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 integration. The velocity reconstruction problem is transformed to a scalar Poisson equation that is discretized with conservative finite differences, and solved using an FFT-accelerated iterative algorithm. The use of conservative differencing throughout leads to exact enforcement of a discrete Kelvin's theorem, which provides the key to simulations with multiply connected domains and outflow boundaries. The method achieves second order spatial accuracy and third order temporal accuracy, and is validated on a variety of 2D flows in internal and free-space domains.
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…
The present paper is devoted to implementation of the immersed boundary technique into the Fourier pseudo-spectral solution of the vorticity-velocity formulation of the two-dimensional incompressible Navier--Stokes equations. The immersed boundary conditions are implemented via direct modification of the convection and diffusion terms, and therefore, in contrast to many other similar methods, there is not an explicit external forcing function in the present formulation. The desired immersed boundary conditions are approximated on some regular grid points, using different orders (up to second-o…
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…
Numerical simulations show that microscopic rod-like bodies suspended in a turbulent flow tend to align with the vorticity vector, rather than with the dominant eignevector of the strain-rate tensor. This paper investigates an analytically solvable limit of a model for alignment in a random velocity field with isotropic statistics. The vorticity varies very slowly and the isotropic random flow is equivalent to a pure strain with statistics which are axisymmetric about the direction of the vorticity. We analyse the alignment in a weakly fluctuating uniaxial strain field, as a function of the pr…
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,…
Deformable bodies in a 3-dimensional viscous flow: Vorticity-Stream vector formulation
Center for Interdisciplinary Research in Biology (CIRB), Collège de France, CNRS, Inserm, Université PSL（跨学科生物研究中心，法兰西学院，法国国家科学研究中心，法国国家健康与医学研究院，巴黎文理研究大学）；Facultat de Física, Universitat de Barcelona（巴塞罗那大学物理学院）；Instituto de Investigación Tecnológica (IIT) and Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Pontificia Comillas（技术研究所和复杂系统跨学科小组，科米利亚斯宗座大学）；Institute of Nanoscience and Nanotechnology (IN2UB)（纳米科学与技术研究所）
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 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…
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 a fully Eulerian solver for the study of multiphase flows for simulating the propagation of surface gravity waves over submerged bodies is presented. We solve the incompressible Navier-Stokes equations coupled with the volume of fluid technique for the modeling of the liquid phases with the interface, an immersed body method for the solid bodies and an iterative strong-coupling procedure for the fluid-structure interaction. The flow incompressibility is enforced via the solution of a Poisson equation which, owing to the density jump across the interfaces of the liquid phases, has…
Deformable elastic bodies in viscous and viscoelastic media constitute a large portion of synthetic and biological complex fluids. We present a parallelized 3D-simulation methodology which fully resolves the momentum balance in the solid and fluid domains. An immersed boundary algorithm is exploited known as the immersed finite element method (IFEM) which accurately determines the internal forces in the solid domain. The scheme utilized has the advantages of requiring no costly re-meshing, handling finite Reynold's number, as well as incorporating non-linear viscoelasticity in the fluid domain…
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…
In this paper we show and discuss the use of a versatile interaction potential approach coupled with an immersed boundary method to simulate a variety of flows involving deformable bodies. In particular, we focus on two kinds of problems, namely (i) deformation of liquid-liquid interfaces and (ii) flow in the left ventricle of the heart with either a mechanical or a natural valve. Both examples have in common the two-way interaction of the flow with a deformable interface or a membrane. The interaction potential approach (de Tullio & Pascazio, Jou. Comp. Phys., 2016; Tanaka, Wada and Nakamura,…
This work investigated the vorticity dynamics and stability of leading-edge vortices (LEVs) in revolving wings. Previous studies suggested that Coriolis acceleration and spanwise flow both played key roles in stabilizing the LEV; however, the exact mechanism remains unclear. The current study examined a mechanism that relates the effects of Coriolis acceleration, spanwise flow, and the tilting of the planetary vortex on limiting the growth of the LEV. Specifically, this mechanism states that a vertical gradient in spanwise flow can create a vertical gradient in Coriolis acceleration, which wil…
IB-Flows: an open-source multi-GPU immersed boundary code for fluid-structure interaction
Gran Sasso Science Institute (GSSI)（格兰萨索科学研究所）；INFN–Laboratori Nazionali del Gran Sasso（意大利国家核物理研究所-格兰萨索国家实验室）；Department of Physics and INFN, University of Rome, Tor Vergata（罗马托尔维加塔大学物理系及意大利国家核物理研究所）；NVIDIA Corporation（英伟达公司）；Physics of Fluids Group, University of Twente（特温特大学流体力学组）
We study the secondary time-averaged flow (streaming) generated by an oscillating cylinder immersed within a fluid, under high amplitude forcing so that inertial effects are significant. This streaming is decomposed into a viscous boundary layer flow where vorticity is created, and an outer flow of larger size. We operate under conditions of relatively low viscosity, so that the boundary layer is smaller than the object diameter. While for low Keulegan-Carpenter (KC) number (small enough amplitude), the size of the outer flow is typically that of the object, here we show that at large enough f…
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…
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…
We consider a coexistence of two axisymmetric liquid bridges LB_i and LB_m of two immiscible liquids i and m which are immersed in a third liquid (or gas) e and trapped between two smooth solid bodies with axisymmetric surfaces S_1,S_2 and free contact lines. Evolution of liquid bridges allows two different configurations of LB_i and LB_m with multiple (five or three) interfaces of non-smooth shape. We formulate a variational problem with volume constraints and present its governing equations supplemented by boundary conditions. We find a universal relationship between curvature of the interfa…
Viscous streaming refers to the rectified, steady flows that emerge when a liquid oscillates around an immersed microfeature, typically a solid body or a bubble. The ability of such features to locally concentrate stresses produces strong inertial effects to which both fluid and immersed particles respond within short length (O(100) microns) and time (milliseconds) scales, rendering viscous streaming arguably the most efficient mechanism to exploit inertia at the microscale. Despite this potential, viscous streaming has been investigated in rather narrow conditions, mostly making use of bodies…
Development of mass-source function based numerical wave tank (NWT) algorithms in the Navier-Stokes (NSE) framework is impeded by multiple design issues such as: (a) optimization of a number of variables characterizing the source region, (b) wave-vorticity interactions and (c) a mandatory requirement of modeling the domain on both sides of the wavemaker. In this paper, we circumvent these hurdles by proposing a volume-preserving inflow-boundary based Navier-Stokes wave tank. Wave generation and propagation is modeled in a two-phase PLIC-VOF set-up. Near-exact volume preservation is achieved (a…
The fluid structure interaction of cylinders in tandem arrangement is used as validation basis of a multi-domain Lagrangian-Eulerian hybrid flow solver. In this hybrid combination, separate grids of limited width are defined around every solid body, on which the Eulerian flow equations are solved using finite volume approximations. In order to interconnect the domains defined by the grids, the entire flow is described in Lagrangian coordinates and the corresponding equations are solved via particle approximations in fully coupled mode with the solutions within the Eulerian grids. The flow solv…
Potential flow has many applications, including the modelling of unsteady flows in aerodynamics. For these models to work efficiently, it is best to avoid Biot-Savart interactions. This work presents a grid-based treatment of potential flows in two dimensions and its use in a vortex model for simulating unsteady aerodynamic flows. For flows consisting of vortex elements, the treatment follows the vortex-in-cell approach and solves the streamfunction-vorticity Poisson equation on a Cartesian grid after transferring the circulation from the vortices onto the grid. For sources and sinks, an analo…
Stokes drift has been as central to the history of wave theory as it has been distressingly absent from experiment. Neither wave tanks nor experiments in open bodies detect this without nearly canceling "eulerian flows." Acoustic waves have an analogous problem that is particularly problematic in the vorticity production at the edges of beams. Here we demonstrate that the explanation for this arises from subtle end-of-packet and wavetrain gradient effects such as microbreaking events and wave-flow decomposition subtleties required to conserve mass and momentum and avoid fictitious external for…
