Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session D5: CFD II: High-order Methods |
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Chair: Peter Diamesis, Cornell University Room: 308 |
Sunday, November 20, 2011 2:10PM - 2:23PM |
D5.00001: High order DG discretizations with p-adaptive limiting for high speed flows on mixed type meshes John Ekaterinaris, Konstandinos Kontzialis High order accurate discontinuous Galerkin (DG) discretizations are applied for mixed-type meshes in two and three dimensions. Collapsed coordinate transformations are used and all calculations of DG discretizations for arbitrary mixed-type meshes are performed in the canonical computational space. High order accurate implicit time marching is used for time advancement. For computations of high speed flows with strong discontinuities, a new limiting approach that is applied in the canonical computational domain and it is suitable for arbitrary-type meshes, is employed. Limiting is applied with a modified total variation bounded (TVB) limiter, previously used for DG discretizations in quadrilateral meshes. Accurate evaluation of the variation of the second derivative of the approximate solution allows to accurately detect regions of discontinuities where limiting must be applied and progressively increase the accuracy of the computed solution away from discontinuities. For the computation of flows with large pressure and density ratios, positivity preserving limiters are used to ensure that density and pressure remain well defined. Application of the new limiting approach and positivity preserving limiters to a number of standard test cases of high speed flows with discontinuities is carried out to demonstrate the versatility and robustness of the proposed method. [Preview Abstract] |
Sunday, November 20, 2011 2:23PM - 2:36PM |
D5.00002: High-Order Finite-Difference Solution of the Poisson Equation Involving Complex Geometries in Embedded Meshes Alexandre Marques, Jean-Christophe Nave, Ruben Rosales The Poisson equation is of central importance in the description of fluid flows and other physical phenomena. In prior work, Marques, Nave, and Rosales introduced the Correction Function Method (CFM) to obtain fourth-order accurate solutions for the constant coefficient Poisson problem with prescribed jump conditions for the solution and its normal derivative across arbitrary interfaces. Here we combine this method with the ideas introduced by Mayo to solve other Poisson problems involving complex geometries. In summary, we are able to rewrite the problem as a boundary integral equation in terms of a potential distribution over the boundary or interface. The solution of this integral equation is discontinuous across the boundary or interface. Hence, after this integral equation is solved using standard techniques, the potential distribution can be used to determine the jump discontinuities. We are then able to use the CFM to solve the resulting Poisson equation with jump discontinuities. The outcome is a fourth-order accurate scheme to solve general Poisson problems which, over arbitrary geometries, has a cost that is approximately twice that of a fast Poisson solver using FFT on a rectangular geometry of the same size. Details of the method and applications will be presented. [Preview Abstract] |
Sunday, November 20, 2011 2:36PM - 2:49PM |
D5.00003: Polynomial Interpolation of 12$^{th}$-Order Combined Compact Difference Schemes onto Non-Uniform Grids in Numerical Simulations of Boundary Layer Turbulence Transition J.C. Chen, Weijia Chen Numerical simulations of boundary layer turbulence transition meet with the challenge of astronomical computational demands needed to visualize the underlying physical phenomena. Reprieve from the onerous computational load avails when recognizing that boundary layer turbulent flow structures intermittently concentrate near the wall region. Astute implementation of non-uniform computational grids with microscopically precise resolution near the wall boundary that tapers off away from the wall offers potential for vast computational efficiency. Importantly, the numerical method applied on non-uniform grids must further consider the issue of numerical stability of the numerical schemes at the wall. Implementation of a piece- wise non-uniform grid accounts for both the numerical demands of realizing turbulent flow structures near the wall and maintaining numerical stability of the wall boundary schemes. Customization of a 12$^{th}$ order Combined Compact Difference Scheme with 10$^{th}$ and 11$^{th}$ order boundary schemes to the non-uniform grid by polynomial interpolation enhances the numerical accuracy near the wall over the use of coordinate transformation. Analyses of the eigenvalue spectrum and modified wave number intimate the stability of the numerical method. [Preview Abstract] |
Sunday, November 20, 2011 2:49PM - 3:02PM |
D5.00004: An Eigen-based Spectral Element Method Suchuan Dong, Xiaoning Zheng We present an efficient high-order spectral element method. The method employs a novel numerically-constructed expansion basis within an element, which represents an optimal set of basis functions and simultaneously diagonalizes the mass and stiffness operators. We compare the new method with the Jacobi polynomial-based spectral element method that is commonly used in computational fluid dynamics. Results demonstrate that the new method enjoys a considerably superior numerical efficiency in terms of numerical conditioning and the number of iterations to convergence for iterative solvers. [Preview Abstract] |
Sunday, November 20, 2011 3:02PM - 3:15PM |
D5.00005: An approach to satisfy pressure and temperature equilibriums at interfaces in compressible multicomponent flows using high-order schemes Hiroshi Terashima, Soshi Kawai, Mitsuo Koshi We present a formulation for high-order simulations of compressible multicomponent flows using a sixth-order compact differencing scheme and a localized artificial diffusivity. The formulation is designed to satisfy both of pressure and temperature equilibriums at fluid interfaces by introducing additional two equations to the Euler equations. In order to deal with sharp initial condition of density, a localized artificial diffusivity term is introduced to the mass conservation equation. Several one-dimensional problems such as advection of contact and material interfaces and a shock tube problems demonstrate that the present method maintains the pressure and temperature equilibriums and also satisfies the mass conservation property. The localized artificial diffusivity for the mass conservation equation enables to start computations even with severe one-point jump condition, effectively reducing numerical wiggles at the fluid interfaces. Comparisons with a conventional full conservative formulation present the superiority of the present method for preventing spurious pressure/velocity/temperature oscillations at the fluid interfaces. Two-dimensional problems such as the Richtmyer-Meshkov instability demonstrate its multidimensional applicability. [Preview Abstract] |
Sunday, November 20, 2011 3:15PM - 3:28PM |
D5.00006: A Quadrilateral Spectral Multidomain Penalty Method Model For High Reynolds Number Incompressible Stratified Flows Jorge Escobar-Vargas, Peter Diamessis We present a spectral multidomain penalty method-based incompressible Navier Stokes solver for high Reynolds number stratified turbulent flows in doubly non-periodic domains. Within the solver, time is discretized with a fractional-step method, and, in space, a Gauss-Lobatto-Legendre collocation approach is used in discontinuous quadrilateral subdomains. Stability of the numerical scheme is guaranteed through a penalty scheme and spectral filtering, further buttressed by a overintegration-based dealiasing technique. The efficient iterative solution of the associated discrete pressure Poisson equation is ensured through a Kronecker product based computation of the null vector associated with the global matrix, plus a two-level preconditioner within a GMRES solver. Efficiency and accuracy of the Navier Stokes solver are assessed through the solution of the lid-driven cavity flow, Taylor vortex and double shear layer. The canonical lock exchange problem is also presented to assess the potential of the solver for the study of environmental stratified flows. [Preview Abstract] |
Sunday, November 20, 2011 3:28PM - 3:41PM |
D5.00007: Spectral element simulations of unsteady flow over a 3D, low aspect-ratio semi-circular wing Sriharsha Kandala, Dietmar Rempfer Numerical simulations of unsteady 3D flow over a low-aspect- ratio semi-circular wing are performed using a spectral element method. Specsolve, a parallel spectral element solver currently under development at IIT, is used for the simulation. The solution is represented locally as a tensor product of Legendre polynomials and $C^0$-continuity is enforced between~adjacent~domains. A BDF/EXT scheme is used for temporal integration. The fractional step method is used for computing velocity and pressure. The code incorporates a FDM (fast diagonalization method) based overlapping Schwarz preconditioner for the consistent Poisson operator and an algebraic multigrid based coarse grid solver (P.F. Fischer et al, J. Phys.: Conf. Ser.(125) 012076, 2008) for pressure. The simulation replicates the conditions of the active flow control experiment (D. Williams et al, AIAA paper, 2010-4969). The Reynolds number based on chord length and free-stream velocity is about 68000. Different angles of attack, encompassing both pre-stall and post-stall regimes, are considered. These results are compared with data from the experiment and numerical simulations based on Lattice Boltzmann method (G. Br\`{e}s et al, AIAA paper, 2010-4713). [Preview Abstract] |
Sunday, November 20, 2011 3:41PM - 3:54PM |
D5.00008: A Computational Study of Transient Couette Flow Over an Embedded Cavity Surface Michael Thompson, Amy Lang, Will Schreiber, Chase Leibenguth, John Palmore Insect flight has become a topic of increased study due to bio-inspired applications for Micro-Air-Vehicles (MAVs). The complex yet efficient flight mechanism of butterflies relies upon flexible, micro-geometrically surface patterned, scaled wings. Effective vortex control, when flapping as well as low-drag gliding, may result from the wing's texture. This hypothesis was tested by focusing on the formation of embedded vortices between the rows of scales on butterfly wings. To calculate the total surface drag induced on the moving cavity surface a computational fluid dynamics study using FLUENT simulated the flow inside and above the embedded cavities under transient Couette flow conditions with Reynolds numbers varied from 0.01 to 100. The computational model consisted of a single embedded cavity with a periodic boundary condition. Based on SEM pictures of Monarch (\textit{Danaus plexippus}) butterfly scales, various cavity geometries were tested to deduce drag reduction. Results showed that the embedded vortex size and shape generated within the cavity depended on which surface moved (top, flat wall or bottom, cavity wall) as well as aspect ratio. Surface drag reduction was confirmed over the cavity surfaces when compared to that of a flat plate, and increased with aspect ratio. [Preview Abstract] |
Sunday, November 20, 2011 3:54PM - 4:07PM |
D5.00009: Computational Analysis of Low Reynolds Number Couette Flow Over an Embedded Cavity Geometry Chase Leibenguth, Amy Lang, Will Schreiber A butterfly utilizes an efficient and complex flight mechanism comprised of multiple interacting flow control devices that include flexible, micro-geometrically surface patterned, scaled wings.~ The following research attempts to deduce any aerodynamic advantages that arise from the formation of vortices in between successive rows of scales on a butterfly wing.~ The simplified computational model consists of an embedded cavity within a Couette flow with the flat plate moving transversally over the cavity. ~The effects of cavity geometry and Reynolds number are analyzed separately.~ The model is simulated in ANSYS FLUENT and provides qualitative insight into the interaction between the scales and the boundary layer.~ Preliminary results indicate that vortices form within the cavity and potentially contribute to a net partial slip condition.~ Further, the embedded cavities contribute to a net reduction in the drag coefficient that varies with Reynolds number and cavity geometry.~ [Preview Abstract] |
Sunday, November 20, 2011 4:07PM - 4:20PM |
D5.00010: A full Navier-Stokes solver on Irregular Domains coupled with a Poisson-Boltzmann solver with Neumann or Robin boundary conditions on Non-Graded Adaptive Grid Asdis Helgadottir, Frederic Gibou We introduce a second-order solver for the full Navier-Stokes equations coupled with the Poisson-Boltzmann equation on irregular domains. This simple fluid solver can be used for simulating fluid flow in microfluidic devices. The irregular domain is described implicitly and the grid needs not to conform to the domain's boundary, which makes grid generation straightforward and robust. Finite Volume approach is used for the Poisson-Boltzmann solver making it straightforward to enforce Neumann or Robin boundary conditions at the irregular domain. The linear system is symmetric, positive definite in the case where the grid is uniform, otherwise nonsymmetric but an invertible M-matrix. The fluid solver is based on the projection method where finite volume approach is used to easily enforce Neumann boundary conditions for pressure at the irregular domain. Extensions from two spatial dimensions to three are straightforward both for the Poisson-Boltzmann solver and the Navier-Stokes solver. The Poisson-Boltzmann solver is solved using Quadtee/Octree grids (in two and three spatial dimensions respectively). The fluid solver is solved on uniform grid and values are interpolated between the two grids using second order accurate interpolation. [Preview Abstract] |
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