Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session R7: CFD: Algorithms |
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Chair: Joseph Powers, University of Notre Dame Room: 107 |
Tuesday, November 24, 2015 12:50PM - 1:03PM |
R7.00001: Physical diffusion suppresses the carbuncle instability Ke Shi, Aleksander Jemcov, Joseph Powers We demonstrate a simple antidote exists to the numerical carbuncle instability predicted by some shock-capturing schemes: inclusion of physical momentum and energy diffusion via a compressible Navier-Stokes solution to the supersonic flow of a calorically perfect ideal gas past a circular cylinder. We demonstrate the carbuncle phenomenon and its rectification by solving two problems. Both employ the same geometry, initial conditions, computational grid, time step size, advective flux model of a Roe-based scheme without an entropy fix, and time-advancement scheme. For the first problem, we neglect physical diffusion, while for the second we include it. When physical diffusion is neglected, we predict a carbuncle phenomenon; however, when it is included and sufficiently resolved, no carbuncle is predicted, in agreement with experiment. [Preview Abstract] |
Tuesday, November 24, 2015 1:03PM - 1:16PM |
R7.00002: Diablo 2.0: A modern DNS/LES code for the incompressible NSE leveraging new time-stepping and multigrid algorithms Daniele Cavaglieri, Thomas Bewley, Ali Mashayek We present a new code, Diablo 2.0, for the simulation of the incompressible NSE in channel and duct flows with strong grid stretching near walls. The code leverages the fractional step approach with a few twists. New low-storage IMEX (implicit-explicit) Runge-Kutta time-marching schemes are tested which are superior to the traditional and widely-used CN/RKW3 (Crank-Nicolson/Runge-Kutta-Wray) approach; the new schemes tested are L-stable in their implicit component, and offer improved overall order of accuracy and stability with, remarkably, similar computational cost and storage requirements. For duct flow simulations, our new code also introduces a new smoother for the multigrid solver for the pressure Poisson equation. The classic approach, involving alternating-direction zebra relaxation, is replaced by a new scheme, dubbed tweed relaxation, which achieves the same convergence rate with roughly half the computational cost. The code is then tested on the simulation of a shear flow instability in a duct, a classic problem in fluid mechanics which has been the object of extensive numerical modelling for its role as a canonical pathway to energetic turbulence in several fields of science and engineering. [Preview Abstract] |
(Author Not Attending)
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R7.00003: Integral Method for the Assessment of U-RANS Effectiveness in Non-Equilibrium Flows and Heat Transfer Ian Pond, Alireza Ebadi, Yves Dubief, Christopher White Reynolds Average Navier Stokes (RANS) modeling has established itself as a critical design tool in many engineering applications, thanks to its superior computational efficiency. The drawbacks of RANS models are well known, but not necessarily well understood: poor prediction of transition, non equilibrium flows, mixing and heat transfer, to name the ones relevant to our study. In the present study, we use a DNS of a reciprocating channel flow driven by an oscillating pressure gradient to test several low- and high-Reynolds RANS models. Temperature is introduced as a passive scalar to study heat transfer modeling. Low-Reynolds models manage to capture the overall physics of wall shear and heat flux well, yet with some phase discrepancies, whereas high Reynolds models fail. Under the microscope of the integral method for wall shear and wall heat flux, the qualitative agreement appears more serendipitous than driven by the ability of the models to capture the correct physics. The integral method is shown to be more insightful in the benchmarking of RANS models than the typical comparisons of statistical quantities. [Preview Abstract] |
Tuesday, November 24, 2015 1:29PM - 1:42PM |
R7.00004: A coarse-grid-projection acceleration method for finite-element incompressible flow computations Ali Kashefi, Anne Staples Coarse grid projection (CGP) methodology provides a framework for accelerating computations by performing some part of the computation on a coarsened grid. We apply the CGP to pressure projection methods for finite element-based incompressible flow simulations. Based on it, the predicted velocity field data is restricted to a coarsened grid, the pressure is determined by solving the Poisson equation on the coarse grid, and the resulting data are prolonged to the preset fine grid. The contributions of the CGP method to the pressure correction technique are twofold: first, it substantially lessens the computational cost devoted to the Poisson equation, which is the most time-consuming part of the simulation process. Second, it preserves the accuracy of the velocity field. The velocity and pressure spaces are approximated by Galerkin spectral element using piecewise linear basis functions. A restriction operator is designed so that fine data are directly injected into the coarse grid. The Laplacian and divergence matrices are driven by taking inner products of coarse grid shape functions. Linear interpolation is implemented to construct a prolongation operator. A study of the data accuracy and the CPU time for the CGP-based versus non-CGP computations is presented. [Preview Abstract] |
Tuesday, November 24, 2015 1:42PM - 1:55PM |
R7.00005: High-order provably stable overset grid methods for hyperbolic problems, with application to the Euler equations Nek Sharan, Carlos Pantano, Daniel Bodony Overset grids provide an efficient and flexible framework to implement high-order finite difference methods for simulations of compressible viscous flows over complex geometries. However, prior overset methods were not provably stable and were applied with artificial dissipation in the interface regions. We will discuss new, provably time-stable methods for solving hyperbolic problems on overlapping grids. The proposed methods use the summation-by-parts (SBP) derivative approximations coupled with the simultaneous-approximation-term (SAT) methodology for applying boundary conditions and interface treatments. The performance of the methods will be assessed against the commonly-used approach of injecting the interpolated data onto each grid. Numerical results will be presented to confirm the stability and the accuracy of the methods for solving the Euler equations. The extension of these methods to solve the Navier-Stokes equations on overset grids in a time-stable manner will be briefly discussed. [Preview Abstract] |
Tuesday, November 24, 2015 1:55PM - 2:08PM |
R7.00006: Study of time-accurate integration of the variable-density Navier-Stokes equations Xiaoyi Lu, Carlos Pantano We present several theoretical elements that affect time-consistent integration of the low-Mach number approximation of variable-density Navier-Stokes equations. The goal is for velocity, pressure, density, and scalars to achieve uniform order of accuracy, consistent with the time integrator being used. We show examples of second-order (using Crank-Nicolson and Adams-Bashforth) and third-order (using additive semi-implicit Runge-Kutta) uniform convergence with the proposed conceptual framework. Furthermore, the consistent approach can be extended to other time integrators. In addition, the method is formulated using approximate/incomplete factorization methods for easy incorporation in existing solvers. One of the observed benefits of the proposed approach is improved stability, even for large density difference, in comparison with other existing formulations. A linearized stability analysis is also carried out for some test problems to better understand the behavior of the approach. [Preview Abstract] |
Tuesday, November 24, 2015 2:08PM - 2:21PM |
R7.00007: Spatially-Anisotropic Parallel Adaptive Wavelet Collocation Method Oleg V. Vasilyev, Eric Brown-Dymkoski Despite latest advancements in development of robust wavelet-based adaptive numerical methodologies to solve partial differential equations, they all suffer from two major ``curses'': 1) the reliance on rectangular domain and 2) the ``curse of anisotropy'' (i.e. homogeneous wavelet refinement and inability to have spatially varying aspect ratio of the mesh elements). The new method addresses both of these challenges by utilizing an adaptive anisotropic wavelet transform on curvilinear meshes that can be either algebraically prescribed or calculated on the fly using PDE-based mesh generation. In order to ensure accurate representation of spatial operators in physical space, an additional adaptation on spatial physical coordinates is also performed. It is important to note that when new nodes are added in computational space, the physical coordinates can be approximated by interpolation of the existing solution and additional local iterations to ensure that the solution of coordinate mapping PDEs is converged on the new mesh. In contrast to traditional mesh generation approaches, the cost of adding additional nodes is minimal, mainly due to localized nature of iterative mesh generation PDE solver requiring local iterations in the vicinity of newly introduced points. [Preview Abstract] |
Tuesday, November 24, 2015 2:21PM - 2:34PM |
R7.00008: A Fully Conservative and Entropy Preserving Cut-Cell Method for Incompressible Viscous Flows on Staggered Cartesian Grids Vincent Le Chenadec, Yong Yi Bay The treatment of complex geometries in Computational Fluid Dynamics applications is a challenging endeavor, which immersed boundary and cut-cell techniques can significantly simplify by alleviating the meshing process required by body-fitted meshes. These methods also introduce new challenges, in that the formulation of accurate and well-posed discrete operators is not trivial. A cut-cell method for the solution of the incompressible Navier-Stokes equation is proposed for staggered Cartesian grids. In both scalar and vector cases, the emphasis is set on the structure of the discrete operators, designed to mimic the properties of the continuous ones while retaining a nearest-neighbor stencil. For convective transport, different forms are proposed (divergence, advective and skew-symmetric), and shown to be equivalent when the discrete continuity equation is satisfied. This ensures mass, momentum and kinetic energy conservation. For diffusive transport, conservative and symmetric operators are proposed for both Dirichlet and Neumann boundary conditions. Symmetry ensures the existence of a sink term (viscous dissipation) in the discrete kinetic energy budget, which is beneficial for stability. The accuracy of method is finally assessed in standard test cases. [Preview Abstract] |
Tuesday, November 24, 2015 2:34PM - 2:47PM |
R7.00009: Characteristic-based Volume Penalization Method for Arbitrary Mach Flows Around Moving and Deforming Complex Geometry Obstacles Nurlybek Kasimov, Eric Brown-Dymkoski, Oleg V. Vasilyev A novel volume penalization method to enforce immersed boundary conditions in Navier-Stokes and Euler equations is presented. Previously, Brinkman penalization has been used to introduce solid obstacles modeled as porous media, although it is limited to Dirichlet-type conditions on velocity and temperature. This method builds upon Brinkman penalization by allowing Neumann conditions to be applied in a general fashion. Correct boundary conditions are achieved through characteristic propagation into the thin layer inside of the obstacle. Inward pointing characteristics ensure nonphysical solution inside the obstacle does not propagate outside to the fluid. Dirichlet boundary conditions are enforced similarly to Brinkman method. Penalization parameters act on a much faster timescale than the characteristic timescale of the flow. Main advantage of the method is systematic means of the error control. This talk is focused on the progress that was made towards the extension of the method to the 3D flows around irregular shapes. [Preview Abstract] |
Tuesday, November 24, 2015 2:47PM - 3:00PM |
R7.00010: Implementing Multiscale Fluid Simulations using Multiscale Universal Interface Yu-Hang Tang, Shuhei Kudo, Xin Bian, Zhen Li, George Karniadakis The power of multiscale fluid simulations lies in its ability to recover a hierarchical levels of details by choreographing multiple solvers, thus extending the length and time scale accessible given a fixed amount of computing power. However, practical difficulties frequently arise when stitching together solvers which were not designed to be coupled, and would often result in tedious and unsustainable coding effort. The Multiscale Universal Interface (MUI) aims to solve this problem by exposing a small set of generalized programming interfaces that can be dropped into existing solvers with minimal intrusion. Three deployment cases will be given for demonstrating real-world applications of MUI. In the first case we used MUI to implement simulations of polymer-grafted surface in flow using Smoothed Particle Hydrodynamics/Dissipative Particle Dynamics (SPH/DPD) and state variable coupling. In the second case we constructed coupled DPD/Finite Element Method (FEM) simulation of conjugate heat transfer in heterogeneous coolant. In the third case we built hybrid DPD/molecular dynamics (MD) simulations by blending the forces on atoms at interface regions. [Preview Abstract] |
Tuesday, November 24, 2015 3:00PM - 3:13PM |
R7.00011: A low-dissipation numerical scheme on Voronoi grids for complex geometries Frank Ham, Sanjeeb Bose, Babak Hejazi, Varun Mittal The generation of high quality meshes in complex geometries suitable for multi-scale computations remains difficult and cumbersome. Inevitably, the lack of regularity, skewness, or other undesirable mesh features leads to compromises in the numerical scheme where either accuracy is sacrificed or dissipation is introduced. Reliance on scheme switching based on grid quality complicates grid convergence, especially when utilizing local refinement. We introduce an alternative strategy where the computational meshes are built from the Voronoi diagram of a prescribed point cloud. The use of the Voronoi diagram naturally leads to a mesh with inherent quality (e.g., alignment of face normals and site displacement vectors). Moreover, because the Voronoi diagram is defined uniquely from a set of points, mesh regularity can be achieved from either proper packing of the generating sites or by straightforward mesh smoothing. The efficiency (of both the diagram generation and solution), convergence, and solution quality will be illustrated using canonical and applied configurations. [Preview Abstract] |
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