TY - JOUR
T1 - A discontinuous Galerkin residual-based variational multiscale method for modeling subgrid-scale behavior of the viscous Burgers equation
AU - Stoter, Stein K.F.
AU - Turteltaub, Sergio R.
AU - Hulshoff, Steven J.
AU - Schillinger, Dominik
N1 - Publisher Copyright:
© 2018 John Wiley & Sons, Ltd.
PY - 2018/10/20
Y1 - 2018/10/20
N2 - We initiate the study of the discontinuous Galerkin residual-based variational multiscale (DG-RVMS) method for incorporating subgrid-scale behavior into the finite element solution of hyperbolic problems. We use the one-dimensional viscous Burgers equation as a model problem, as its energy dissipation mechanism is analogous to that of turbulent flows. We first develop the DG-RVMS formulation for a general class of nonlinear hyperbolic problems with a diffusion term, based on the decomposition of the true solution into discontinuous coarse-scale and fine-scale components. In contrast to existing continuous variational multiscale methods, the DG-RVMS formulation leads to additional fine-scale element interface terms. For the Burgers equation, we devise suitable models for all fine-scale terms that do not use ad hoc devices such as eddy viscosities but instead directly follow from the nature of the fine-scale solution. In comparison to single-scale discontinuous Galerkin methods, the resulting DG-RVMS formulation significantly reduces the energy error of the Burgers solution, demonstrating its ability to incorporate subgrid-scale behavior in the discrete coarse-scale system.
AB - We initiate the study of the discontinuous Galerkin residual-based variational multiscale (DG-RVMS) method for incorporating subgrid-scale behavior into the finite element solution of hyperbolic problems. We use the one-dimensional viscous Burgers equation as a model problem, as its energy dissipation mechanism is analogous to that of turbulent flows. We first develop the DG-RVMS formulation for a general class of nonlinear hyperbolic problems with a diffusion term, based on the decomposition of the true solution into discontinuous coarse-scale and fine-scale components. In contrast to existing continuous variational multiscale methods, the DG-RVMS formulation leads to additional fine-scale element interface terms. For the Burgers equation, we devise suitable models for all fine-scale terms that do not use ad hoc devices such as eddy viscosities but instead directly follow from the nature of the fine-scale solution. In comparison to single-scale discontinuous Galerkin methods, the resulting DG-RVMS formulation significantly reduces the energy error of the Burgers solution, demonstrating its ability to incorporate subgrid-scale behavior in the discrete coarse-scale system.
KW - Burgers turbulence
KW - discontinuous Galerkin methods
KW - residual-based multiscale modeling
KW - variational multiscale method
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U2 - 10.1002/fld.4662
DO - 10.1002/fld.4662
M3 - Article
AN - SCOPUS:85050660716
SN - 0271-2091
VL - 88
SP - 217
EP - 238
JO - International Journal for Numerical Methods in Fluids
JF - International Journal for Numerical Methods in Fluids
IS - 5
ER -