A hybridized discontinuous Galerkin method on mapped deforming domains

Fidkowski, Krzysztof J.

doi:10.1016/j.compfluid.2016.04.004

Title: A hybridized discontinuous Galerkin method on mapped deforming domains

Journal Article · Wed Apr 06 00:00:00 EDT 2016 · Computers and Fluids

DOI:https://doi.org/10.1016/j.compfluid.2016.04.004· OSTI ID:1533676

^[1]

University of Michigan, Ann Arbor, MI (United States)

Here in this paper we present a hybridized discontinuous Galerkin (HDG) discretization for unsteady simulations of convection-dominated flows on mapped deforming domains. Mesh deformation is achieved through an arbitrary Lagrangian-Eulerian transformation with an analytical mapping. We present details of this transformation applied to the HDG system of equations, with focus on the auxiliary gradient equation, viscous stabilization, and output calculation. We discuss conditions under which optimal unsteady output convergence rates can be attained, and we show that both HDG and discontinuous Galerkin (DG) achieve these rates in advection-dominated flows. Results for scalar advection-diffusion and the Euler equations verify the implementation of the mesh motion mapping for both discretizations, show that HDG and DG yield similar results on a given mesh, and demonstrate differences in output convergence rates depending on the choice of HDG viscous stabilization. We note that such similar results bode well for HDG, which has fewer globally-coupled degrees of freedom compared to DG. A simulation of the unsteady compressible Navier-Stokes equations demonstrates again very similar results for HDG and DG and illustrates a pitfall of using steady-state adapted meshes for accurate unsteady simulations.

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Research Organization:: Univ. of Michigan, Ann Arbor, MI (United States)

Sponsoring Organization:: USDOE Office of Science (SC); US Air Force Office of Scientific Research (AFOSR)

Grant/Contract Number:: SC0010341; FA9550-11-1-0081; FG02-13ER26146; FG02-13ER26146/DE-SC0010341

OSTI ID:: 1533676

Alternate ID(s):: OSTI ID: 1396441

Journal Information:: Computers and Fluids, Vol. 139, Issue C; ISSN 0045-7930

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 10 works

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References (23)

Adaptive Discontinuous Galerkin Finite Element Methods for the Compressible Euler Equations Hartmann, Ralf; Houston, Paul Journal of Computational Physics, Vol. 183, Issue 2 https://doi.org/10.1006/jcph.2002.7206	journal	December 2002
Discontinuous Galerkin solution of the Navier–Stokes equations on deformable domains Persson, P. -O.; Bonet, J.; Peraire, J. Computer Methods in Applied Mechanics and Engineering, Vol. 198, Issue 17-20 https://doi.org/10.1016/j.cma.2009.01.012	journal	April 2009
Anisotropic grid adaptation for functional outputs: application to two-dimensional viscous flows Venditti, David A.; Darmofal, David L. Journal of Computational Physics, Vol. 187, Issue 1 https://doi.org/10.1016/S0021-9991(03)00074-3	journal	May 2003
Numerical evaluation of two discontinuous Galerkin methods for the compressible Navier-Stokes equations Bassi, F.; Rebay, S. International Journal for Numerical Methods in Fluids, Vol. 40, Issue 1-2 https://doi.org/10.1002/fld.338	journal	January 2002
Runge-Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems Cockburn, Bernardo; Shu, Chi-Wang Journal of Scientific Computing, Vol. 16, Issue 3, p. 173-261 https://doi.org/10.1023/A:1012873910884	journal	September 2001
A comparison of hybridized and standard DG methods for target-based hp-adaptive simulation of compressible flow Woopen, Michael; Balan, Aravind; May, Georg Computers & Fluids, Vol. 98 https://doi.org/10.1016/j.compfluid.2014.03.023	journal	July 2014
An implicit high-order hybridizable discontinuous Galerkin method for linear convection–diffusion equations Nguyen, N. C.; Peraire, J.; Cockburn, B. Journal of Computational Physics, Vol. 228, Issue 9 https://doi.org/10.1016/j.jcp.2009.01.030	journal	May 2009
p-Multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier–Stokes equations Fidkowski, Krzysztof J.; Oliver, Todd A.; Lu, James Journal of Computational Physics, Vol. 207, Issue 1 https://doi.org/10.1016/j.jcp.2005.01.005	journal	July 2005
Time accurate anisotropic goal-oriented mesh adaptation for unsteady flows Belme, A.; Dervieux, A.; Alauzet, F. Journal of Computational Physics, Vol. 231, Issue 19 https://doi.org/10.1016/j.jcp.2012.05.003	journal	August 2012
Discontinuous Galerkin Methods for First-Order Hyperbolic Problems Brezzi, F.; Marini, L. D.; SÜLi, E. Mathematical Models and Methods in Applied Sciences, Vol. 14, Issue 12 https://doi.org/10.1142/S0218202504003866	journal	December 2004
hp-Version discontinuous Galerkin methods for hyperbolic conservation laws Bey, Kim S.; Tinsley Oden, J. Computer Methods in Applied Mechanics and Engineering, Vol. 133, Issue 3-4 https://doi.org/10.1016/0045-7825(95)00944-2	journal	July 1996
A Hybridizable Discontinuous Galerkin Method for Steady-State Convection-Diffusion-Reaction Problems Cockburn, Bernardo; Dong, Bo; Guzmán, Johnny SIAM Journal on Scientific Computing, Vol. 31, Issue 5 https://doi.org/10.1137/080728810	journal	January 2009
Approximate Riemann solvers, parameter vectors, and difference schemes Roe, P. L. Journal of Computational Physics, Vol. 43, Issue 2 https://doi.org/10.1016/0021-9991(81)90128-5	journal	October 1981
Adjoint Recovery of Superconvergent Functionals from PDE Approximations Pierce, Niles A.; Giles, Michael B. SIAM Review, Vol. 42, Issue 2 https://doi.org/10.1137/S0036144598349423	journal	January 2000
Error estimation and adaptation for functional outputs in time-dependent flow problems Mani, Karthik; Mavriplis, Dimitri J. Journal of Computational Physics, Vol. 229, Issue 2 https://doi.org/10.1016/j.jcp.2009.09.034	journal	January 2010
Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems Cockburn, Bernardo; Gopalakrishnan, Jayadeep; Lazarov, Raytcho SIAM Journal on Numerical Analysis, Vol. 47, Issue 2 https://doi.org/10.1137/070706616	journal	January 2009
Output-based mesh adaptation for high order Navier–Stokes simulations on deformable domains Kast, Steven M.; Fidkowski, Krzysztof J. Journal of Computational Physics, Vol. 252 https://doi.org/10.1016/j.jcp.2013.06.007	journal	November 2013
Review of Output-Based Error Estimation and Mesh Adaptation in Computational Fluid Dynamics Fidkowski, Krzysztof J.; Darmofal, David L. AIAA Journal, Vol. 49, Issue 4 https://doi.org/10.2514/1.J050073	journal	April 2011
Output-based space–time mesh adaptation for the compressible Navier–Stokes equations Fidkowski, Krzysztof J.; Luo, Yuxing Journal of Computational Physics, Vol. 230, Issue 14 https://doi.org/10.1016/j.jcp.2011.03.059	journal	June 2011
Goal-oriented space-time adaptivity in the finite element Galerkin method for the computation of nonstationary incompressible flow: SPACE-TIME ADAPTIVITY FOR NONSTATIONARY INCOMPRESSIBLE FLOW Besier, Michael; Rannacher, Rolf International Journal for Numerical Methods in Fluids, Vol. 70, Issue 9 https://doi.org/10.1002/fld.2735	journal	January 2012
A space–time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains Rhebergen, Sander; Cockburn, Bernardo Journal of Computational Physics, Vol. 231, Issue 11 https://doi.org/10.1016/j.jcp.2012.02.011	journal	June 2012
Adaptivity with Dynamic Meshes for Space-Time Finite Element Discretizations of Parabolic Equations Schmich, Michael; Vexler, Boris SIAM Journal on Scientific Computing, Vol. 30, Issue 1 https://doi.org/10.1137/060670468	journal	January 2008
“Natural norm” a posteriori error estimators for reduced basis approximations Sen, S.; Veroy, K.; Huynh, D. B. P. Journal of Computational Physics, Vol. 217, Issue 1 https://doi.org/10.1016/j.jcp.2006.02.012	journal	September 2006

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Efficient discontinuous Galerkin implementations and preconditioners for implicit unsteady compressible flow simulations Franciolini, Matteo; Fidkowski, Krzysztof; Crivellini, Andrea arXiv https://doi.org/10.48550/arxiv.1812.04789	preprint	January 2018

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