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 R5: Computational Fluid Dynamics VIII |
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Chair: Hamid Rahai, California State University, Long Beach Room: 24A |
Tuesday, November 20, 2012 1:00PM - 1:13PM |
R5.00001: A high order solver for the unbounded Poisson equation with specific application to the equations of fluid kinematics M.M. Hejlesen, J.T. Rasmussen, P. Chatelain, J.H. Walther This work improves upon Hockney and Eastwood's Fourier-based algorithm for the unbounded Poisson equation to formally achieve an arbitrary high order of convergence. The high order convergence is achieved by constructing regularized Green's functions through a filtering procedure. High order filters and regularized kernels are obtained by canceling the corresponding moments, a task which we show can be performed through a recursive application of extrapolation. We assess the methodology on the kinematic relations between the velocity and vorticity fields. In fluid mechanics the velocity is determined from the curl of the stream function which in turn is related to vorticity through the Poisson equation. The curl operator can be computed analytically, as a multi-component convolution kernel or, alternatively, computed directly in Fourier space through a spectral differentiation of the convolution product. The latter solution allows to reduce the computational cost and memory footprint of the algorithm while conserving its convergence order. [Preview Abstract] |
Tuesday, November 20, 2012 1:13PM - 1:26PM |
R5.00002: A fully spectral efficient algorithm for Stokes suspension simulations in doubly periodic confined geometries Jae Sung Park, David Saintillan The calculation of hydrodynamic interactions between suspended particles under confinement in low-Reynolds number flows is a computationally expensive task. In this study, we develop an efficient spectral method for the calculation of these interactions in a doubly periodic geometry between two infinite parallel no-slip walls in Stokes flow, a geometry commonly encountered in microfluidic devices. We consider the flow generated by a distribution of point forces inside a unit cell, and decompose it into the sum of two Stokes problems. The first one involves triply periodic boundary conditions and makes use of our previously developed fast smooth particle-mesh Ewald algorithm, while the second one provides a correction to the periodic solution to satisfy the no-slip boundary condition on the confining walls. This second problem is based on an analytic solution for the flow between two flat plates with prescribed Dirichlet wall boundary conditions that are determined from the first problem, and the total solution can be then obtained by superimposing the solution of each problem using the linearity of the Stokes equations. We conclude by presenting an application of this method to a confined suspension of spherical particles. [Preview Abstract] |
Tuesday, November 20, 2012 1:26PM - 1:39PM |
R5.00003: Multithreaded Impliclty Dealiased Convolutions for Pseudospectral Simulations Malcolm Roberts, John C. Bowman Convolutions form the crux of the pseudospectral method for direct numerical simulations of nonlinear PDEs such as the Navier--Stokes equations and magnetohydrodynamic flows. The computation of convolutions is an expensive task that is facilitated by the use of the convolution theorem and FFTs. However, input data must be zero-padded in order to remove aliased terms and recover a linear convolution. Here, we present a multithreaded version of the method of implicit dealiasing (Bowman and Roberts, SIAM J. Sci. Comput. 33, 2011). Implicit dealiasing has computational complexity identical to the conventional zero-padding technique, but is twice as fast in practice and requires $(2/3)^{d-1}$ the memory of a conventional $d$-dimensional centred convolution. High-performance implicitly dealiased convolution routines are available under the LGPL at \texttt{fftwpp.sourceforge.net}. [Preview Abstract] |
Tuesday, November 20, 2012 1:39PM - 1:52PM |
R5.00004: A spectral multi domain decomposition method for computing the 2D backward facing step flow Arjun Jagannathan, Manhar Dhanak, Ranjith Mohan A Chebyshev spectral domain decomposition method is developed for computing the characteristics of the 2D incompressible backward facing step flow at low to moderate Reynolds numbers. A step to channel height of 1:2 and an inlet channel of length twenty times the step height are chosen for the study. A total of five sub domains is used and an influence matrix technique is employed for carrying out the domain decomposition. The unsteady 2D Navier Stokes equations are solved in the vorticity-streamfunction formulation with an explicit second order Adams Bashforth time marching scheme. At the inlet, a parabolic velocity profile is initialized and the outflow boundary is located sufficiently far away from the step so that for the particular Reynolds numbers studied, the parabolic velocity profile is retrieved at the outlet. A non-reflecting boundary condition (cf. Jin and Braza, 1993) wherein we set the elliptic $(\partial ^2/\partial x^2)$ terms in the governing equations to zero at the outflow boundary is found to work well for this purpose. Detailed steady state results for Reynolds numbers in the range 100 to 800 are presented and compared with other numerical and experimental results found in the literature. [Preview Abstract] |
Tuesday, November 20, 2012 1:52PM - 2:05PM |
R5.00005: A deformed spectral quadrilateral multi-domain penalty model for the incompressible Navier-Stokes equations Sumedh Joshi, Peter Diamessis A penalty method is a variant of a spectral element method that weakly enforces continuity between adjacent elements and weakly enforces continuity at physical boundaries. Furthermore, at the boundaries, the PDE is also partially satisfied. The spirit of such a formulation is that in theory, a PDE operates arbitrarily close to any measure-zero boundary. Here, a previous spectral multi-domain penalty model for the incompressible Navier-Stokes equations is extended to include deformed boundaries for shoaling-type problems encountered in environmental fluid mechanics. Some difficulties addressed include satisfying compatibility conditions in a (pseudo-)pressure Poisson equation that arises. A previous strategy to satisfy compatibility by use of a null singular vector is presented and strategies to enforce compatibility for the deformed problem are discussed. Results are shown for standard incompressible flow benchmarks. The primary goal of this work is to model nonlinear internal wave propagation along a shallow, sloping bathymetry, as may be characteristic of a continental shelf region. [Preview Abstract] |
Tuesday, November 20, 2012 2:05PM - 2:18PM |
R5.00006: Direct Numerical Simulation of Compressible Turbulent Flows with Weighted Non-Linear Compact Schemes Debojyoti Ghosh, Shivaji Medida, James Baeder The numerical solution of compressible, turbulent flows requires a high-resolution, non-oscillatory algorithm to resolve a large range of length scales. Conventional non-linear flux limited schemes are too dissipative for length scales relevant to turbulent flow features, while compact interpolation schemes with high spectral resolution require monotonicity-preserving filtering for flows with discontinuities. The Compact Reconstruction WENO (CRWENO) scheme (\textit{Ghosh and Baeder, SIAM J. Sci. Comput., 34(3), 2012}) uses a non-linear, solution-dependent combination of low-order compact interpolation schemes to yield a high-order accurate, non-oscillatory reconstruction scheme with high spectral resolution. Previous studies by the authors have demonstrated the improved performance of the CRWENO scheme at preserving and resolving smooth and discontinuous flow features (for one- and two-dimensional flow problems), compared to the WENO scheme of the same order of convergence. In the present study, the CRWENO scheme is applied to the direct numerical simulation of benchmark turbulent flow problems. In particular, the decay of isotropic turbulence and the shock-turbulence interactions are studied and the results are presented. The solutions from the CRWENO scheme are compared with those in the literature, obtained using WENO schemes and compact schemes with filtering. [Preview Abstract] |
Tuesday, November 20, 2012 2:18PM - 2:31PM |
R5.00007: DNS of homogeneous turbulent shear flow using a hybrid Pseudospectral-WENO Method Parvez Sukheswalla, T. Vaithianathan, Lance Collins Pseudospectral-based direct numerical simulations (DNS) of homogeneous turbulent shear flow (HTSF) have been shown to inevitably suffer from numerical resolution problems that become more severe with increasing Reynolds number [Sukheswalla et al., in review]. The resulting Gibbs oscillations can be removed using low-pass spectral filters that stabilize the simulations and enable attainment of higher asymptotic Reynolds numbers. However, while low-pass filtering does not appear to impact large-scale statistics, it does compromise small-scale statistics such as vorticity, with unclear consequences on the overall dynamics over time. In this presentation, we put forth an alternative approach based on a hybrid DNS method, wherein a Weighted Essentially Non-oscillatory (WENO) scheme is used to compute the nonlinear convective term that is the primary source of the Gibbs oscillations, while a pseudospectral method is used for the other terms. The resulting hybrid scheme yields large- and small-scale statistics in good agreement with the experiments of Isaza et al. [\emph{Phys. Fluids} 21(6), 2009] and Gylfason et al. [\emph{J. Fluid Mech.} 501:213--229, 2004]. The effectiveness of the new scheme for the fluid velocity lays the groundwork for future DNS of inertial particles in HTSF. [Preview Abstract] |
Tuesday, November 20, 2012 2:31PM - 2:44PM |
R5.00008: A High Order Volume Penalty Method David Shirokoff, Jean-Christophe Nave The volume penalty method provides a simple, efficient approach for solving the incompressible Navier-Stokes equations in domains with boundaries or in the presence of moving objects. Despite the simplicity, the method suffers from poor convergence in the penalty parameter, thereby restricting accuracy of any numerical method. We demonstrate that one may achieve high order accuracy by altering the form of the penalty term. We discuss how to construct the modified penalty term, and provide 2D numerical examples demonstrating improved convergence for the heat equation and Navier-Stokes equations. [Preview Abstract] |
Tuesday, November 20, 2012 2:44PM - 2:57PM |
R5.00009: Assessing the Recovery-based Discontinuous Galerkin Method for Turbulence Simulations Aditya Nair, Eric Johnsen, Sreenivas Varadan The Discontinuous Galerkin (DG) method offers significant advantages over traditional finite difference and finite volume methods, such as high parallel scalability, portability to complex geometries and super-convergence. However, DG has yet to emerge as a viable option for turbulence simulations, due to the lack of a consistent and accurate diffusion scheme. Currently, orders of $p+1$ are achieved, where $p$ is the polynomial order within a cell. A promising approach is that of recovery, which has been shown to exhibit convergence rates up to $3p+2$ in one dimension. This technique is based on the idea of enhanced recovery, where the underlying solution is recovered over neighboring cells and appropriately enhanced in the face-tangential directions. We use several test problems (pure diffusion, Taylor-Green vortex) to show that we achieve the same convergence rates in multiple dimensions, and compare this approach to other common diffusion schemes. [Preview Abstract] |
Tuesday, November 20, 2012 2:57PM - 3:10PM |
R5.00010: Approach for robustly simulating supercritical fluid mixing with large density contrast using high-order schemes Hiroshi Terashima, Mitsuo Koshi We present a robust yet efficient approach for simulating supercritical fluid mixing with large density contrast using a high-order central differencing scheme. The present method is designed to maintain the pressure and velocity equilibriums at fluid interfaces for any type of discretization and equation of state: the pressure evolution equation is introduced for the pressure equilibrium and the numerical diffusion terms for the mass and momentum equations are consistently constructed for the velocity equilibrium. Thus, spurious oscillations possibly generated at interfaces are prevented, enabling robust applications of high-order schemes to severe thermodynamic fluid conditions. The consistent numerical diffusion term is also constructed for the species-mass conservation equation. Several examples of supercritical fluid problems such as interface advection and jet mixing problems demonstrate the robustness and superiority of the present method over a conventional conservative method. [Preview Abstract] |
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