54th AIAA Aerospace Sciences Meeting 2016
DOI: 10.2514/6.2016-1334
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A Direct Discontinuous Galerkin method for the compressible Navier-Stokes equations on arbitrary grids

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Cited by 7 publications
(11 citation statements)
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“…Thus, the characteristic face length ∆, also termed as mesh size, in the DDG numerical flux still needs to be carefully examined and re-evaluated. In our previous work [34], it showed that the characteristic face length impacts both the magnitude of error and the order of convergence of the DDG method. Inappropriate definition of the characteristic face length can bring a detrimental effect to the convergence of numerical results.…”
Section: A Direct Dg Methods For Rans Equations With Sa Modelmentioning
confidence: 99%
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“…Thus, the characteristic face length ∆, also termed as mesh size, in the DDG numerical flux still needs to be carefully examined and re-evaluated. In our previous work [34], it showed that the characteristic face length impacts both the magnitude of error and the order of convergence of the DDG method. Inappropriate definition of the characteristic face length can bring a detrimental effect to the convergence of numerical results.…”
Section: A Direct Dg Methods For Rans Equations With Sa Modelmentioning
confidence: 99%
“…Later, Kannan and Wang [17] analyzed and optimized the DDG method based on Fourier analysis and successfully implemented it for two dimensional Navier-Stokes equations based on a spectral volume (SV) [18] framework. Very recently, Cheng et al [34] developed and extended the DDG method for solving the Navier-Stokes equations on arbitrary grids in the framework of DG methods. The numerical results indicated that the DDG method can achieve the designed order of accuracy and is able to deliver the same accuracy as the widely used BR2 scheme at a significantly reduced cost.…”
Section: Introductionmentioning
confidence: 99%
“…However, how to define a characteristic face length on nonuniform grids is a critical issue in extending the DDG method to arbitrary or unstructured grids, as the numerical viscous flux function explicitly depends on it. In the work of Cheng et al, three choices for the characteristic face length are given as follows: -1.7emnormalΔ=false|boldIefalse|, normalΔ=false|boldIe·boldnefalse|, or 2.2emnormalΔ=false|normalΩ+false|+false|normalΩfalse|2false|normalΓefalse|, where I e is the displacement vector from the centroid of the element K + to the centroid of the element K − , Γ e is the common internal face shared by both K + and K − , n e is the unit normal vector at the middle point of face Γ e , and |Ω ± | is the area of K ± , respectively (see Figure A).…”
Section: High‐order Dg Methods On Arbitrary Gridmentioning
confidence: 99%
“…It can be easily verified that all of the three expressions above are consistent with the original definition of the characteristic length if a uniform Cartesian grid is used. Extensive numerical experiments in the work of Cheng et al indicate that the second choice defined by Equation delivers the best results and, thus, is adopted in this work.…”
Section: High‐order Dg Methods On Arbitrary Gridmentioning
confidence: 99%
“…A variety of numerical methods have been proposed in the literature, such as symmetric interior penalty (SIP) 5-6 , local discontinuous Galerkin (LDG) 7 , compact discontinuous Galerkin (CDG) 8 , reconstructed DG (rDG) 9 , and the second Bassi-Rebay (BR2) 10 schemes. Recently, inspired by the formula of general Riemann solution for a purely diffusion equation, a direct discontinuous Galerkin (DDG) 11 method was introduced by Liu and Yan and extended to solve compressible Navier-Stokes equations 37 . Compared to the BR2 scheme, DDG method shows attractive protentialty for solving diffusion problems owning to its simplicity in implementation and efficiency in computational cost.…”
Section: Introductionmentioning
confidence: 99%