Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session M5: CFD VII: Numerical Methods I 
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Chair: Daniel Haworth, Pennsylvania State University Room: 327 
Tuesday, November 26, 2013 8:00AM  8:13AM 
M5.00001: Using AdjointBased Approach to Understand FlappingWing Aerodynamics Min Xu, Mingjun Wei The study of flappingwing aerodynamics is a problem with very large control space. Adjointbased approach, by solving an inverse problem, can be used here as an efficient tool for optimization and physical understanding. However, the adjoint equation is typically formulated in a fixed domain. The moving boundary or morphing domain brings in an inconsistency in the definition of arbitrary perturbation at the boundary, which then proposes a new challenge if the control parameters happen to be also at the boundary. An unsteady mapping function, as a usual remedy for such problems, would make the whole formulation too complex to be feasible. Instead, we use noncylindrical calculus to redefine the perturbation and solve the inconsistency problem caused by moving/morphing solid boundaries. The approach is first validated for a simple case of a plate plunging in an incoming flow. Then we extend the approach to drag reduction and efficiency improvement of more complex cases. The optimized parameters provide a unique opportunity for physical understanding by comparison to the initial parameters. [Preview Abstract] 

M5.00002: ABSTRACT WITHDRAWN 

M5.00003: ABSTRACT WITHDRAWN 
Tuesday, November 26, 2013 8:39AM  8:52AM 
M5.00004: A Monolithic Algorithm for High Reynolds Number FluidStructure Interaction Simulations Erika Lieberknecht, Jason Sheldon, Jonathan Pitt Simulations of fluidstructure interaction problems with high Reynolds number flows are typically approached with partitioned algorithms that leverage the robustness of traditional finite volume method based CFD techniques for flows of this nature. However, such partitioned algorithms are subject to many subiterations per simulation timestep, which substantially increases the computational cost when a tightly coupled solution is desired. To address this issue, we present a finite element method based monolithic algorithm for fluidstructure interaction problems with high Reynolds number flow. The use of a monolithic algorithm will potentially reduce the computational cost during each timestep, but requires that all of the governing equations be simultaneously cast in a single Arbitrary LagrangianEulerian (ALE) frame of reference and subjected to the same discretization strategy. The formulation for the fluid solution is stabilized by implementing a Streamline Upwind Galerkin (SUPG) method, and a projection method for equal order interpolation of all of the solution unknowns; numerical and programming details are discussed. Preliminary convergence studies and numerical investigations are presented, to demonstrate the algorithm's robustness and performance. [Preview Abstract] 
Tuesday, November 26, 2013 8:52AM  9:05AM 
M5.00005: Partitioned fluidstructure interaction scheme for bodies with high flexibility Timothy Fitzgerald, Marcos Vanella, Elias Balaras, Balakumar Balachandran There are many interesting problems involving fluidstructure interaction (FSI) systems such as flapping wings in microairvehicles. In order to better understand these systems, highfidelity simulation tools are needed to do the following: (i) fully capture the physics and (ii) provide a basis to construct lowfidelity models used in design. Here, a novel FSI strategy is introduced, through which a large scale fluids solver is combined with a solver for solids with high flexibility. The NavierStokes equations for incompressible flow are discretized by using standard central finite differences on a staggered mesh. The fluid domain is spatially decomposed through the use of the FLASH modeling framework. The solid body is discretized via geometrically exact Total Lagrangian finite elements. A novel hyperelastic material law that extends the engineering stressstrain law to finite deformations and arbitrary rotations is also implemented. The Lagrangian body is embedded in the Cartesian fluid grid by immersed boundary methods. The time marching predictorcorrector coupling procedure is based on the use of Adams methods for the fluid and the Generalized$\alpha$ method for the body. We will present examples of flexible oscillating plates and a flapping Manduca Sexta wing. [Preview Abstract] 
Tuesday, November 26, 2013 9:05AM  9:18AM 
M5.00006: Richardson Extrapolation using DNAD Ismail B. Celik, Hayri Sezer, Suryanarayana R. Pakalapati Dual Number Automatic Derivation (DNAD) is a technique whereby a computer code can be executed with additional variable declarations to extend real number to a two dimensional space which is then used to evaluate derivatives to machine accuracy. In the literature this technique is usually applied to study sensitivities of calculations to model parameters, but not the mesh size. The current study explores possibilities of using the same technique to evaluate the derivative of the numerical solution with respect to mesh size which in turn can be used in the Taylor series expansion of the discretization error to calculate the error itself by way of extrapolation. Thus the new method enables explicit Richardson extrapolation by using only one set of calculations on a single grid. The extrapolation can be improved if an additional set of calculations are performed on a finer or a coarser mesh. The concept is demonstrated using onedimensional example problems. Possible extension to multidimensions is discussed. [Preview Abstract] 
Tuesday, November 26, 2013 9:18AM  9:31AM 
M5.00007: A balancedforce finiteelement method for surfacetensiondriven interfacial flows using interfacecapturing approaches Zhihua Xie, Dimitrios Pavlidis, James Percival, Jefferson Gomes, Christopher Pain, Omar Matar Interfacial flows with surface tension are often found in industrial and practical engineering applications, including bubbles, droplets, liquid film and jets. Accurate modelling of such flows is challenging due to their highly complex dynamics, which often involve changes of interfacial topology. We present a balancedforce finiteelement method with adaptive unstructured meshes for interfacial flows. The method uses a mixed controlvolume and finite element formulation, which ensures the surface tension forces, and the resulting pressure gradients, are exactly balanced, minimising the spurious velocities often found in numerical simulations of such flows. A volumeoffluidtype method is employed for interface capturing based on a compressive controlvolume advection method, and secondorder finite element methods. A distance function is reconstructed from the volume fraction on the unstructured meshes, which provides accurate estimation of the curvature. Numerical examples of an equilibrium drop and dynamics of bubbles (droplets) are presented to demonstrate the capability of this method. [Preview Abstract] 
Tuesday, November 26, 2013 9:31AM  9:44AM 
M5.00008: Application of Kelvin's Inversion Theorem in mesh based numerical simulation of flows in unbounded domains John Russell One may decompose an unbounded domain exterior to a solid body into two parts separated by a sphere of radius $a$, which I will call the \emph{Reflecting Sphere\/}. The \emph{Near Exterior\/} is exterior to the solid body but interior to the Reflecting Sphere while the \emph{Far Exterior\/} is exterior to both. Suppose the velocity field in the Far Exterior has a velocity potential, $\phi$. In the 1840s \textsc{Kelvin} showed that the change of position variable ${\mathbf r}\to{\mathbf q}$ defined by ${\mathbf r}/r={\mathbf q}/q$ and $rq=a^2$ (in which $r={\mathbf r}$ and $q={\mathbf q}$) maps the Far Exterior to an \emph{Inverted Far Exterior\/} (the interior of the Reflecting Sphere). Furthermore, if ${\mathbf r}\mapsto\phi$ is a solution of \textsc{Laplace}'s equation in the {\textbf r}coordinates then ${\mathbf q}\mapsto\Phi$, in which $\phi=(q/a)\Phi$, is a solution of \textsc{Laplace}'s equation in the {\textbf q}coordinates. Boundedness of both the Near Exterior and Inverted Far Exterior enables simultaneous solution of the relevant partial differential equations provided one applies suitable compatibility conditions on the Reflecting Sphere. The talk will present simulations of this kind along with comparisons with analytical solutions. [Preview Abstract] 
Tuesday, November 26, 2013 9:44AM  9:57AM 
M5.00009: Smoothed Particle Hydrodynamics Continuous Boundary Force method for NavierStokes equations subject to a Robin boundary condition Wenxiao Pan, Jie Bao, Alexandre Tartakovsky A Continuous Boundary Force (CBF) method was developed for implementing Robin (Navier) boundary condition (BC) that can describe noslip or slip conditions (slip length from zero to infinity) at the fluidsolid interface. In the CBF method the Robin BC is replaced by a homogeneous Neumann BC and an additional volumetric source term in the governing momentum equation. The formulation is derived based on an approximation of the sharp boundary with a diffuse interface of finite thickness, across which the BC is reformulated by means of a smoothed characteristic function. The CBF method is easy to be implemented in Lagrangian particlebased methods. We first implemented it in smoothed particle hydrodynamics (SPH) to solve numerically the NavierStokes equations subject to spatialindependent or dependent Robin BC in two and three dimensions. The numerical accuracy and convergence is examined through comparisons with the corresponding finite difference or finite element solutions. The CBF method is further implemented in smoothed dissipative particle dynamics (SDPD), a mesoscale scheme, for modeling slip flows commonly existent in micro/nano channels and microfluidic devices. [Preview Abstract] 
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