Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session L7: CFD: Immersed Boundary Method |
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Chair: Tim Colonius, Caltech Room: 107 |
Monday, November 23, 2015 4:05PM - 4:18PM |
L7.00001: A fast lattice Green's function method for solving viscous incompressible flows on unbounded domains Sebastian Liska, Tim Colonius A novel, parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. The method formally discretizes the incompressible Navier-Stokes equations on an infinite staggered Cartesian grid. Operations are limited to a finite computational domain through a lattice Green's function technique. This technique obtains solutions to inhomogeneous difference equations through the discrete convolution of source terms with the fundamental solutions of the discrete operators. The differential algebraic equations describing the temporal evolution of the discrete momentum equation, incompressibility constraint, and the no-slip constraint are numerically solved by combining an integrating factor technique for the viscous term and a half-explicit Runge-Kutta scheme for the convective term. A nested projection that exploits the mimetic and commutativity properties of the discrete operators is used to efficiently solve the system of equations that arises in each stage of the time integration scheme. Linear complexity, fast computation rate, and parallel scalability are achieved using recently developed fast multipole methods for difference equations. Results for three-dimensional test problems are presented, and the performance and scaling of the present implementation are discussed. [Preview Abstract] |
Monday, November 23, 2015 4:18PM - 4:31PM |
L7.00002: Computational Analysis of Flow Field Inside Coral Colony Md Monir Hossain, Anne Staples Development of the flow field inside coral colonies is a key issue for understanding coral natural uptake, photosynthesis and wave dissipation capabilities. But most of the computations and experiments conducted earlier, measured the flow outside the coral reef canopies. Experimental studies are also constrained due to the limitation of measurement techniques and limited environmental conditions. Numerical simulations can be an answer to overcome these shortcomings. In this work, a detailed, three-dimensional simulation of flow around a single coral colony was developed to examine the interaction between coral geometry and hydrodynamics. To simplify grid generation and minimize computational cost, Immersed Boundary method (IBM) was implemented. The computation of IBM involves identification of the interface between the solid body and the fluid, establishment of the grid/interface relation and identification of the forcing points on the grid and distribution of the forcing function on the corresponding points. LES was chosen as the framework to capture the turbulent flow field without requiring extensive modeling. The results presented will give insight into internal coral colony flow fields and the interaction between coral and surrounding ocean hydrodynamics. [Preview Abstract] |
Monday, November 23, 2015 4:31PM - 4:44PM |
L7.00003: A cut-cell immersed boundary technique for fire dynamics simulation Marcos Vanella, Randall McDermott, Glenn Forney Fire simulation around complex geometry is gaining increasing attention in performance based design of fire protection systems, fire-structure interaction and pollutant transport in complex terrains, among others. This presentation will focus on our present effort in improving the capability of FDS (Fire Dynamics Simulator, developed at the Fire Research Division, NIST. https://github.com/firemodels/fds-smv) to represent fire scenarios around complex bodies. Velocities in the vicinity of the bodies are reconstructed using a classical immersed boundary scheme (Fadlun and co-workers, J. Comput. Phys., 161:35-60, 2000). Also, a conservative treatment of scalar transport equations (i.e. for chemical species) will be presented. In our method, discrete conservation and no penetration of species across solid boundaries are enforced using a cut-cell finite volume scheme. The small cell problem inherent to the method is tackled using explicit-implicit domain decomposition for scalar, within the FDS time integration scheme. Some details on the derivation, implementation and numerical tests of this numerical scheme will be discussed. [Preview Abstract] |
Monday, November 23, 2015 4:44PM - 4:57PM |
L7.00004: An Adaptive and Implicit Immersed Boundary Method for Cardiovascular Device Modeling Amneet Pal S. Bhalla, Boyce E. Griffith Computer models and numerical simulations are playing an increasingly important role in understanding the mechanics of fluid-structure interactions (FSI) in cardiovascular devices. To model cardiac devices realistically, there is a need to solve the classical fluid-structure interaction equations efficiently. Peskin’s explicit immersed boundary method is one such approach to model FSI equations for elastic structures efficiently. However, in the presence of rigid structures the IB method faces a severe timestep restriction. To overcome this limitation, we are developing an implicit version of immersed boundary method on adaptive Cartesian grids. Higher grid resolution is employed in spatial regions occupying the structure while relatively coarser discretization is used elsewhere. The resulting discrete system is solved using geometric multigrid solver for the combined Stokes and elasticity operators. We use a rediscretization approach for standard finite difference approximations to the divergence, gradient, and viscous stress. In contrast, coarse grid versions of the Eulerian elasticity operator are constructed via a Galerkin approach. The implicit IB method is tested for a pulse duplicator cardiac device system that consists of both rigid mountings and elastic membrane. [Preview Abstract] |
Monday, November 23, 2015 4:57PM - 5:10PM |
L7.00005: A high-order Immersed Boundary method for solving fluid problems on arbitrary smooth domains David Stein, Robert Guy, Becca Thomases We present a robust, flexible, and high-order Immersed Boundary method for solving the equations of fluid motion on domains with smooth boundaries using FFT-based spectral methods. The solution to the PDE is coupled with an equation for a smooth extension of the unknown solution; high-order accuracy is a natural consequence of this additional global regularity. The method retains much of the simplicity of the original Immersed Boundary method, and enables the use of simple implicit and implicit/explicit timestepping schemes to be used to solve a wide range of problems. We show results for the Stokes, Navier-Stokes, and Oldroyd-B equations. [Preview Abstract] |
Monday, November 23, 2015 5:10PM - 5:23PM |
L7.00006: Implicit solution of Navier-Stokes equations on staggered curvilinear grids using a Newton-Krylov method with a novel analytical Jacobian. Iman Borazjani, Hafez Asgharzadeh Flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates with explicit and semi-implicit schemes. Implicit schemes can be used to overcome these restrictions. However, implementing implicit solver for nonlinear equations including Navier-Stokes is not straightforward. Newton-Krylov subspace methods (NKMs) are one of the most advanced iterative methods to solve non-linear equations such as implicit descritization of the Navier-Stokes equation. The efficiency of NKMs massively depends on the Jacobian formation method, e.g., automatic differentiation is very expensive, and matrix-free methods slow down as the mesh is refined. Analytical Jacobian is inexpensive method, but derivation of analytical Jacobian for Navier-Stokes equation on staggered grid is challenging. The NKM with a novel analytical Jacobian was developed and validated against Taylor-Green vortex and pulsatile flow in a 90 degree bend. The developed method successfully handled the complex geometries such as an intracranial aneurysm with multiple overset grids, and immersed boundaries. It is shown that the NKM with an analytical Jacobian is 3 to 25 times faster than the fixed-point implicit Runge-Kutta method, and more than 100 times faster than automatic differentiation depending on the grid (size) and the flow problem. The developed methods are fully parallelized with parallel efficiency of 80-90{\%} on the problems tested. [Preview Abstract] |
Monday, November 23, 2015 5:23PM - 5:36PM |
L7.00007: An efficient immersed boundary projection method for flow around moving bodies Wei-Xi Huang, Ru-Yang Li, Chun-Mei Xie, Chun-Xiao Xu An immersed boundary method based on the projection approach is proposed for simulation of flow over moving bodies. In this framework, the momentum forcing added to the incompressible Navier-Stokes equations acts as a Lagrangian multiplier to satisfy the no-slip condition on the immersed boundary, as the role of the pressure on enforcing the divergence-free constraint. The fractional step method with a fully implicit time-advancement scheme is adopted to compute the system, thus eliminating the CFL limitation. Based on the approximate block LU decomposition, velocity-pressure-momentum forcing decoupling is achieved. Moreover, decoupling of the intermediate velocity components and further decoupling of the three directions of the Cartesian coordinates for each velocity component are also performed. As a result, tridiagonal matrix systems for the intermediate velocity, the pressure Poisson equation, and a linear system for the momentum forcing which is one-order lower than the fluid dimensions, are solved, resulting in a significant saving of the computation cost. Both the temporal and spatial accuracies of the proposed method are tested. For validation, several benchmark numerical examples are presented, including flow over 2D and 3D moving bodies. [Preview Abstract] |
Monday, November 23, 2015 5:36PM - 5:49PM |
L7.00008: A discrete-forcing immersed boundary method with a semi-implicit predictor for weakly-coupled fluid-structure interaction Woojin Kim, Injae Lee, Haecheon Choi We present a weak coupling approach for the fluid-structure interaction using a discrete-forcing immersed boundary method. The incompressible Navier-Stokes equations and the motion of a solid body are based on the Eulerian and Lagrangian coordinates, respectively. A semi-implicit Euler method is applied to the governing equation of a solid body for obtaining provisional position and velocity of a solid body prior to implicitly solving each governing equation. Then, both equations are implicitly solved to obtain a sufficiently large computational time step size. The present weak-coupling approach shows a second-order temporal accuracy and stable solutions for the problems with a low density ratio (fluid to solid) without requiring an iterative method. With the present method, we simulate several fluid-structure interaction problems including the flows around a freely vibrating circular cylinder, a flexible beam attached to a circular cylinder, a flapping flag, a flexible plate, and an elastic vocal fold. The results obtained agree well with those from previous studies. All the simulations are conducted at maximum CFL numbers of 1.0-1.5. [Preview Abstract] |
Monday, November 23, 2015 5:49PM - 6:02PM |
L7.00009: Numerical simulation of Shallow water wave propagation around arrays of emerged bodies Amir Zainali, Robert Weiss Flow around the fixed groups of localized bodies are often encountered in the context of environmental fluid mechanics. Common examples include surface wave propagation through vegetation and flow around the offshore and onshore structures. In the literature, shallow water equations (SWE) are frequently used to model environmental flows. Due to conservative and shock-capturing properties they provide us with good approximations of the wave breaking and runup. In addition, various studies have shown that the inclusion of dispersive effects before the wave breakup can be of a crucial importance. To model the interaction of the wave with the emerged bodies, the exact geometry of the emerged bodies can be considered in the model. However, this approach can be computationally very expensive, particularly if we want to model the interaction of arrays of bodies with complicated geometries. Alternatively, an immersed boundary method can be used. This approach provides us with a significant improvement in numerical efficiency with a negligible numerical accuracy loss. In this study, we use the fully nonlinear and weakly dispersive Green–Naghdi model, coupled with Brinkman penalization technique to simulate the interaction between fluid flow and emerged bodies. [Preview Abstract] |
Monday, November 23, 2015 6:02PM - 6:15PM |
L7.00010: Level set immersed boundary method for gas-liquid-solid interactions Shizhao Wang, Elias Balaras We will discuss an approach to simulate the interaction between free surface flows and deformable structures. In our formulation the Navier-Stokes equations are solved on a block-structured grid with adaptive mesh refinement, and the pressure jumps across the interface between different phases, which is tracked using a level set approach, are sharply defined. Deformable structures are simulated with a solid mechanics solver utilizing a finite element method. The overall approach is tailored to problems with large displacement/deformations. The boundary conditions on a solid body are imposed using a direct forcing, immersed boundary method (Vanella \& Balaras, J. Comput. Physics, 228(18), 6617-6628, 2009). The flow and structural solvers are coupled by a predictor-corrector, strong-coupling scheme. The consistency between the Eulerian field based level set method for fluid-fluid interface and Lagrangian marker based immersed boundary method for fluid-structure interface is ensured by reconstructing the flow field around the three phase intersections. A variety of 2D and 3D problems ranging from water impact of wedges, entry and exit of cylinders and flexible plates interacting with a free surfaces, are presented to demonstrate the accuracy of the proposed approach. [Preview Abstract] |
Monday, November 23, 2015 6:15PM - 6:28PM |
L7.00011: A 2D domain decomposition, a customized immersed boundary method and a zest of numerical dissipation: a successful cocktail to tackle turbulence on HPC systems Sylvain Laizet, Eric Lamballais, J. Christos Vassilicos Incompact3d is a high-order flow solver dedicated to Direct and Large Eddy Simulations (DNS/LES) using High Performance Computing (HPC) systems which isdevoted to turbulent flows at the interface between academic research and upstream industrial R{\&}D. It is originating from the University of Poitiers (France) and was developed there as well as, more recently, in the Turbulence, Mixing and Flow Control Group at Imperial College London (UK). This high-order flow solver can reconcile accuracy, efficiency, versatility and scalability using a simple Cartesian mesh and up to one million computational cores. The three key ingredients of this successful cocktail to tackle turbulence on HPC systemswill be given in this talkfollowed by various applications such as fractal-generated turbulence, gravity currents in an open basin, impinging jets on a heated plate and a micro-jet device to control a turbulent jet. [Preview Abstract] |
Monday, November 23, 2015 6:28PM - 6:41PM |
L7.00012: Detached eddy simulation of high-Reynolds-number turbulent flows using the immersed boundary method Matteo Bernardini, Sergio Pirozzoli, Paolo Orlandi Detached Eddy Simulation based on the Spalart-Allmaras turbulence model is applied in conjunction with the immersed boundary method to simulate high-Reynolds number turbulent flows in complex geometries. A fourth-order, finite-difference solver capable of discretely preserving the kinetic energy in the limit of inviscid flow is adopted to solve the compressible Navier-Stokes equations and model-consistent, adaptive wall functions are employed to provide the proper numerical boundary conditions at the fluid/solid interface. Numerical tests, performed for several configurations involving massively separated flows, demonstrate that computations at high-Reynolds number, as typically occurring in flows of industrial relevance, can be successfully carried out using the immersed boundary strategy, providing predictions whose accuracy is comparable to that of standard, body-fitted, structured or unstructured flow solvers. [Preview Abstract] |
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