Robust Implicit Direct Discontinuous Galerkin Method for Simulating the Compressible Turbulent Flows

Yang, Xiaoquan; Cheng, Jian; Luo, Hong; Zhao, Qijun

doi:10.2514/1.j057172

Cited by 22 publications

(7 citation statements)

References 28 publications

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“…Both references report similar convergence history using numerical Jacobian and analytical Jacobians. However, reference [45] finds that simulations with analytical Jacobian has better efficiency. From the point of view of software design, this replaces a numerical method and a set of operations that are highly dependent of the type of equation solved by a more general finite difference scheme and an existing residual evaluator N(u).…”

Section: Implementation Of the Ns Equations Related Operationsmentioning

confidence: 99%

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Nektar++: Design and implementation of an implicit, spectral/hp element, compressible flow solver using a Jacobian-free Newton Krylov approach

Yan

Pan

Castiglioni

et al. 2021

Computers & Mathematics with Applications

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At high Reynolds numbers the use of explicit in time compressible flow simulations with spectral/hp element discretization can become significantly limited by time step. To alleviate this limitation we extend the capability of the spectral/hp element open-source software framework, Nektar++, to include an implicit discontinuous Galerkin compressible flow solver. The integration in time is carried out by a singly diagonally implicit Runge-Kutta method. The non-linear system arising from the implicit time integration is iteratively solved by the Jacobian-free Newton Krylov (JFNK) method. A favorable feature of the JFNK approach is its extensive use of the explicit operators available from the previous explicit in time implementation. The functionalities of different building blocks of the implicit solver are analyzed from the point of view of software design and placed in appropriate hierarchical levels in the C++ libraries. In the detailed implementation, the contributions of different parts of the solver to computational cost, memory consumption and programming complexity are also analyzed. A combination of analytical and numerical methods is adopted to simplify the programming complexity in forming the preconditioning matrix. The solver is verified and tested using cases such as manufactured compressible tex, turbulent flow over a circular cylinder at Re = 3900 and shock wave boundary-layer interaction. The results show that the implicit solver can speed-up the simulations while maintaining good simulation accuracy.

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Section: Implementation Of the Ns Equations Related Operationsmentioning

confidence: 99%

Section: Implementation Of the Ns Equations Related Operationsmentioning

confidence: 99%

Nektar++: Design and implementation of an implicit, spectral/hp element, compressible flow solver using a Jacobian-free Newton Krylov approach

Yan

Pan

Castiglioni

et al. 2021

Computers & Mathematics with Applications

View full text Add to dashboard Cite

show abstract

“…Then, it is combined with the simple numerical flux formula of the direct DG method to approximate the gradient of conserved variables. In summary, the new DDGIC method defines multiple individual diffusion processes, each of which is combined to calculate the viscous numerical fluxes for 2-D compressible NS equations as (21) + ∇(ρu) h • ξ (22) + ∇(ρv) h • ξ (23) ∇ρ h • ξ (31) + ∇(ρu) h • ξ (32) + ∇(ρv) h • ξ (33) ∇ρ h • ξ (41) + ∇(ρu) h • ξ (42) + ∇(ρv) h • ξ (43)…”

Section: The New Ddgic Scheme Formulation For 2-d Compressible Navier...mentioning

confidence: 99%

“…Similarly, the interface correction term can be simplified and computed as follows (21) + (ρu) h ξ (22) + (ρv) h ξ (23) • ∇φ j (x, y) ρ h ξ (31) + (ρu) h ξ (32) + (ρv) h ξ (33) • ∇φ j (x, y) ρ h ξ (41) + (ρu) h ξ (42) + (ρv) h ξ (43) + E h ξ (44) • ∇φ j (x, y)…”

Section: The New Ddgic Scheme Formulation For 2-d Compressible Navier...mentioning

confidence: 99%

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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 robust implicit high-order discontinuous Galerkin method for solving compressible Navier-Stokes equations on arbitrary grids

Yan,

Yang,

Weng

2024

Acta Mech. Sin.

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Robust Implicit Direct Discontinuous Galerkin Method for Simulating the Compressible Turbulent Flows

Cited by 22 publications

References 28 publications

Nektar++: Design and implementation of an implicit, spectral/hp element, compressible flow solver using a Jacobian-free Newton Krylov approach

Nektar++: Design and implementation of an implicit, spectral/hp element, compressible flow solver using a Jacobian-free Newton Krylov approach

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

A robust implicit high-order discontinuous Galerkin method for solving compressible Navier-Stokes equations on arbitrary grids

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