Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session E31: CFD: Higher-Order Methods |
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Chair: Timothy Colonius, CalTech University Room: 2018 |
Sunday, November 23, 2014 4:45PM - 4:58PM |
E31.00001: Discontinuous Galerkin Methods and High-Speed Turbulent Flows Muhammed Atak, Johan Larsson, Claus-Dieter Munz Discontinuous Galerkin methods gain increasing importance within the CFD community as they combine arbitrary high order of accuracy in complex geometries with parallel efficiency. Particularly the discontinuous Galerkin spectral element method (DGSEM) is a promising candidate for both the direct numerical simulation (DNS) and large eddy simulation (LES) of turbulent flows due to its excellent scaling attributes. In this talk, we present a DNS of a compressible turbulent boundary layer along a flat plate at a free-stream Mach number of M=2.67 and assess the computational efficiency of the DGSEM at performing high-fidelity simulations of both transitional and turbulent boundary layers. We compare the accuracy of the results as well as the computational performance to results using a high order finite difference method. [Preview Abstract] |
Sunday, November 23, 2014 4:58PM - 5:11PM |
E31.00002: CoreSVM: a generalized high-order spectral volume method bearing Conservative Order RElease Raphael Lamouroux, Jeremie Gressier, Laurent Joly, Gilles Grondin The spectral volume method (SVM) introduced by Wang in 2002 is based on a compact polynomial reconstruction where the interpolation's degree is driven by the partition of the spectral volumes. We propose a generalization of the SVM which releases the polynomial degree from this constraint and more importantly that allows to resort to any polynomial order inferior to the regular stencil order without changing the original spectral volume partition. Using one-dimensional advection and Burgers equation, we prove that the proposed extended method exhibits versatile high-order convergence together with conservativity properties. This new method is thus named the CoreSVM for Conservative Order-REleased SVM and we therefore explore its potential towards the numerical simulation of stiff problems. It is stressed that CoreSVM is indeed particularly suited to handle discontinuities, as the order-reduction serves to damp the numerical oscillations due to Runge's phenomenon. To ensure computational stability, local p-coarsening is used to obtain the highest adequate polynomial degree. It is advocated finally that, since the CoreSVM sets the polynomial order adaptation free from any stencil changes, these features do not come at the expense of any extra remeshing or data adaptation cost. [Preview Abstract] |
Sunday, November 23, 2014 5:11PM - 5:24PM |
E31.00003: Stable, high-order SBP-SAT finite difference operators to enable accurate simulation of compressible turbulent flows on curvilinear grids, with application to predicting turbulent jet noise Jaeseung Byun, Daniel Bodony, Carlos Pantano Improved order-of-accuracy discretizations often require careful consideration of their numerical stability. We report on new high-order finite difference schemes using Summation-By-Parts (SBP) operators along with the Simultaneous-Approximation-Terms (SAT) boundary condition treatment for first and second-order spatial derivatives with variable coefficients. In particular, we present a highly accurate operator for SBP-SAT-based approximations of second-order derivatives with variable coefficients for Dirichlet and Neumann boundary conditions. These terms are responsible for approximating the physical dissipation of kinetic and thermal energy in a simulation, and contain grid metrics when the grid is curvilinear. Analysis using the Laplace transform method shows that strong stability is ensured with Dirichlet boundary conditions while weaker stability is obtained for Neumann boundary conditions. Furthermore, the benefits of the scheme is shown in the direct numerical simulation (DNS) of a Mach 1.5 compressible turbulent supersonic jet using curvilinear grids and skew-symmetric discretization. Particularly, we show that the improved methods allow minimization of the numerical filter often employed in these simulations and we discuss the qualities of the simulation. [Preview Abstract] |
Sunday, November 23, 2014 5:24PM - 5:37PM |
E31.00004: Positivity-preserving and entropy-bounded Discontinuous Galkerin method for conservation laws Yu Lv, Matthias Ihme Although Discontinuous Galerkin (DG) methods have gained considerable success for application to advection-dominated flows, the robustness and the treatment of geometric singularities and flow-field discontinuities remain open problems. In this talk, a DG-method is formulated that is positivity-preserving and entropy-bounded to guarantee algorithmic stability and conservation. After demonstrating the efficacy in one- and two-dimensional tests, this formulation is generalized to unstructured and curvilinear meshes. Details on the algorithmic implementation are presented, and applications to complex geometries in three dimensions are discussed. [Preview Abstract] |
Sunday, November 23, 2014 5:37PM - 5:50PM |
E31.00005: A New Approach for Imposing Artificial Viscosity for Explicit Discontinuous Galerkin Scheme Yee Chee See, Yu Lv, Matthias Ihme The development of high-order numerical methods for unstructured meshes has been a significant area of research, and the discontinuous Galerkin (DG) method has found considerable interest. However, the DG-method exhibits robustness issues in application to flows with discontinuities and shocks. To address this issue, an artificial viscosity method was proposed by Persson et al. for steady flows. Its extension to time-dependent flows introduces substantial time-step restrictions. By addressing this issue, a novel method, which is based on an entropy formulation, is proposed. The resulting scheme doesn't impose restrictions on the CFL-constraint. Following a description of the formulation and the evaluation of the stability, this newly developed artificial viscosity scheme is demonstrated in application to different test cases. [Preview Abstract] |
Sunday, November 23, 2014 5:50PM - 6:03PM |
E31.00006: Towards A Fast High-Order Method for Unsteady Incompressible Navier-Stokes Equations using FR/CPR Christopher Cox, Chunlei Liang, Michael Plesniak A high-order compact spectral difference method for solving the 2D incompressible Navier-Stokes equations on unstructured grids is currently being developed. This method employs the gGA correction of Huynh, and falls under the class of methods now refered to as Flux Reconstruction/Correction Procedure via Reconstruction. This method and the artificial compressibility method are integrated along with a dual time-integration scheme to model unsteady incompressible viscous flows. A lower-upper symmetric Gauss-Seidel scheme and a backward Euler scheme are used to efficiently march the solution in pseudo time and physical time, respectively. We demonstrate order of accuracy with steady Taylor-Couette flow at Re$=$10. We further validate the solver with steady flow past a NACA0012 airfoil at zero angle of attack at Re$=$1850 and unsteady flow past a circle at Re$=$100. The implicit time-integration scheme for the pseudo time derivative term is proved efficient and effective for the classical artificial compressibility treatment to achieve the divergence-free condition of the continuity equation. [Preview Abstract] |
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