Fast time implicit–explicit discontinuous Galerkin method for the compressible Navier–Stokes equations

Renac, Florent; Gérald, Sophie; Marmignon, Claude; Coquel, Fré́dé́ric

doi:10.1016/j.jcp.2013.05.043

Cited by 17 publications

(8 citation statements)

References 39 publications

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“…In the nodal representation of the numerical solution, the unknowns are the values of the solution at interpolation points, while in the modal representation, the unknowns are the expansion coefficients in a given basis of the underlying function space [28]. We use an orthonormal and hierarchical modal basis for flexibility reasons [12], [13], [14], [15], [27], [29]. In this study, Gauss-Legendre polynomials are used.…”

Section: Fluid Domainmentioning

confidence: 99%

Adaptive interface treatment for aerothermal coupling using a Discontinuous Galerkin method

Nguyen

Errera

Labbé

et al. 2020

International Journal of Thermal Sciences

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This paper presents the application of a discontinuous Galerkin method to conjugate heat transfer problems using a Dirichlet-Robin interface treatment. The use of optimal coefficients derived from a Godunov-Ryabenkii stability analysis is adapted to the discontinuous Galerkin discretization. The stability and convergence of different coupling coefficients are explored for fluid-structure interactions of varying strength. The effects of increasing the order of the polynomial approximation are examined. It was found that for weak fluid-structure interactions, the optimal coefficients provide stable and quickly converged results. However, for moderate and strong interactions, relaxation coefficients that are larger than optimal must be used to stabilize the process. Because the coupling coefficient was adapted to the polynomial order of approximation, increasing the order of the polynomial was not found to destabilize conjugate heat transfer processes using adaptive coefficients.Finally, at the end of the paper, a validation vs empirical correlations is presented.

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Section: Fluid Domainmentioning

confidence: 99%

Adaptive interface treatment for aerothermal coupling using a Discontinuous Galerkin method

Nguyen

Errera

Labbé

et al. 2020

International Journal of Thermal Sciences

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“…In previous works, various numerical methods have been proposed for fast implicit time integrations. [13][14][15]24) This study employs quadrature simplification by orthogonality (QSO) which was proposed in our previous work 25) to generate a large matrix quickly by simplifying the quadratures using the orthogonality of the basis functions. Although QSO assumes that the flux Jacobians are constant in each cell, it has been shown that the error of this assumption is negligibly small for unsteady flow problems.…”

Section: Implicit Time Integration Schemementioning

confidence: 99%

“…Rasetarinera and Hussaini 12) proposed a matrix-free GMRES to solve the problem of prohibitive storage using the GMRES method. Renac et al 13,14) proposed SIMP p s methods, whereby a large matrix is simplified by approximating the components associated with high-order DOFs. Dolej si and Feistauer 15) developed a semi-implicit method based on the homogeneity of inviscid fluxes.…”

Section: Introductionmentioning

confidence: 99%

A Simple Cellwise High-order Implicit Discontinuous Galerkin Scheme for Unsteady Turbulent Flows

Asada

Kawai

2019

Trans. Japan Soc. Aero. S Sci.

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A simple cellwise implicit time integration scheme for high-order discontinuous Galerkin (DG) methods is presented for solving unsteady turbulent flows. One motivation of this study is to utilize the advantages of the cellwise feature of DG methods in implicit time integration to accurately predict the time evolution of unsteady turbulent flows. Our approach is to extend a block Jacobi (BJ) scheme to high-order implicit DG schemes. With the BJ scheme, the cellwise feature is ensured because sweeps referring to up-to-date solutions in nearby cells are not required, and accurate time evolution can be simulated by iteratively solving a linear system formulated in implicit time integration. Although the computational cost required for iterative solutions is of some concern, we found that few sub-iterations are needed to simulate unsteady turbulent flows accurately when the flowfield is well-resolved by high-order DG methods. These advantages are demonstrated through problems such as canonical vortex advection and the inviscid Taylor-Green vortex. The developed BJ-based implicit DG methods were applied to a large eddy simulation of turbulent channel flow, and the results show that, in addition to being a cellwise scheme, the proposed scheme outperforms explicit time integration in terms of the computation time.

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“…There has been significant progress in the development of time integrators for high-order spatial operators in the past decades, e.g. the LU-SGS algorithm [70,71], hp-multigrid solvers [72][73][74][75][76], Krylov subspace methods such as GMRES with various preconditioners [77,78] and mixed explicit/implicit approaches [79]. The most used turbulent flow solvers appear to employ a GMRES algorithm with either an ILU, hp-multigrid or a line preconditioner [75].…”

Section: (C) Efficient Time Integration Algorithmsmentioning

confidence: 99%

High-order computational fluid dynamics tools for aircraft design

Wang

2014

Phil. Trans. R. Soc. A.

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Most forecasts predict an annual airline traffic growth rate between 4.5 and 5% in the foreseeable future. To sustain that growth, the environmental impact of aircraft cannot be ignored. Future aircraft must have much better fuel economy, dramatically less greenhouse gas emissions and noise, in addition to better performance. Many technical breakthroughs must take place to achieve the aggressive environmental goals set up by governments in North America and Europe. One of these breakthroughs will be physics-based, highly accurate and efficient computational fluid dynamics and aeroacoustics tools capable of predicting complex flows over the entire flight envelope and through an aircraft engine, and computing aircraft noise. Some of these flows are dominated by unsteady vortices of disparate scales, often highly turbulent, and they call for higher-order methods. As these tools will be integral components of a multi-disciplinary optimization environment, they must be efficient to impact design. Ultimately, the accuracy, efficiency, robustness, scalability and geometric flexibility will determine which methods will be adopted in the design process. This article explores these aspects and identifies pacing items.

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Fast time implicit–explicit discontinuous Galerkin method for the compressible Navier–Stokes equations

Cited by 17 publications

References 39 publications

Adaptive interface treatment for aerothermal coupling using a Discontinuous Galerkin method

Adaptive interface treatment for aerothermal coupling using a Discontinuous Galerkin method

A Simple Cellwise High-order Implicit Discontinuous Galerkin Scheme for Unsteady Turbulent Flows

High-order computational fluid dynamics tools for aircraft design

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