Bulletin of the American Physical Society
73rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 65, Number 13
Sunday–Tuesday, November 22–24, 2020; Virtual, CT (Chicago time)
Session F11: Computational Fluid Dynamics: DG and Higher Order Schemes (3:55pm - 4:40pm CST)Interactive On Demand
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F11.00001: A Level-Set Approach to Simulating Incompressible Multiphase Flows on Adaptive Cartesian Grids. Tommaso Zanelli, Guillaume Oger, Louis Vittoz, Zhe Li, David Le Touzé Gridflow is an in-house CFD solver based on high-order (WENO) finite volumes for Cartesian grids with Adaptive Mesh Refinement (AMR). This solver is jointly developed by the LHEEA laboratory of Ecole Centrale de Nantes and Nextflow Software. Originally based on an explicit weakly-compressible formulation, an incompressible scheme has been added recently, employing the Chorin's projection scheme and using the PETSc library for computing the pressure field. The present work focuses on the implementation of a method for simulating multiphase flows in the incompressible formulation. A Level-Set method is used for tracking the interface between the different phases. The projection method is modified to account for the discontinuity in fluid properties at the interface. Further improvements to the basic method are considered and tested. High order reconstruction methods (5$^{\mathrm{th}}$ order WENO scheme) for solving the Level-Set transport equation are compared with a lower order reconstruction, and the advantages in terms of mass conservation are considered. The method is then tested on academic and industrial cases. [Preview Abstract] |
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F11.00002: HDG vs FV: Turbulent incompressible flows Hashim Elzaabalawy, Ganbo Deng, Luís Eça, Michel Visonneau Solving the Reynolds averaged Navier-Stokes equations using high-order methods is known to be challenging due to their high stiffness. Strategies to overcome this problem under the hybridizable discontinuous Galerkin framework are presented for the Wilcox 98, TNT, BSL, and SST $k-\omega$ models. Special treatment of $\omega$ near the wall to fit the high-order polynomial approximation is proposed. Moreover, scaling limiters are introduced to preserve the positivity as well as the high-order accuracy of the turbulence variables. The turbulence model is coupled with the pointwise divergence-free hybridizable discontinuous Galerkin solver for incompressible flows and solved implicitly. The method of manufactured solution is employed to assess the formulation and the treatment of each equation separately. Further, the formulation is tested on the 2D channel flow, the zero pressure gradient flat plate, and the NACA 0012 airfoil test cases. Preliminary results show significant improvements regarding the error magnitudes and number of iterations compared to finite volume based solvers. Additionally, optimal convergence rates are obtained. Finally, the possibilities and limitations for the high-order methods in RANS simulations are discussed and compared with finite volume approach. [Preview Abstract] |
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F11.00003: A High Accuracy/Resolution Spectral Element/Fourier-Galerkin Method for the Simulation of Shoaling Non-Linear Internal Waves of Depression Over Realistic Bathymetry Theodore Diamantopoulos, Sumedh Joshi, Greg Thomsen, Gustavo Rivera, Peter Diamessis, Kristopher Rowe Internal solitary waves (ISWs) are ubiquitous oceanic phenomena found on continental slopes/shelves, in submarine canyons, and in the vicinity of distinct features in the oceanic bottom topography. The shoaling of ISWs of depression over the continental shelf can lead to a convective breaking of the wave along with the formation of a recirculating core, which has critical implications on the continental shelf/slope energetics. To successfully simulate the turbulence forming in the interior of a shoaling ISW, a high-order spectral-element-method-Fourier-Galerkin numerical approach for the spatial discretization is adopted. In tandem with an implicit/explicit time-splitting scheme of the incompressible Navier-Stokes equations (INSE), a pressure-Poisson-equation (PPE) accounts for the most computational challenging part of an INSE solver. Consequently, a crucial component for the simulation of shoaling ISWs, is the development of a robust PPE solver. Adopting a domain decomposition technique in combination with a deflated preconditioned conjugate gradient solver, the PPE solve can be leveraged to achieve a high convergence rate with a decrease on the introduced communication overhead compared to other type of solvers. Aspects of performance /scalability of the PPE solver and preliminary three-dimensional results of the INSE solver, as applied to shoaling ISWs, will be demonstrated. [Preview Abstract] |
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F11.00004: Recovery-Assisted Discontinuous Galerkin Discretization for Compressible Multiphase Flows Loc Khieu, Eric Johnsen Since the beginning of CFD, the striving for accurate simulations has been relentless, and discontinuous Galerkin (DG) method is among the recent developments, arguably the most popular. Its substantial potential lies in its ability to systematically produce numerical schemes of arbitrarily high orders of accuracy on a compact computational stencil. Recovery-assisted discontinuous Galerkin (RAD) is our own development, aiming at further improving the conventional advection--diffusion DG scheme (upwind DG for advection and BR2 for diffusion) with respect to accuracy, while retaining the stencil compactness. In RAD, the diffusion terms are discretized by a combination of Van Leer's recovery concept (known for its accuracy) and the mixed formulation (widely used for its compactness, among others). For advection terms, the numerical solution is first enhanced by applying recovery in a biased manner, then the interface fluxes are calculated via upwinding. The resulted scheme is then coupled with a Riemann solver suitably modified for multiphase flows, then a variety of binary multiphase problems are simulated to verify RAD's numerical performance. [Preview Abstract] |
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F11.00005: Exponentially-accurate Chebyshev-collocation methods for elliptic and parabolic differential equations with complex interfacial geometries Sudipta Ray, Sandeep Saha We present a Chebyshev-collocation method for obtaining the piecewise-smooth solution of parabolic and elliptic partial differential equations. Spectral discretization of a piecewise-smooth solution leads to \emph{Gibbs oscillations} around the interface of discontinuity, leading to large discretization errors. We reconstruct the solution as the sum of a smooth function and a weighted Heaviside function. The jump conditions at the interface are utilized to formulate a smooth correction function for weighing the Heaviside function. The correction function is presented using a weak-form representation. The use of the interface jump condition to form the correction function ensures that the conditions at the interface are satisfied exactly. The approach requires global information of the discontinuities; the interface conditions are obtained by assuming smooth extension of the solution in one domain into the other. The two and three-dimensional Poisson equation and the one-dimensional Stefan problem are solved using the weak-formulation and exponential convergence is achieved in both the cases. A grid sensitivity analysis shows that the method is insensitive to sub-grid scale perturbations to the interface location. [Preview Abstract] |
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F11.00006: Discontinuous Galerkin Spectral Element Method with HyperViscosity Bradford Durant, Jason Hackl, S. Balachandar Discontinuous Galerkin Spectral Element Method (DGSEM) is a high-order CFD method with that provides great performance in smooth flows. However, DGSEM requires extra work to stabilize discontinuities. We study the performance of DGSEM combined with the artificial viscosity scheme known as Hyperviscosity. Hyperviscosity is a gradient based artificial viscosity scheme for use in shock turbulence interactions. Originally created for a compact finite difference scheme, Hyperviscosity is adapted to the DGSEM framework. Due to the nature of adapting Hyperviscosity to DGSEM, the value of the tuning parameters of the artificial viscosity scheme are reassessed. Various shock problems are used to tune Hyperviscosity in the new DGSEM framework. [Preview Abstract] |
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