We present an immersed boundary projection method formulated in a body-fixed frame of reference for flow-structure interaction (FSI) problems involving rigid bodies with complex geometries. The body-fixed formulation is aimed at maximizing the accuracy of surface stresses on the FSI body (the target) on during spatial and temporal discretization. The incompressible vorticity equations and Newton's equations of motion are coupled implicitly so that the method remains stable for low solid-to-fluid mass ratios. The influence of fictitious fluid inside the rigid bodies is considered and the spurious oscillations in surface stresses are filtered to impose physically correct rigid body dynamics. Similar to many predecessors of the immersed boundary projection method, the resulting discrete system is solved efficiently using a block-LU decomposition. We then validate the method with two-dimensional test problems of a neutrally buoyant cylinder migrating in a planar Couette flow and a freely falling or rising cylindrical rigid body.
We present an immersed interface method for the vorticity-velocity form of the 2D Navier Stokes equations that directly addresses challenges posed by multiply connected domains, nonconvex obstacles, and the calculation of force distributions on immersed surfaces. The immersed interface method is re-interpreted as a polynomial extrapolation of flow quantities and boundary conditions into the obstacle, reducing its computational and implementation complexity. In the flow, the vorticity transport equation is discretized using a conservative finite difference scheme and explicit Runge-Kutta time i…
Dispersion of low-density rigid particles with complex geometries is ubiquitous in both natural and industrial environments. We show that while explicit methods for coupling the incompressible Navier-Stokes equations and Newton's equations of motion are often sufficient to solve for the motion of cylindrical particles with low density ratios, for more complex particles - such as a body with a protrusion - they become unstable. We present an implicit formulation of the coupling between rigid body dynamics and fluid dynamics within the framework of the immersed boundary projection method. Simila…
This work outlines a new multi-physics-compatible immersed rigid body method for Eulerian finite-volume simulations. To achieve this, rigid bodies are represented as a diffuse scalar field and an interface seeding method is employed to mediate the interface boundary conditions. The method is based on an existing multi-material diffuse interface method that is capable of handling an arbitrary mixture of fluids and elastoplastic solids. The underlying method is general and can be extended to a range of different applications including high-strain rate deformation in elastoplastic solids and reac…
This paper presents a novel particle method to compute strongly coupled incompressible fluid and rigid bodies. The method adopts a velocity-based formulation and utilizes the linear complementarity problem for the incompressibility constraint. Since all the constraints for incompressibility, inter-rigid-body contacts, and interaction between incompressible fluid and rigid bodies are mathematically compatible, strongly coupled simulation is achieved using the method, where the shapes of the rigid bodies are represented by particles as well. The abstract concept of velocity-based constraints is …
Fluctuating hydrodynamics based techniques have been developed in recent years for the simulation of Brownian motion of particles. These mesoscale simulation tools are viable approaches for problems where molecular dynamics simulations may be deemed expensive. We have developed a rigid constraint-based formulation where the key idea is to assume that the entire domain is a fluctuating fluid. Rigid motion constraints are then imposed in regions that are occupied by rigid particles. The resulting solution gives the Brownian motion of the particles. This approach is shown to be viable for the sim…
We consider the free fall of slender rigid bodies in a viscous incompressible fluid. We show that the dimensional reduction (DR), performed by substituting the slender bodies with one-dimensional rigid objects, together with a hyperviscous regularization (HR) of the Navier--Stokes equation for the three-dimensional fluid lead to a well-posed fluid-structure interaction problem. In contrast to what can be achieved within a classical framework, the hyperviscous term permits a sound definition of the viscous force acting on the one-dimensional immersed body. Those results show that the DR/HR proc…
The dynamics of a molecule immersed in a superfluid medium are considered. Results are derived using a classical hydrodynamic approach followed by canonical quantization. The classical model, a rigid body immersed in incompressible fluid, permits a thorough analysis; its effective Hamiltonian generalizes the usual rigid-rotor Hamiltonian. In contrast to the free rigid rotor, the immersed body is shown to have chaotic dynamics. Quantization of the classical model leads to new and experimentally verifiable features. It is shown, for instance, that chiral molecules can behave as "quantum propelle…
A new formulation of the immersed boundary method, which facilitates accurate simulation of incompressible isothermal and natural convection flows around immersed bodies and which may be applied for accurate linear stability analysis of the flows, is presented. The method is based on the fully pressure-velocity coupled approach, implicitly satisfying the divergence-free velocity constraint with no need for an extra projection-correction step, which is a significant advantage for the computational efficiency. The method treats pressure, boundary forces, and heat sources as Lagrange multipliers,…
The analytical theories derived here for the acoustic load impedance measured by a quartz crystal microbalance (QCM), due to the presence of layers of different types (rigid, elastic and viscous) immersed in a fluid, display generic properties, such as "vanishing mass" and positive frequency shifts, which have been observed in QCM experiments with soft-matter systems. These phenomena seem to contradict the well-known Sauerbrey relation at the heart of many QCM measurements, but here we show that they arise as a natural consequence of hydrodynamics. We compare our one-dimensional immersed plate…
We present a new higher-order accurate finite difference explicit jump Immersed Interface Method (HEJIIM) for solving two-dimensional elliptic problems with singular source and discontinuous coefficients in the irregular region on a compact Cartesian mesh. We propose a new strategy for discretizing the solution at irregular points on a nine point compact stencil such that the higher-order compactness is maintained throughout the whole computational domain. The scheme is employed to solve four problems embedded with circular and star shaped interfaces in a rectangular region having analytical s…
In the present study, a discrete forcing Immersed Boundary Method (IBM) is proposed for the numerical simulation of high-speed flow problems including heat exchange. The flow field is governed by the compressible Navier-Stokes equations, which are resolved by using the open source library OpenFOAM. The numerical solver is modified to include source terms in the momentum equation and in the energy equation, which account for the presence of the immersed body. The method is validated on some benchmark test cases dealing with forced convection problems and moving immersed bodies. The results obta…
We report on a series of fully resolved simulations of the flow around a rigid sphere translating steadily near a wall, either in a fluid at rest or in the presence of a uniform shear. Non-rotating and freely rotating spheres subject to a torque-free condition are both considered to evaluate the importance of spin-induced effects. The separation distance between the sphere and wall is varied from values at which the wall influence is weak down to gaps of half the sphere radius. The Reynolds number based on the sphere diameter and relative velocity with respect to the ambient fluid spans the ra…
We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the Hamiltonian formulation via symplectic reduction from a canonical Hamiltonian system. The reduced system is described by a non-canonical symplectic form, which has previously been derived for a single, circular disk using heavy differential-geometric machinery in an infinite-dimensional setting. In contrast, our derivation makes use of the fact that the dynamics of…
We present a strongly-coupled immersed-boundary method for flow-structure interaction problems involving thin deforming bodies. The method is stable for arbitrary choices of solid-to-fluid mass ratios and for large body motions. As with many strongly-coupled immersed-boundary methods, our method requires the solution of a nonlinear algebraic system at each time step. The system is solved through iteration, where the iterates are obtained by linearizing the system and performing a block LU factorization. This restricts all iterations to small-dimensional subsystems that scale with the number of…
Recent experiments showed that standing acoustic waves could be exploited to induce self-propulsion of rigid metallic particles in the direction perpendicular to the acoustic wave. We propose in this paper a physical mechanism for these observations based on the interplay between inertial forces in the fluid and the geometrical asymmetry of the particle shape. We consider an axisymmetric rigid near-sphere oscillating in a quiescent fluid along a direction perpendicular to its symmetry axis. The kinematics of oscillations can be either prescribed or can result dynamically from the presence of a…
Strongly coupled immersed boundary (IB) methods solve the nonlinear fluid and structural equations of motion simultaneously for strongly enforcing the no-slip constraint on the body. Handling this constraint requires solving several large dimensional systems that scale by the number of grid points in the flow domain even though the nonlinear constraints scale only by the small number of points used to represent the fluid-structure interface. These costly large scale operations for determining only a small number of unknowns at the interface creates a bottleneck to efficiently time-advancing st…
In this paper we study the two dimensional motion of three linked rigid bodies moving through a fluid. The bodies change their orientation relative to each other in a way which mimics the swimming of fish. In contrast to previous simulations the bodies are connected by an elastic skin. The skin responds to the movement of the bodies and the pressure of the fluid and alters the flow around the bodies. In particular it prevents fluid moving between them. The system of bodies and skin is similar in appearance to a swimming leech or tadpole depending on the relative size of the bodies. We simulate…
An extended immersed boundary method utilizing a semi-implicit direct forcing approach for the simulation of confined incompressible viscous thermal flow problems is presented. The method utilizes a Schur complement approach to enforce the kinematic constraints of no-slip and the corresponding thermal boundary conditions for immersed surfaces. The developed methodology can be straightforwardly adapted to any existing incompressible time marching solver based on a segregated pressure-velocity coupling. The method accurately meets the thermal and the no-slip boundary conditions on the surfaces o…
This paper explores the fluid-elastic response of a cantilevered flexible sheet in the presence of uniform airflow. The leading edge of the sheet is clamped, while at the trailing edge, in-plane tension is applied to provide additional rigidity to the sheet's small but finite bending stiffness. We outline a series of experiments performed in a wind tunnel with the purpose of examining fluid-elastic instabilities. In particular, we examine the role of in-plane tension induced rigidity and how it influences static divergence and convected wave instabilities. The flow is characterised by Reynolds…
In this work, a dynamic-Immersed--Boundary method combined with a BGK-Lattice--Boltzmann technique is developed and critically discussed. The fluid evolution is obtained on a three-dimensional lattice with 19 reticular velocities (D3Q19 computational molecule) while the immersed body surface is modeled as a collection of Lagrangian points responding to an elastic potential and a bending resistance. A moving least squares reconstruction is used to accurately interpolate flow quantities and the forcing field needed to enforce the boundary condition on immersed bodies. The proposed model is widel…
