Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session D32: Computational Fluid Dynamics: Time-Stepping with Split, Operator Splitting and Mesh AdaptingCFD
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Chair: Prakash Vedula, University of Oklahoma Room: 104 |
Sunday, November 19, 2017 2:15PM - 2:28PM |
D32.00001: Dedalus: A spectral solver for PDEs with diverse applications to CFD Keaton J Burns, Geoffrey M Vasil, Jeffrey S Oishi, Daniel Lecoanet, Benjamin P Brown Dedalus is an open-source framework for solving general partial differential equations with spectral methods. It is designed for maximum flexibility and incorporates features such as symbolic equation entry, custom domain construction, and automatic MPI parallelization. We will briefly describe key algorithmic features of the code, including our sparse discretization and multidimensional domain distribution. We will then discuss implementations of incompressible and compressible hydrodynamics using the Dedalus framework. For incompressible flow, we simultaneously solve for the pressure as a Lagrange multiplier enforcing the divergence-free constraint as we implicitly evolve the velocity field. This avoids operator splitting and allows for the use of high-order DAE timestepping methods. For compressible flows, we implement a mixed implicit-explicit formulation that allows us to implicitly timestep sound waves and efficiently simulate low-Mach-number but large-scale flows prevalent in astrophysics and atmospheric science. [Preview Abstract] |
Sunday, November 19, 2017 2:28PM - 2:41PM |
D32.00002: A Spectral Multi-Domain Penalty Method for Elliptic Problems Arising From a Time-Splitting Algorithm For the Incompressible Navier-Stokes Equations Theodore Diamantopoulos, Kristopher Rowe, Peter Diamessis The Collocation Penalty Method (CPM) solves a PDE on the interior of a domain, while weakly enforcing boundary conditions at domain edges via penalty terms, and naturally lends itself to high-order and multi-domain discretization. Such spectral multi-domain penalty methods (SMPM) have been used to solve the Navier-Stokes equations. Bounds for penalty coefficients are typically derived using the energy method to guarantee stability for time-dependent problems. The choice of collocation points and penalty parameter can greatly affect the conditioning and accuracy of a solution. Effort has been made in recent years to relate various high-order methods on multiple elements or domains under the umbrella of the Correction Procedure via Reconstruction (CPR). Most applications of CPR have focused on solving the compressible Navier-Stokes equations using explicit time-stepping procedures. A particularly important aspect which is still missing in the context of the SMPM is a study of the Helmholtz equation arising in many popular time-splitting schemes for the incompressible Navier-Stokes equations. Stability and convergence results for the SMPM for the Helmholtz equation will be presented. Emphasis will be placed on the efficiency and accuracy of high-order methods. [Preview Abstract] |
Sunday, November 19, 2017 2:41PM - 2:54PM |
D32.00003: Efficient Simulation of Compressible, Viscous Fluids using Multi-rate Time Integration Cory Mikida, Andreas Kloeckner, Daniel Bodony In the numerical simulation of problems of compressible, viscous fluids with single-rate time integrators, the global timestep used is limited to that of the finest mesh point or fastest physical process. This talk discusses the application of multi-rate Adams-Bashforth (MRAB) integrators to an overset mesh framework to solve compressible viscous fluid problems of varying scale with improved efficiency, with emphasis on the strategy of timescale separation and the application of the resulting numerical method to two sample problems: subsonic viscous flow over a cylinder and a viscous jet in crossflow. The results presented indicate the numerical efficacy of MRAB integrators, outline a number of outstanding code challenges, demonstrate the expected reduction in time enabled by MRAB, and emphasize the need for proper load balancing through spatial decomposition in order for parallel runs to achieve the predicted time-saving benefit. [Preview Abstract] |
Sunday, November 19, 2017 2:54PM - 3:07PM |
D32.00004: A Modified Consistent Splitting Scheme for Convective-Like Energy-Stable Open Boundary Conditions for Simulating Incompressible Outflows Sri Harsha Challa, Suchuan Dong We present a modified consistent splitting type scheme together with the recently-developed convective-like energy-stable open boundary condition for incompressible outflow simulations. The key distinction of the scheme is an algorithmic reformulation of the viscous term, which enables the simulation of outflow problems on severely-truncated flow domains at moderate to high Reynolds numbers. In contrast, it is observed that the standard consistent-splitting scheme exhibits a numerical instability even at fairly low Reynolds numbers (e.g. several hundred), and this numerical instability is in addition to the backflow instability commonly known to be associated with strong vortices or backflows at the outflow boundary. Extensive numerical experiments will be presented for a range of Reynolds numbers to demonstrate the effectiveness and accuracy of the presented method for this class of flows. [Preview Abstract] |
Sunday, November 19, 2017 3:07PM - 3:20PM |
D32.00005: Comparing Split and Unsplit Numerical Methods for Simulating Low and High Mach Number Turbulent Flows in Xrage Juan Saenz, Fernando Grinstein, Joshua Dolence, Rick Rauenzahn, Thomas Masser, Marianne Francois We report progress in evaluating an unsplit hydrodynamic solver being implemented in the radiation adaptive grid Eulerian (xRAGE) code, and compare to a split scheme. xRage is a Eulerian hydrodynamics code used for implicit large eddy simulations (ILES) of multi-material, multi-physics flows where low and high Mach number (Ma) processes and instabilities interact and co-exist. The hydrodynamic solver in xRAGE uses a directionally split, second order Godunov, finite volume (FV) scheme. However, a standard, unsplit, Godunov-type FV scheme with 2nd and 3rd order reconstruction options, low Ma correction and a variety of Riemann solvers has recently become available. To evaluate the hydrodynamic solvers for turbulent low Ma flows, we use simulations of the Taylor Green Vortex (TGV), where there is a transition to turbulence via vortex stretching and production of small-scale eddies. We also simulate a high-low Ma shock-tube flow, where a shock passing over a perturbed surface generates a baroclinic Richtmyer--Meshkov instability (RMI); after the shock has passed, the turbulence in the accelerated interface region resembles Rayleigh Taylor (RT) instability. We compare turbulence spectra and decay in simulated TGV flows, and we present progress in simulating the high-low Ma RMI-RT flow. [Preview Abstract] |
Sunday, November 19, 2017 3:20PM - 3:33PM |
D32.00006: A Characteristic-Based, Spectral Element Method for Moving-Domain Problems Saumil Patel, Paul Fischer, Ananias Tomboulides, Misun Min In this paper, we present a characteristic-based numerical procedure for simulations of incompressible flows in domains with moving boundaries. Our approach utilizes an operator-integration-factor splitting (OIFS) technique to help produce an efficient and stable numerical scheme. Using the spectral element method (SEM) and an arbitrary Lagrangian-Eulerian (ALE) formulation, we investigate flows where the convective acceleration effects are non-negligible. Several examples, ranging from laminar to turbulent flows, are considered. Comparisons with a standard, semi-implicit time-stepping procedure illustrate the improved performance of the scheme. [Preview Abstract] |
Sunday, November 19, 2017 3:33PM - 3:46PM |
D32.00007: Flexibly imposing periodicity in kernel independent FMM: A Multipole-To-Local operator approach Wen Yan, Michael Shelley An important but missing component in the application of the kernel independent fast multipole method (KIFMM) is the capability for imposing singly, doubly, and triply periodic boundary conditions. In most popular packages such periodicities are imposed with the hierarchical repetition of periodic boxes, which may give an incorrect answer due to the conditional convergence of some kernel sums. Here we present an efficient method to properly impose periodic boundary conditions using a near-far splitting scheme. The near-field contribution is directly calculated with the KIFMM method, while the far-field contribution is calculated with a multipole-to-local operator which is independent of the source and target point distribution. This new method is designed to observe the same $\mathcal{O}(N)$ complexity as KIFMM and to have small cost by reusing the data computed by KIFMM for the near-field. We present accuracy and timing test results for the Laplace kernel with single periodicity and the Stokes velocity kernel with double and triple periodicity. We further present applications of this method in the study of wall-bounded Stokes flow and the active stress of cytoplasmic suspensions. [Preview Abstract] |
Sunday, November 19, 2017 3:46PM - 3:59PM |
D32.00008: Level-Set Methodology on Adaptive Octree Grids Frederic Gibou, Arthur Guittet, Mohammad mirzadeh, Maxime Theillard Numerical simulations of interfacial problems in fluids require a methodology capable of tracking surfaces that can undergo changes in topology and capable to imposing jump boundary conditions in a sharp manner. In this talk, we will discuss recent advances in the level-set framework, in particular one that is based on adaptive grids. [Preview Abstract] |
Sunday, November 19, 2017 3:59PM - 4:12PM |
D32.00009: A Strategy to Reduce Numerical Oscillations by Aggressive Grid Stretching Haosen Xu, Xiang Yang Unphysical numerical oscillations arise in CFD calculations where~central difference schemes are~used~along with coarse grids. Often used remedies for such unphysical oscillations include filtering,~upwind schemes~and grid stretching/compression. While the former two approaches are known to be overly dissipative,~the latter can~many times be~expensive. In this work, we attempt to find~an optimal~mesh deployment. While~it is conventional acknowledged that~more grid points are to be used in regions where unphysical numerical oscillations are detected, our approach requires only one single refined grid in regions where drastic~acceleration/deceleration occurs, and numerical oscillations in the bulk region~are~suppressed without further mesh refinements there. The proposed grid stretching strategy is then tested in several flow~configurations, including two- and three-dimensional lid driven cavity, flow passing wall-mounted cubes, flow passing~two-/three-dimensional objects.~Two-grid-spacing~oscillations are found to be substantially suppressed in all cases. Possible use of this strategy may be in adaptive-mesh-refinement, where nowadays more grid points are immediately used~wherever the spatial gradients of, e.g., velocity~is large. [Preview Abstract] |
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