Bulletin of the American Physical Society
63rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 55, Number 16
Sunday–Tuesday, November 21–23, 2010; Long Beach, California
Session AD: CFD: Algorithms I |
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Chair: Carlos Pantano, University of Illinois at Urbana-Champaign Room: Long Beach Convention Center 102B |
Sunday, November 21, 2010 8:00AM - 8:13AM |
AD.00001: Incompact3d: a powerful tool to tackle turbulence problems with up to hundreds of thousands computational cores Sylvain Laizet, Ning Li Understanding the nature of complex turbulent flows remains one of the most challenging problems in classical physics. Significant progress has been made recently using High Performance Computing, and Computational Fluid Dynamics is now a credible alternative to experiments and theories in order to understand the rich physics of turbulence. In this work, we present an efficient numerical tool called ``Incompact3d'' that can be coupled with massive parallel platforms in order to simulate turbulence problems with as much complexity as possible, using up to hundreds of thousands computational cores by means of Direct Numerical Simulation. ``Incompact3d,'' that solved the incompressible Navier-Stokes equation, is a finite-difference code (sixth order schemes in space) that can be combined with an Immersed Boundary Method (IBM) in order to simulate flow with complex geometry. The originality of this code is that the Poisson equation is solve in the spectral space in the framework of the modified wave number. We will demonstrate that ``Incompact3d'' is a powerful tool that can undertake DNS with up to hundreds of thousands computational cores thanks to an efficient 2D domain decomposition. [Preview Abstract] |
Sunday, November 21, 2010 8:13AM - 8:26AM |
AD.00002: A spectral multidomain penalty method model for high Reynolds number incompressible flows Jorge Escobar-Vargas, Peter Diamessis We present the latest results of a spectral multidomain penalty method-based incompressible Navier Stokes solver for high Reynolds number stratified turbulent flows in doubly non-periodic domains that is currently under development. Time is discretized with a high-order stiffly stable scheme, whereas space is discretized with a Gauss-Lobatto-Legendre collocation approach in discontinuous quadrilateral subdomains. Numerical stability is guaranteed through a penalty scheme, spectral filtering and dealiasing techniques. The Poisson system of equations that arises from the temporal discretization is analyzed in detail as well as different preconditioning strategies to solve it efficiently, such as Kronecker product, deflation, multigrid, Jacobi, and finite difference based techniques. The efficiency and accuracy of the Navier Stokes solver are assessed through the solution of the driven cavity flow, Taylor vortex, and Couette flow. [Preview Abstract] |
Sunday, November 21, 2010 8:26AM - 8:39AM |
AD.00003: An efficient method for the incompressible Navier-Stokes equations on irregular domains with no-slip boundary conditions, high order up to the boundary David Shirokoff, Ruben Rosales Common efficient schemes for the incompressible Navier-Stokes equations, such as projection or fractional step methods, have limited temporal accuracy as a result of matrix splitting errors, or introduce errors near the domain boundaries, resulting in weakly convergent solutions. We recast the Navier-Stokes incompressibility constraint as a pressure Poisson equation with velocity dependent boundary conditions. Applying the remaining velocity boundary conditions to the momentum equation, we obtain a pair of equations, for the primary variables velocity and pressure, equivalent to the incompressible Navier-Stokes. Since in this recast system the pressure can be efficiently recovered from the velocity, this reformulation is ideal for numerical marching methods. The equations can be discretized using a variety of methods, in principle to any desired order of accuracy. In this work we illustrate the approach with a 2-D second order finite difference scheme on a Cartesian grid, and devise an algorithm to solve the equations on domains with curved (non-conforming) boundaries, including a case with a non-trivial topology (a circular obstruction inside the domain). This algorithm achieves second order accuracy in the $L^{\infty}$ norm for both the velocity and the pressure. The scheme has a natural extension to 3-D. [Preview Abstract] |
Sunday, November 21, 2010 8:39AM - 8:52AM |
AD.00004: A Finite-Volume ADI Method for Simulation of Incompressible Flows on Curvilinear Grids Satbir Singh, Donghyun You A second-order accurate finite-volume-based alternating direction implicit (ADI) method is proposed for the solution of incompressible Navier-Stokes equations on structured curvilinear meshes. Numerical accuracy and stability at high Reynolds numbers are achieved with the selection of the discrete operators and solution algorithms which assure discrete kinetic energy conservation in the inviscid limit. Unlike the conventional finite-difference-based ADI schemes, in which the factorization is performed along the transformed generalized-coordinate directions, in the proposed method, the discretized equations are factored along the curvilinear mesh lines without coordinate transformation. The accuracy, stability, and efficiency of the proposed method are assessed in simulations of an unsteady convection-diffusion equation on Cartesian and skewed meshes, and simulations of lid- driven cavity flow, flow over a circular cylinder, and turbulent channel flow. In the proposed method, the computational cost required for the solution of momentum equations is found to be 3 to 5 times smaller than that required when a bi-conjugate gradient stabilized (BCGSTAB) iterative method is employed. [Preview Abstract] |
Sunday, November 21, 2010 8:52AM - 9:05AM |
AD.00005: Discretely conservative, non-dissipative, and stable collocated method for solving the incompressible Navier-Stokes equations Reetesh Ranjan, Carlos Pantano We present a new method for solving the incompressible Navier-Stokes equations. The method utilizes a collocated arrangement of all variables in space. It uses centered second-order accurate finite-difference approximations for all spatial derivatives and a third-order IMEX approach for time integration. The proposed method ensures discrete conservation of mass and momentum by discretizing the conservative form of the equations from the outset and never relying on continuum relations afterward. This ensures uniform high order of accuracy in time for all fields, including pressure. The pressure-momentum coupled equations can be easily segregated and solved sequentially, as in the pressure projection method but without a splitting error. In this approach there are no spurious kernel modes, checkerboard, in the embedded elliptic pressure problem. The method has been applied to different canonical problems, including a fully periodic box, a periodic channel, an inflow-outflow channel and a lid-driven cavity flow. Near wall boundaries, spatial derivatives are obtained using the weak form of the conservation equations, similar to a finite element approach. The results from some of the sample cases will be presented to illustrate the features of the method. [Preview Abstract] |
Sunday, November 21, 2010 9:05AM - 9:18AM |
AD.00006: Robust and accurate finite volume method on highly skewed unstructured meshes Hyunchul Jang, Krishnan Mahesh Geometric complexity often causes highly skewed meshes, which can affect stability and accuracy of numerical scheme. It is well known that the accuracy of numerical methods degrades rapidly with increase of internal angles in skewed elements. A regularized least squared method with multi-dimensional slope limiters is derived for convective flux reconstruction. Two deferred correction methods are also derived for diffusive flux reconstruction and the Poisson equation. Those methods show considerable improvement and converge even on highly skewed meshes. Also, the second-order accuracy is held with those methods on both of mildly and highly skewed meshes. This numerical method is applied to a realistic complex problem such as the large eddy simulation for marine propulsor in an extreme operating condition. This work is supported by the United States Office of Naval Research under ONR Grant N00014-02-1-0978. [Preview Abstract] |
Sunday, November 21, 2010 9:18AM - 9:31AM |
AD.00007: Large Eddy Simulation of Flow Over Surface-Mounted Cube Using a Spectral Element Method Sriharsha Kandala, Dietmar Rempfer Unsteady three dimensional flow over a surface-mounted cube, with its rich set of features like flow turbulence, upstream boundary layer separation, curved mixing layer, unsteady three dimensional wake, etc., provides an excellent test case for evaluating the performance of CFD codes. We are developing a parallel spectral element code, SpecSolve, with the objective of modeling incompressible flows in complex geometries. The code is based on the fractional step method and uses the operator-integrating factor splitting scheme for temporal integration. In this talk, we provide a brief overview of the algorithm and implementation details. We present results from large-eddy simulations of flow over a surface-mounted cube using SpecSolve. The Reynolds number, based on bulk flow velocity and height of the cube, is 40,000. The dynamic Smagorinsky model is used for modeling turbulence. These results are compared with experimental data of Martinuzzi and Tropea, LES results of Shah and Ferziger and our FLUENT LES simulations. [Preview Abstract] |
Sunday, November 21, 2010 9:31AM - 9:44AM |
AD.00008: A time-stepping scheme for flow simulations that allows the use of large time step sizes Steven Dong We present a time-stepping scheme for incompressible Navier-Stokes equations that allows the use of time step sizes considerably larger than the commonly used semi-implicit type schemes. The scheme is based on a velocity correction type formulation, and involves only linear algebraic equations after discretization. Moreover, the computations of the velocity and pressure are decoupled. The proposed scheme and the semi-implicit scheme will be compared with several numerical problems. [Preview Abstract] |
Sunday, November 21, 2010 9:44AM - 9:57AM |
AD.00009: Accurate Solution of Steady Navier--Stokes System in Unbounded Domains Jonathan Gustafsson, Bartosz Protas A long--term goal of this research is to accurately compute solutions of the steady Navier--Stokes equations in unbounded domains and identify the Euler flows arising as limits when $Re \rightarrow \infty$. Motivated by results in the mathematical literature on the ``Physically Reasonable'' solutions (Finn \& Smith, 1967), we ensure our solutions are characterized by a suitable rate of decay at infinity. Since this cannot be achieved in classical CFD methods based on a truncation of the infinite domain to a finite ``computational box'', we propose an alternative approach in which the Navier--Stokes equation is rewritten as a perturbation to the Oseen equations whose solutions are determined in a semi--analytic form. The resulting problem is discretized using a combination of Fourier--Galerkin and tau--collocation method based on the rational Chebyshev functions. We will present results showing how the wake structure changes with increasing Reynolds number. [Preview Abstract] |
Sunday, November 21, 2010 9:57AM - 10:10AM |
AD.00010: Variational integrator preserving Lie-symmetry Marx Chhay Many physical systems can be expressed with a Lagrangian formalism. The underlying role of the variational symmetries occurring in the computation of the dynamics equation reveals the intrinsic conservation properties of the system. For numerical design, it is well-known that the discrete version of the variational derivation of finite dimensional time independent Lagrangian systems yields a symplectic integrator that preserves exactly the discrete energy when the time step is considered as a variable. But it is not enough for the integrator to preserve the other conservation laws. Indeed the discrete Lagrangian must also be invariant under the variational symmetries. Such Lie-symmetry variational integrators can be constructed thanks to the concept of moving frames. Numerical properties are shown on academic examples. [Preview Abstract] |
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