Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session A31: Discontinuous Galerkin and High Order Methods |
Hide Abstracts |
Chair: Matthias Ihme, Stanford University Room: Georgia World Congress Center B403 |
Sunday, November 18, 2018 8:00AM - 8:13AM |
A31.00001: An Euler-Lagrange formulation for simulating high-speed dusty flows using discontinuous Galerkin schemes Eric Ching, Steven Brill, Yu Lv, Matthias Ihme This works presents an Euler-Lagrange formulation for simulating particle-laden flows using discontinuous Galerkin schemes. The method uses a mesoscopic modeling approach in which particles are tracked as point sources while the carrier gas is described using an Eulerian field. We discuss an efficient tracking algorithm that not only locates the host element of a particle for subsequent interpolation of the carrier gas state but also accurately detects particle-wall collisions and computes post-collision trajectories. The algorithm is well-suited for curved, high-aspect-ratio elements. A series of test cases is presented that assesses the accuracy of the method on high-order spatial discretizations. Emphasis is placed on application of the method to investigate surface heat flux augmentation in hypersonic dusty flows over blunt bodies. We examine the importance of various forcing terms, drag correlations, and Nusselt number correlations in the particle momentum and energy equations for these types of flows. Quantitative comparisons with experiments are provided. |
Sunday, November 18, 2018 8:13AM - 8:26AM |
A31.00002: A Fast High-Order Solver For Stratified Flows on Massively Multi-cored Architectures Kristopher Rowe, Peter Diamessis, Greg Thomsen The simulation of high Reynolds number stratified flows has important oceanographic and atmospheric applications. In many flows the presence of strongly stratified turbulence leads to the formation of thin horizontal regions of high shear, necessitating the use of high resolution non-uniform grids in the vertical. Additionally, long-time integrations are required as fluid motions persist for much greater durations than their unstratified counterparts. We will present a fast, high-order solver for stratified flows utilizing a Fourier pseudo-spectral method in the horizontal and a spectral element discretization in the vertical. An IMEX time-splitting scheme is used, requiring the solution of several 1D Helmholtz equations during each time-step. Ultraspherical polynomial basis functions in combination with static condensation subsequently result in a large number of small tridiagonal systems, and hence an algorithm that is as inexpensive as second-order finite difference schemes. Many levels of coarse and fine grain parallelism are exploited to achieve optimal performance on massively multi-cored processors, which are prevalent in today’s high-performance computing environment. Simulations of a stratified turbulent wake are used as a numerical example. |
Sunday, November 18, 2018 8:26AM - 8:39AM |
A31.00003: A path-conservative DG formulation for large-eddy simulations of reacting and multi-physics flows Yu Lv, Yuan Liu, Xiang Yang The present study proposes a new DG formulation to address the numerical issues associated with the application of DG scheme to flow problems with complex thermodynamic models. Specifically, the proposed formulation solves an auxiliary pressure variable, of which the governing equation is derived based on the equation of state (EoS) and the consistent LES-filtering. As a result, the LES-resolved pressure is obtained by solving a time-dependent PDE, instead of inversion based directly on the EoS that introduces formulation inconsistency and large modeling errors in the context of LES. The proposed method is firstly validated by considering a set of homogeneous isotropic turbulence cases. The advantages of the proposed numerical treatment will be highlighted in the comparison between LES results obtained using both the new and classical EoS-based formulations. Finally, the capability of the proposed method will be demonstrated in the application to the simulation of a turbulent jet flame. |
Sunday, November 18, 2018 8:39AM - 8:52AM |
A31.00004: A Nodal Spectral Element Method for the Simulation of Internal Solitary Waves Over an Actual Bathymetry. Theodore Diamantopoulos, Kristopher Rowe, Peter Diamessis, Greg Thomsen Internal Solitary Waves (ISW) are large amplitude internal waves which travel with relatively unchanging form, playing an important role in near-shelf energetics and transporting salt, heat, and nutrients into shallower coastal waters. Much remains unknown about ISWs and accurate numerical modelling of such waves using realistic bathymetry can provide insight. The existence of an ISW is a precarious balance between dispersive and nonlinear effects, therefore the use of a high-order numerical methods is imperative. The Nodal Spectral Element Method has been used extensively for the solution of the Incompressible Navier-Stokes equations in complex geometries. Realistic ocean bathymetry has a high-aspect ratio, causing great difficulty in the solution of elliptic problems arising in many time-splitting. One approach to mitigate this difficulty is static condensation. The degrees of freedom on each spectral element are reduced to a smaller system on the interfaces between elements with improved conditioning. Subsequently, independent solves are performed for the degrees of freedom on the spectral element interiors, leading to a highly parallelizable algorithm. The efficacy of this method will be demonstrated by solving numerically the Helmholtz problem. |
Sunday, November 18, 2018 8:52AM - 9:05AM |
A31.00005: Variational Multiscale SGS modeling for LES using high-order Discontinuous Galerkin method. Kihiro Bando, Fabio Naddei, Marta de la Llave Plata, Matthias Ihme High-order methods for the simulation of turbulent flows have gained significant attention for their attractive numerical dissipative and dispersive properties. Among others, the Discontinuous Galerkin (DG) method has been the focus of active research. One of the main challenges of using DG methods for Large Eddy Simulations (LES) is the solution stabilization on underresolved meshes. Recently, an entropy-bounded scheme has been proposed for the solution stabilization in the context of Implicit LES (ILES). In contrast, the Variational Multiscale (VMS) formulation exploits the flexibility and |
Sunday, November 18, 2018 9:05AM - 9:18AM |
A31.00006: A Compact Recovery-Assisted DG Method for Advection-Diffusion Problems Philip Johnson, Eric Johnsen We propose an improved discontinuous Galerkin (DG) spatial discretization for advection-diffusion problems. Our approach makes use of our improved schemes for diffusive (Compact Gradient Recovery, CGR) and advective (Interface-Centered Binary reconstruction, ICB) fluxes. Compared to conventional DG methods, our new approach offers improved accuracy and larger allowable timestep sizes when explicit time integration is employed. However, unlike other accuracy-enhancing schemes for DG, our approach maintains a compact, nearest-neighbors stencil. Superior performance is facilitated via careful use of the Recovery concept: the CGR method benefits from the accuracy of the Recovery concept without requiring differentiation of the recovered polynomial, while the ICB method makes use of biased recovered solutions at each interface to maintain stability. We will further demonstrate how the recovered solution at an element-element interface can be recast as a set of derivative-based penalty terms. Fourier analysis and compressible Navier-Stokes test problems will be presented to demonstrate our new DG approach. |
Sunday, November 18, 2018 9:18AM - 9:31AM |
A31.00007: An Enriched Discontinuous Galerkin Method for Representing High-Gradient Features in Fluid Dynamics Steven R. Brill, Matthias Ihme Discontinuous Galerkin (DG) methods have difficulty resolving high gradient solutions, such as shocks and boundary layers, without stabilization to remove spurious oscillations or significant mesh refinement in regions of high-gradient feature. We present a DG scheme that enriches the standard basis polynomials with analytical solutions to canonical problems. This strategy allows one to capture large gradient features without spurious oscillations or significant mesh refinement, while also retaining the higher order accuracy of the scheme. We discuss the procedure to choose the analytical enrichment functions and integrate them into the DG framework. The method is evaluated in application to fluid dynamics problems with high gradient solutions, such as boundary layers and transient shock-flow interaction. |
Sunday, November 18, 2018 9:31AM - 9:44AM |
A31.00008: A Foundation for High-Order Cut-cell Methods: Stable Derivatives on Degenerate Meshes Peter Brady, Daniel Livescu Cut-cell methods for unsteady flow problems can greatly simplify the grid generation process and allow for high-fidelity simulations on complex geometries. However, cut-cell methods have been limited to low orders of accuracy. This is driven, largely, by the variety of procedures typically introduced to evaluate derivatives in a stable manner near the highly irregular embedded geometry. In the present work, a completely new approach is taken to solve this problem. The approach is based on two simple and intuitive design principles. These principles, and an a-priori optimization process, allow for the construction of stable 8th order approximations to elliptic and parabolic problems and stable and conservative 5th order approximations to hyperbolic problems. This is done for both explicit and compact finite differences and is accomplished without any geometric transformations or artificial stabilization procedures. |
Sunday, November 18, 2018 9:44AM - 9:57AM |
A31.00009: A Deep Neural Network-Based Shock Capturing Method Benjamin C Stevens, Timothy E Colonius Deep neural networks (DNN’s) have the ability to approximate extremely complicated nonlinear functions. Due to their flexibility, DNN’s present a promising solution to developing highly accurate shock-capturing methods. Because shock capturing methods, such as WENO5, often make use of complicated nonlinear functions that are hand designed to accurately predict weak solutions to hyperbolic conservation laws, we teach a DNN to approximate the best possible nonlinear function to avoid relying on human intuition in the design of the numerical scheme. We structure the model as a directed acyclic graph network to embed arbitrarily high orders of accuracy into the solution that the DNN outputs. Additionally, a convolutional layer is used to reduce the dimensionality of the network, since the derivative can be computed using only local information. We also explore training the DNN using a recurrent architecture to optimize the model weights such that long-term error is minimized and stable solutions are encouraged. |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2024 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700