Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session M5: Computational Fluid Dynamics VII |
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Chair: Tim Colonius, California Institute of Technology Room: 24A |
Tuesday, November 20, 2012 8:00AM - 8:13AM |
M5.00001: A numerical method for Stokes flow in a complex geometry coupled to dynamic rigid structures and filaments Tamar Shinar, Michael Shelley We present a numerical method for the simulation of Stokes flow coupled to fixed and dynamic rigid bodies. The method uses an immersed boundary formulation for the fluid problem, where the problem domain is embedded in a periodic domain, and the boundary conditions are enforced through singular source terms. Rigid body generalized coordinates and velocities are used for the structures, though the method could be extended to deformable structures as well. The structure forces are nonlinear in general and we solve the coupled problem using a Newton-Krylov method, where the associated linear systems are symmetric indefinite. The coupling forces between the fluid and structures are treated in a fully implicit manner, making the choice of stable time step independent of those forces. We demonstrate the method by studying the dynamics of mitotic spindle positioning in a model of a single-celled \emph{C. elegans} embryo. [Preview Abstract] |
Tuesday, November 20, 2012 8:13AM - 8:26AM |
M5.00002: Coupled level-set CURVIB method for fluid-structure interaction simulations of arbitrarily complex floating rigid bodies Antoni Calderer, Seokkoo Kang, Fotis Sotiropoulos We develop a fluid-structure interaction (FSI) model for simulating arbitrarily complex floating rigid bodies interacting with nonlinear free-surface flows. The FSI curvilinear immersed boundary (CURVIB) method of Borazjani et al. (JCP 2008) is integrated with the LES CURVIB method of Kang et al. (Adv. in Water Resources 2010) and the recently developed level set-CURVIB method (Kang and Sotiropoulos, Adv. in Water Res. 2012) to develop a powerful method for simulating 3D nonlinear turbulent free-surface flows. To demonstrate the predictive capabilities of the method and its ability to simulate non-linear free-surface phenomena, such as breaking waves, we apply it to simulate various cases involving 2D/3D free surface-rigid body interactions. The computed results are shown to be in excellent agreement with available experimental measurements. [Preview Abstract] |
Tuesday, November 20, 2012 8:26AM - 8:39AM |
M5.00003: The immersed interface method without interface parametrization Glen Pearson, Sheng Xu To simulate fluid-solid interaction or two-fluid flows on Cartesian grids by the immersed interface method, we incorporate into a numerical scheme the jump conditions of the first- and second-order Cartesian derivatives of the velocity and pressure. These Cartesian jump conditions can be systematically derived from the principal jump conditions for the velocity and the pressure [Sheng Xu, Z. Jane Wang, Systematic derivation of jump conditions for the immersed interface method in three dimensional flow simulation, SIAM J. Sci. Comput. Vol 27, No. 6, pp. 1948-1980.], i.e. the jump conditions of the velocity and the pressure, their normal derivatives and their Laplacians. However, this previous derivation requires the global parametrization of a fluid-solid or two-fluid interface. In this talk, we present a new derivation which is based on the triangulation of an interface and avoids the interface parametrization. The new derivation makes the immersed interface method more robust for applications. We will test our new derivation by solving Poisson equations with discontinuous solutions across triangulated interfaces. [Preview Abstract] |
Tuesday, November 20, 2012 8:39AM - 8:52AM |
M5.00004: Fully resolved immersed electrohydrodynamics for target-detection, particle motion, and self propulsion Amneet P.S. Bhalla, Boyce E. Griffith, Neelesh A. Patankar Motion of particles, rigid or deforming, through conductive fluid media under the presence of electric fields require the solution of coupled electrodynamics and hydrodynamics equations. In this work we present a numerical method for modeling such coupled equations in an adaptive mesh refinement and immersed body framework. The methodology permits us to locally resolve high electric field gradients and boundary layers near the fluid-structure interfaces at a moderate computational expense. Using such a framework a broad range of problems such as ``electrolocation'' (a technique used by knifefish to detect its target due to the distortion of self generated electric field by a prey in its vicinity), dielectrophoretic motion of particles in microfluidic channels, development of artificial ``electrosense'' for underwater vehicles, among others, can be addressed. [Preview Abstract] |
Tuesday, November 20, 2012 8:52AM - 9:05AM |
M5.00005: A local grid refinement curvilinear immersed boundary method for multi-resolution simulations of complex turbulent flows Dionysios Angelidis, Fotis Sotiropoulos A novel numerical method for multi-resolution real life simulations is developed, solving the Navier-Stokes equations on curvilinear locally refined grids in conjunction with the Curvilinear Immersed Boundary Method (CURVIB) (Ge and Sotiropoulos, J. Comp. Phys. 2007). The governing equations are discretised on 3D unstructured grids using a hybrid staggered/non-staggered approach and employing the fractional step method; thus discretising the momentum equations fully implicitly using second-order scheme in time. The momentum equations are solved with the matrix free Newton-Krylov method, while the Poisson equation is solved by implementing the algebraic multigrid method (AMR). By using the unstructured approach, the memory requirements are minimized since all the data are stored in one dimensional arrays. Thus, adaptive cells' splitting and merging is related with memory allocation and deallocation respectively. Partitioning of the unstructured grid and parallel computing enhance the solver's performance, making the code a powerful tool capable for multi-resolution calculations of complex turbulent flows involving a large disparity of spatial scales, such as flows past wind turbine arrays. The flow solver is developed to enable large-eddy simulations, with low computational cost. [Preview Abstract] |
Tuesday, November 20, 2012 9:05AM - 9:18AM |
M5.00006: A Numerical study of ablative flow driven by thermodynamics and kinetics Ryan Crocker, Yves Dubief, Christopher White The main focus of this research is to elucidate the relationship between ablative/erosive flows and their interaction with a spatially dynamic boundary conditions. The fluid-solid interface is described by a level-set (LS) approach, enabling efficient and accurate computation of wall-normal vectors and other geometrical properties. Boundary conditions at the interface are imposed using immersed boundary methods (IBM). Our LS/IBM ablation algorithm is able to simulate various ablation processes, in particular ablation by chemical reactions and phase-change. The momentum boundary conditions are handled through cut cell IBM applied implicitly. This method is fully mass conserving and eliminates issues with spurious pressure oscillations. Scalar boundary conditions are simulated with a form of the ghost fluid method, with known thermal and chemical physics, to interpolate values across the fluid/solid interface after they are decoupled. We will discuss two applications of this algorithm. The first is the simulation of an experiment of the oxidation of a carbon material at around 1000K conducted at NASA AMES. The second focuses on the interactions between heated wall-turbulence and a low-melting point material in collaboration with parallel experiments at University of New Hampshire. [Preview Abstract] |
Tuesday, November 20, 2012 9:18AM - 9:31AM |
M5.00007: An Immersed Boundary Method for the Incompressible Navier-Stokes Equations Based on the Lattice Green's Function Method Sebastian Liska, Tim Colonius A parallel, three-dimensional immersed boundary method is developed to solve external, viscous incompressible flows on an infinite domain. The equations are formally discretized on an infinite staggered Cartesian grid. An advantage of the infinite grid is automatic commutativity of operators and associated conservation properties. The Lattice Green's Function (LGF) method is used to reduce the solution to a finite portion of the grid. The LGF method uses the fundamental solutions of discrete operators on infinite grids analogously to solving continuous inhomogeneous differential equations using Green's functions. The differential-algebraic-equations that describe the temporal evolution of the discrete momentum equation, the 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 technique is used to efficiently solve the algebraic system of equations involved in each stage of the time march. Fast solutions to the discrete elliptic problems that arise from the projection technique are obtained through a new solver based on the LGF that shares constructs from fast multipole methods and tree-algorithms. Results for three-dimensional test problems are presented, and the performance and scaling of the present implementation are discussed. [Preview Abstract] |
Tuesday, November 20, 2012 9:31AM - 9:44AM |
M5.00008: Multi-Implicit Blob Projection Method Lauren Fovargue Many problems in biological fluid-structure interaction have been studied with C. S. Peskin's immersed boundary method (IBM). This method defines a relatively simple mathematical modeling framework, and allows for the use of standard fluid solvers. Often, when this is evaluated computationally in many applications, a very small time step is required. This time step is not restricted by accuracy, but stability, causing the temporal problem to be stiff. Previous attempts to address the stability restriction of IBM use semi or fully implicit schemes that require the code, including the fluid solver, to be rewritten, and these have yet to be implemented in application focused studies. Here, new ideas for addressing the computational cost of IBM are presented, which rely on a novel method for splitting the spatial field into stiff and non-stiff components. With this splitting, the impact on the largest stable time step and computational cost for stiff problems is investigated through a multi-implicit technique, which focuses on the treatment of the immersed boundary, where no changes to the fluid solver are necessary. [Preview Abstract] |
Tuesday, November 20, 2012 9:44AM - 9:57AM |
M5.00009: A sharp, robust, conservative cut-cell immersed boundary technique Peter Brady, Olivier Desjardins Simulation of solid-fluid systems with complex boundaries can be greatly simplified using immersed boundary (IB) methods. IB methods have have been used for many years because they provide an alternative to using a full body-fitted mesh, which often requires an unstructured CFD code. However, using a non body-fitted mesh with IB creates new challenges, including insufficient accuracy in the application of boundary conditions and the potential lack of conservation properties. Yet, discrete conservation can be obtained by using a cut-cell IB approach, where the cells that intersect with the solid body are cut such that they become body-fitted. Challenges typically associated with cut-cell methods include: expensive geometry manipulations (especially in three dimensions), the creation of arbitrarily small cut-cells and a modified discretization in those cut-cells. We address these issues by representing the interface implicitly and computing the cut-cell geometry using a marching tetrahedra algorithm. The discretization is then modified in the cut-cells using this geometric information. The code is verified and several techniques for handling small cells and the application of boundary conditions at the IB surface are evaluated using the method of manufactured solutions. [Preview Abstract] |
Tuesday, November 20, 2012 9:57AM - 10:10AM |
M5.00010: An improved direct-forcing immersed boundary method for fluid-structure interaction of a flexible filament Xing Zhang, Xiaojue Zhu We present an improved immersed boundary method for the simulation of fluid structure interaction (FSI) of a slender body. Our numerical method is based on the one proposed by Wang and Zhang (J. Comput. Phys. 30:3479-3499, 2011). Although an accurate prediction of total force can be achieved by using this method, unphysical spatial oscillation is observed in the force distribution. This oscillation is detrimental to the prediction of structure response in FSI. In this work, several modifications are made to improve this method. Firstly, the implicit forcing is replaced by an explicit forcing. Secondly, a more consistent way of computing each component of the forcing on a staggered mesh is proposed. Thirdly, for a slender body of zero thickness, the discrete delta-function with a ``negative-tail'' is adopted for the interpolation at the endpoints. Numerical simulations are performed to test the efficacy of the modifications. It is found that the measures taken successfully reduce the oscillation and the results obtained agree well with those from the literatures. [Preview Abstract] |
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