit midpoint method on a shifted temporal mesh. With this insight, we demonstrate generalized-\(\alpha \) time integration of a finite element spatial discretization of a conservation law system results in a fully-discrete method admitting discrete balance laws when (i) the time integration is second-order accurate, (ii) a uniform temporal mesh is employed, (iii) the spatial discretization is conservative, and (iv) conservation variables are discretized.

Fluid flows with moving boundaries are ubiquitous and have been widely studied, but they continue to pose challenges for computational methods. Phase-field models have unique advantages for moving-interface flow simulations emerging in phase separation, multiphase flow, phase transition, and more. In this work, we illustrate the potential of the phase-field approach by presenting a derivation and a discretization scheme for three state-of-the-art phase-field models, namely, the Navier-Stokes-Cahn-Hilliard model for fluid flow of two immiscible components, the thermally-coupled Navier-Stokes-Korteweg model for liquid-vapor phase transition of a single fluid component, and a dewetting model for the evolution of ultrathin liquid films on a solid substrates. For each model, we start with universal conservation laws and complete the model derivation by invoking the Coleman-Noll argument. Next, numerical methods, including isogeometric analysis for spatial discretization and the generalized-\(\alpha \) method for temporal discretization, are briefly discussed. Finally, flow simulations are presented to showcase the capabilities of these phase-field models.

In this chapter, we present a recently proposed approach for performing multiphysics analysis using immersogeometric analysis (IMGA) on complex geometries represented by point clouds. Point cloud objects are represented by unstructured points in Euclidean space with orientation information. However, due to the absence of topological information, there are no guarantees for the geometric representation to be watertight or 2-manifold or to have consistent normals. This chapter provides the mathematical foundations of IMGA and introduces a method for estimating inside-outside information and surface normals directly from point clouds. Additionally, a technique is presented for computing the Jacobian determinant for surface integration over the point cloud, enabling the weak enforcement of Dirichlet boundary conditions. The proposed approach is tested on benchmark problems with a wide range of Reynolds and Mach numbers, demonstrating its robustness and accuracy. Furthermore, the framework is applied to a large industrial-scale construction vehicle represented by a point cloud containing over 12 million points, highlighting its applicability to real-world problems. This novel method provides a more flexible and direct approach for performing CFD simulations using complex geometric information, eliminating the need for well-defined B-rep CAD models.

Valvular heart disease has recently become an increasing public health concern due to the high prevalence of valve degeneration in aging populations. For high-risk patients, bioprosthetic valve replacement through percutaneous procedures offers a minimally invasive option for treatment. However, the use of thinner, more flexible biological tissues in these valves can induce leaflet flutter during the cardiac cycle, which may lead to cardiovascular dysfunction and reduced valve durability. While previous studies have observed this phenomenon, the mechanics underlying leaflet flutter are not well understood. This chapter reviews two of the author’s recent computational studies of heart valve leaflet flutter in bioprosthetic tissues. Both investigations utilized high-fidelity computational methods to model aortic valve implants and isolate leaflet flutter phenomena and the fundamental mechanics that contribute to leaflet flutter. The results indicate that thinner tissues induce flutter in heart valve leaflets, and reduced flexural stiffness is the primary factor that induces flutter in these biological tissues. These studies provide essential knowledge about leaflet flutter and offer significant insight into possible developments in the design of bioprosthetic heart valves.

In this chapter, we review some recent work on adapting code generation technology from finite element (FE) methods to isogeometric and immersed analysis methods, which are useful both for fluid–structure interaction (FSI) anlaysis and within each of its fluid and structure subproblems. We cover several related implementations of isogeometric and/or immersed numerical methods based on the FEniCS Project toolchain for FE automation, and highlight some interesting applications of these implementations from the literature, including FSI analysis of heart valves, coupling between isogeometric discretizations of separately-parameterized components in aerospace shell structures, and immersogeometric analysis of shell structures whose geometries are defined by trimming rectangular spline patches. We also discuss ongoing research, future directions, and the potential for code generation technology (and its union with emerging numerical methods beyond FE analysis) to transform education in fields involving partial differential equations.

In this chapter, we present a numerical formulation for modelling multi-phase, multi-fluid flows over complex marine devices. The set of equations governing the fluid flow consists of the Navier–Stokes equations together with a transport equation governing the vapor volume fraction evolution in the computational domain, and a conservation equation of a geometric function, namely, the signed-distance-function describing the air-water interface in the context of the level-set method. For applications on moving marine devices, we adopt an Arbitrary-Lagrangian-Eulerian (ALE) description of the continuum where domain motions occur independently of the fluid flow. Moreover, the variational multi-scale (VMS) method is used for turbulence modelling resulting in the so-called ALE-VMS formulation. The formulation is first used for investigating the performance of vertical-axis hydrokinetic turbines installed in in-line arrays in a pure hydrodynamic flow. Second, as a proof of concept, the multi-phase modelling capabilities and the stability of the numerical solver are tested in a simulation of a hydrokinetic turbine under severe cavitation conditions. Finally, we investigate the effect of a free surface on the performance of hydrokinetic turbines and the effects of having different blade-strut configurations.

We are presenting a multiscale space–time (ST) isogeometric analysis framework for car and tire aerodynamics with road contact and tire deformation. It is a framework of full-domain computation to high-resolution tire-domain computations. The geometries of the computational models for the car body and tires are close to the actual geometries. The computational challenges include (i) the complexities of these geometries, (ii) the tire rotation, (iii) maintaining accurate representation of the boundary layers near the tire while being able to deal with the flow-domain topology change created by the road contact, (iv) the turbulent nature of the flow, (v) the aerodynamic interaction between the car body and the tires, (vi) NURBS mesh generation for the complex geometries, and (vii) the need for high-resolution flow representation around the tires. The computational framework is made of the ST Variational Multiscale method, ST Slip Interface and ST Topology Change methods, ST Isogeometric Analysis (ST-IGA), integrated combinations of these ST methods, methods for calculating the stabilization parameters and related element lengths targeting IGA discretization, element-based mesh relaxation, Complex-Geometry IGA Mesh Generation method, NURBS Surface-to-Volume Guided Mesh Generation method, Multidomain Method (MDM), and the “ST-C” data compression. We first carry out a global computation with near-actual car body and tire geometries, using a reasonable mesh resolution. That is followed by a high-resolution local computation for the left tires, in a nested MDM sequence over three subdomains. The high resolution is in both space and time. The first subdomain has the front tire. The second subdomain, with the inflow velocity from the first subdomain, is for the front-tire wake flow. The third subdomain, with the inflow velocity from the second subdomain, has the rear tire. All other boundary conditions for the three subdomains are extracted from the global computation. The car and tire aerodynamics computations we present show the effectiveness of the computational framework we have built for this class of problems, including high-resolution analysis around the tires.

Modeling of structural damage, fracture, and disintegration into fragments due to blast loads, is a fluid–structure interaction (FSI) problem of great significance due to its relevance to national security and defense applications. However, its numerical modeling remains challenging due to the presence of underlying complex physics, such as high Mach and Reynolds numbers, large inelastic structural deformations, fracture and fragmentation, and very rapid transients. In this book chapter we summarize recent developments in modeling air-blast–structure interaction (ABSI) using an immersed approach, in which the fluid is modeled in a background Eulerian domain and the solid is discretized with Lagrangian particles. The immersed nature of the framework leads to an a-priori monolithic FSI formulation with intrinsic contact detection between solid objects, and without formal restrictions on the solid motions. The background computational domain is discretized with isogeometric shape functions and exploits the higher order accuracy and smoothness of the method. Finally, the approach is enhanced with a recently-developed hyperbolic phase field model of brittle fracture that is solved on the foreground particles with the reproducing kernel particle method (RKPM). The framework is verified and validated against published literature and a few challenging “capabilities-demonstration” problems are presented towards the end.

Flow computations with semi-discrete and space–time (ST) methods have been relying on, as core methods, variational multiscale methods and, more generally, stabilized methods. As needed, these methods are supplemented with discontinuity-capturing (DC) methods. Most of these methods have some embedded stabilization and DC parameters. These parameters play an important role and need to be defined carefully. Many well-performing parameters have been introduced over the years in both the semi-discrete and ST contexts. The parameters almost always involve some element length expressions, most of the time in specific directions, such as the direction of the flow or solution gradient. Until recently, stabilization and DC parameters originally intended for finite element discretization were being used also for isogeometric discretization. In late 2017, element lengths and stabilization and DC parameters targeting isogeometric discretization were introduced for ST and semi-discrete computations, and they are of course also applicable to finite element discretization. The key stages of deriving the direction-dependent element length expression were mapping the direction vector from the physical (ST or space-only) element to the parent element in the parametric space, accounting for the discretization spacing along each of the parametric coordinates, and mapping what has been obtained back to the physical element. In late 2019, targeting B-spline meshes for complex geometries, new element length expressions, which are outcome of a clear and convincing derivation and more suitable for element-level evaluation, were introduced. The new expressions are based on a preferred parametric space and a transformation tensor that represents the relationship between the integration and preferred parametric spaces. In this chapter, we provide an overview of these new element length expressions and the test computations performed with them. The test computations, which include advection-dominated problems in 2D and aerodynamics of a tsunami-shelter vertical-axis wind turbine, show that the new element length expressions result in good solution profiles and can be used in complex-geometry flow computations.

In this chapter on a hyperelastic extended Kirchhoff–Love shell model with out-of-plane normal stress, we present the derivation of the new model, with focus on the mechanics of the out-of-plane deformation. Accounting for the out-of-plane normal stress distribution in the out-of-plane direction affects the accuracy in calculating the deformed-configuration out-of-plane position, and consequently the nonlinear response of the shell. The improvement is beyond what we get from accounting for the out-of-plane deformation mapping. By accounting for the out-of-plane normal stress, the traction acting on the shell can be specified on the upper and lower surfaces separately. With that, the new model is free from the “midsurface” location in terms of specifying the traction. We also present derivations related to the variation of the kinetic energy and the form of specifying the traction and moment acting on the upper and lower surfaces and along the edges. We present test computations for unidirectional plate bending. We use the neo-Hookean and Fung’s material models, for the compressible- and incompressible-material cases, and with the out-of-plane normal stress and without, which is the plane-stress case.

We present an overview our computational framework for heart valve flow analysis with boundary layer and leaflet contact representation. The challenge of representing the contact between the leaflets without giving up on high-resolution flow representation near the leaflet surfaces has been overcome. This challenge and other challenges encountered in heart valve computational flow analysis are mainly addressed with a space–time (ST) method that integrates three special ST methods around the core, ST Variational Multiscale (ST-VMS) method. The three special methods are the ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods and ST Isogeometric Analysis (ST-IGA). The ST-discretization feature of the integrated method, ST-SI-TC-IGA, provides higher-order accuracy compared to standard discretization methods. The VMS feature addresses the computational challenges associated with the multiscale nature of the unsteady flow. The moving-mesh feature of the ST context enables high-resolution computation near the leaflets. The ST-TC enables moving-mesh computation even with the topology change created by the contact between the leaflets, dealing with the contact while maintaining high-resolution representation near the leaflets. The ST-IGA provides smoother representation of the valve and artery surfaces and increased accuracy in the flow solution. The ST-SI connects the mesh zones containing the leaflets, enabling a more effective mesh moving, helps the ST-TC deal with leaflet–leaflet contact location change and contact sliding, and helps the ST-TC and ST-IGA keep the element density in the narrow spaces near the contact areas at a reasonable level. The ST-SI-TC-IGA is supplemented with the Constrained-Flow-Profile (CFP) Traction, a method that provides flow stability at the inflow boundary when we have a traction boundary condition there. We present test computations with the CFP Traction to show its effectiveness as an inflow stabilization method. To show the effectiveness of our computational framework, we present flow computations for a bioprosthetic heart valve, at two time-step sizes and two IGA mesh resolutions, with the higher-resolution mesh being a T-splines mesh.

This chapter reviews the work conducted by our team on scan-based immersed isogeometric analysis for flow problems. To leverage the advantageous properties of isogeometric analysis on complex scan-based domains, various innovations have been made: (i) A spline-based segmentation strategy has been developed to extract a geometry suitable for immersed analysis directly from scan data; (ii) A stabilized equal-order velocity-pressure formulation for the Stokes problem has been proposed to attain stable results on immersed domains; (iii) An adaptive integration quadrature procedure has been developed to improve computational efficiency; (iv) A mesh refinement strategy has been developed to capture small features at a priori unknown locations, without drastically increasing the computational cost of the scan-based analysis workflow. We review the key ideas behind each of these innovations, and illustrate these using a selection of simulation results from our work. A patient-specific scan-based analysis case is reproduced to illustrate how these innovations enable the simulation of flow problems on complex scan data.

In this chapter, we present a workflow for Isogeometric Analysis (IGA) that incorporates an advanced mesh generation method Otoguro et al. (Comput Fluids 158:189–200, 2017). The process is flexible and can be easily adjusted to accommodate challenging applications in computational mechanics. In addition, IGA is compared to the finite element (FE) method in terms of accuracy per degree-of-freedom in structural vibrations. The results obtained demonstrate that the use of NURBS meshes leads to faster convergence and higher accuracy compared to linear and quadratic FE meshes. A clearly defined workflow for mesh generation and significant advantages of IGA over FE in terms of per-degree-of-freedom accuracy make IGA more accessible, reliable, and attractive in applications of both academic and industrial interest. We note that the accuracy of a structural mechanics discretization, which may be assessed through eigenfrequency analysis, plays an important role in the overall accuracy of fluid–structure interaction computations.

Thermal multi-phase flow simulations are indispensable to understanding the multi-scale and multi-physics phenomena in metal additive manufacturing (AM) processes, yet accurate and robust predictions remain challenging. This book chapter summarizes the recent method development by Yan, Zhu, and Zhao at University of Illinois Urbana-Champaign Champaign for simulating thermal multi-phase flows in laser powder bed fusion (LPBF) and directed energy deposition (DED) processes. Two main method developments are discussed. The first is a mixed interface-capturing/interface-tracking computational framework aiming to explicitly treat the gas-metal interface without mesh motion/re-meshing. The second is a physics-based and non-empirical deposit geometry model for DED processes. The proposed framework’s accuracy is assessed by thoroughly comparing the simulated results against experimental measurements on various quantities. We also report critical quantities that experiments can not measure to show the predictive capability of the developed methods.