A fast, implicit discontinuous Galerkin method based on analytical Jacobians for the compressible Navier-Stokes equations

Yang, Xiaoquan; Cheng, Jian; Wang, Chuanjin; Luo, Hong; Si, Jiangtao; Pandare, Aditya

doi:10.2514/6.2016-1326

Cited by 8 publications

(3 citation statements)

References 21 publications

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“…It does not require any additional data structure for auxiliary variables or lifting operators, nor intricate manipulation of the partial differential equations, as is the case with LDG method. Furthermore, the simple definition of the DDG viscous fluxes enables us to obtain its Jacobian matrix exactly and much more easily [37], which is of importance in the implementation of implicit methods. The simulation of high Reynolds number flows usually requires curved and highly stretched grids in the near-wall region due to the reason that the thin boundary layer must be resolved correctly.…”

Section: A Direct Dg Methods For Rans Equations With Sa Modelmentioning

confidence: 99%

A Direct Discontinuous Galerkin Method for Computation of Turbulent Flows on Hybrid Grids

Cheng

Liu

Yang

et al. 2016

46th AIAA Fluid Dynamics Conference

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A Direct Discontinuous Galerkin (DDG) method is developed for solving the compressible Reynolds-averaged Navier-Stokes (RANS) equations with a modified Spalart-Allmaras (SA) model on hybrid grids. The characteristic face length in the numerical flux functions defined by the DDG method is carefully examined and re-evaluated to take into consideration the fact that grids in near-wall regions for high Reynolds number flows are generally curved and highly stretched. The effect with respect to the different choices of penalty parameter in simulating turbulent flows is also discussed in this work. A number of typical test cases are presented to demonstrate the performance of applying DDG method for high Reynolds number turbulent flows. Numerical results obtained demonstrate that the developed DDG method is able to deliver satisfactory and reliable results for simulating high Reynolds number turbulent flows and indicates its potential for practical engineering applications.

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Section: A Direct Dg Methods For Rans Equations With Sa Modelmentioning

confidence: 99%

A Direct Discontinuous Galerkin Method for Computation of Turbulent Flows on Hybrid Grids

Cheng

Liu

Yang

et al. 2016

46th AIAA Fluid Dynamics Conference

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“…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. Furthermore, the simple definition of the DDG viscous fluxes enables us to obtain its Jacobian matrix exactly and much more easily 38 , which is of importance in the implementation of implicit methods.…”

Section: Introductionmentioning

confidence: 99%

A Reconstructed Direct Discontinuous Galerkin Method for Compressible Turbulent Flows on Hybrid Grids

Yang

Cheng

Liu

et al. 2016

46th AIAA Fluid Dynamics Conference

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In this paper, a reconstructed direct discontinuous Galerkin (DDG) method is developed for solving RANS equations with the latest negative Spalart-Allamars (SA) turbulence model based on the framework of hybrid reconstructed DG (rDG) methods. The previous successful experience of applying DDG method for solving compressible laminar flows intrigues us to further unreveal the possibility and assess the capability of using DDG method for simulating high Reynolds number turbulent flows. Several typical test case are selected to assess the performance of applying DDG method for solving high Reynolds turbulent flows. Numerical results show that the grid curvature must be taken into consideration for the formulation of DDG numerical flux. Through the numerical experiments, the reconstructed DDG method clearly demonstrates its capability for solving high Reynolds turbulent flows with highly stretched and curved grids and indicates its further potential for real engineering applications.

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“…The first discussion was carried out by Kannan and Wang in [34] in a spectral volume method setting. Recently, in a sequence of articles [35,36,37,38], Cheng and Luo et al applied the first direct DG method [28] to compressible NS equations, in which only quadratic polynomials were considered and no interface correction term was added. Regarding the viscous numerical flux, they employed a productrule approach that is consistent with our method on the continuous level.…”

Section: Introductionmentioning

confidence: 99%

A new direct discontinuous Galerkin method with interface correction for two-dimensional compressible Navier-Stokes equations

Danis,

Yan

2021

Preprint

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We propose a new formula for the nonlinear viscous numerical flux and extend the direct discontinuous Galerkin method with interface correction (DDGIC) of Liu and Yan [1] to compressible Navier-Stokes equations. The new DDGIC framework is based on the observation that the nonlinear diffusion can be represented as a sum of multiple individual diffusion processes corresponding to each conserved variable. A set of direction vectors corresponding to each individual diffusion process is defined and approximated by the average value of the numerical solution at the cell interfaces. The new framework only requires the computation of conserved variables' gradient, which is linear and approximated by the original direct DG numerical flux formula. The proposed method greatly simplifies the implementation, and thus, can be easily extended to general equations and turbulence models. Numerical experiments with P 1 , P 2 , P 3 and P 4 polynomial approximations are performed to verify the optimal (k + 1) th high-order accuracy of the method. The new DDGIC method is shown to be able to accurately calculate physical quantities such as lift, drag, and friction coefficients as well as separation angle and Strouhal number.

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A fast, implicit discontinuous Galerkin method based on analytical Jacobians for the compressible Navier-Stokes equations

Cited by 8 publications

References 21 publications

A Direct Discontinuous Galerkin Method for Computation of Turbulent Flows on Hybrid Grids

A Direct Discontinuous Galerkin Method for Computation of Turbulent Flows on Hybrid Grids

A Reconstructed Direct Discontinuous Galerkin Method for Compressible Turbulent Flows on Hybrid Grids

A new direct discontinuous Galerkin method with interface correction for two-dimensional compressible Navier-Stokes equations

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