Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session R27: CFD: Discontinuous Galerkin and Higher Order Schemes |
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Chair: Shervin Sammak, University of Pittsburgh Room: E147-148 |
Tuesday, November 22, 2016 1:30PM - 1:43PM |
R27.00001: A New Discontinuous Galerkin Method for Convection-Diffusion Problems: The Gradient-Recovery DG Method Philip Johnson, Eric Johnsen The Discontinuous Galerkin (DG) numerical method, while well-suited for hyperbolic PDE systems such as the Euler equations, is not naturally competitive for convection-diffusion systems, such as the Navier-Stokes equations. Where the DG weak form of the Euler equations depends only on the field variables for calculation of numerical fluxes, the traditional form of the Navier-Stokes equations requires calculation of the gradients of field variables for flux calculations. It is this latter task for which the standard DG discretization is ill-suited, and several approaches have been proposed to treat the issue. The most popular strategy for handling diffusion is the ``mixed'' approach, where the solution gradient is constructed from the primal as an auxiliary. We designed a new mixed approach, called Gradient-Recovery DG; it uses the Recovery concept of Van Leer \& Nomura with the mixed approach to produce a scheme with excellent stability, high accuracy, and unambiguous implementation when compared to typical mixed approach concepts. In addition to describing the scheme, we will perform analysis with comparison to other DG approaches for diffusion. Gas dynamics examples will be presented to demonstrate the scheme's capabilities. [Preview Abstract] |
Tuesday, November 22, 2016 1:43PM - 1:56PM |
R27.00002: High-order Hybridized Discontinuous Galerkin methods for Large-Eddy Simulation Pablo Fernandez, Ngoc-Cuong Nguyen, Jaime Peraire With the increase in computing power, Large-Eddy Simulation emerges as a promising technique to improve both knowledge of complex flow physics and reliability of flow predictions. Most LES works, however, are limited to simple geometries and low Reynolds numbers due to high computational cost. While most existing LES codes are based on 2nd-order finite volume schemes, the efficient and accurate prediction of complex turbulent flows may require a paradigm shift in computational approach. This drives a growing interest in the development of Discontinuous Galerkin (DG) methods for LES. DG methods allow for high-order, conservative implementations on complex geometries, and offer opportunities for improved sub-grid scale modeling. Also, high-order DG methods are better-suited to exploit modern HPC systems. In the spirit of making them more competitive, researchers have recently developed the hybridized DG methods that result in reduced computational cost and memory footprint. In this talk we present an overview of high-order hybridized DG methods for LES. Numerical accuracy, computational efficiency, and SGS modeling issues are discussed. Numerical results up to Re=460k show rapid grid convergence and excellent agreement with experimental data at moderate computational cost. [Preview Abstract] |
Tuesday, November 22, 2016 1:56PM - 2:09PM |
R27.00003: Extending the dynamic slip-wall model to a compressible discontinuous-Galerkin method Corentin Carton de Wiart, Scott Murman Standard equilibrium wall models suffer from both a strong dependence upon mesh resolution and the equilibrium turbulence assumption. Non-equilibrium wall models similarly have limitations for complex geometry due to the need for an auxiliary semi-structured mesh solver, and coupling between the LES and wall-model regions. Bose and Moin's dynamic slip-wall model\footnote{Bose and Moin, Phys. Fluids \textbf{26}(1), (2014)} offers a new modeling paradigm that does not rely upon assumptions about the local flow physics and uses a dynamic procedure so that the results are independent of resolution. Despite this, the model has not gained significant traction and few independent implementations have been tested. The current work implements the dynamic slip-wall model in an entropy-stable Discontinuous-Galerkin spectral-element solver with a dynamic variational multiscale sub-grid model\footnote{Murman {\em{et al.}}, AIAA 2016-1059}. This involves both extending the model to a compressible formulation and to a different numerical method. The compressible model is outlined and tested on both attached and separated flows of aerodynamic interest. [Preview Abstract] |
Tuesday, November 22, 2016 2:09PM - 2:22PM |
R27.00004: DG-FDF solver for large eddy simulation of compressible flows Shervin Sammak, Michael Brazell, Dimitri Mavriplis, Peyman Givi A new computational scheme is developed for large eddy simulation (LES) of compressible turbulent flows with the filtered density function (FDF) subgrid scale closure. This is a hybrid scheme, combining the discontinuous Galerkin (DG) Eulerian solver with a Lagrangian Monte Carlo FDF simulator. The methodology is shown to be suitable for LES, as a larger portion of the resolved energy is captured as the order of spectral approximation increases. Simulations are conducted of both subsonic and supersonic flows. The consistency and the overall performance of the DG-FDF solver are demonstrated, together with its shock capturing capabilities. [Preview Abstract] |
Tuesday, November 22, 2016 2:22PM - 2:35PM |
R27.00005: A fully-coupled discontinuous Galerkin spectral element method for two-phase flow in petroleum reservoirs Ankur Taneja, Jonathan Higdon A spectral element method (SEM) is presented to simulate two-phase fluid flow (oil and water phase) in petroleum reservoirs. Petroleum reservoirs are porous media with heterogeneous geologic features, and the flow of two immiscible phases involves sharp, moving interfaces. The governing equations of motion are time-dependent, non-linear PDEs with strong hyperbolic nature. A fully-coupled numerical scheme using discontinuous Galerkin (DG) method with nodal spectral element basis functions for spatial discretization, and an implicit Runge-Kutta type time-stepping is developed to solve the PDEs in a robust, stable manner. Isoparameteric mapping is used to generate grids for reservoir and well geometry. We present the performance capabilities of the DG scheme with high-order basis functions to accurately resolve sharp fluid interfaces and a variety of heterogeneous geologic features. High-order convergence of SEM is demonstrated. Numerical results are presented for reservoir flows with various injection-production patterns. Typical reservoir heterogeneities like low-permeable regions, impermeable shale barriers, etc. are included in the numerical tests. Comparisons with commonly used finite volume methods and linear and quadratic finite element methods are presented. [Preview Abstract] |
Tuesday, November 22, 2016 2:35PM - 2:48PM |
R27.00006: Discontinuous Galerkin method for predicting heat transfer in hypersonic environments Eric Ching, Yu Lv, Matthias Ihme This study is concerned with predicting surface heat transfer in hypersonic flows using high-order discontinuous Galerkin methods. A robust and accurate shock capturing method designed for steady calculations that uses smooth artificial viscosity for shock stabilization is developed. To eliminate parametric dependence, an optimization method is formulated that results in the least amount of artificial viscosity necessary to sufficiently suppress nonlinear instabilities and achieve steady-state convergence. Performance is evaluated in two canonical hypersonic tests, namely a flow over a circular half-cylinder and flow over a double cone. Results show this methodology to be significantly less sensitive than conventional finite-volume techniques to mesh topology and inviscid flux function. The method is benchmarked against state-of-the-art finite-volume solvers to quantify computational cost and accuracy. [Preview Abstract] |
Tuesday, November 22, 2016 2:48PM - 3:01PM |
R27.00007: Dynamic mesh adaptation for front evolution using discontinuous Galerkin based weighted condition number relaxation Patrick Greene, Sam Schofield, Robert Nourgaliev A new mesh smoothing method designed to cluster cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function being computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin (DG) projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered fields, such as a volume fraction or index function, is provided. Results show that the low-order level set works equally well for the weight function as the actual level set. The method retains the excellent smoothing capabilities of condition number relaxation, while providing a method for clustering mesh cells near regions of interest. Dynamic cases for moving interfaces are presented to demonstrate the method's potential usefulness as a mesh relaxer for arbitrary Lagrangian Eulerian (ALE) methods. [Preview Abstract] |
Tuesday, November 22, 2016 3:01PM - 3:14PM |
R27.00008: A three dimensional Dirichlet-to-Neumann map for surface waves over topography Andre Nachbin, David Andrade We consider three dimensional surface water waves in the potential theory regime. The bottom topography can have a quite general profile. In the case of linear waves the Dirichlet-to-Neumann operator is formulated in a matrix decomposition form. Computational simulations illustrate the performance of the method. Two dimensional periodic bottom variations are considered in both the Bragg resonance regime as well as the rapidly varying (homogenized) regime. In the three-dimensional case we use the Luneburg lens-shaped submerged mound, which promotes the focusing of the underlying rays. [Preview Abstract] |
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