Assessment of a high-order accurate Discontinuous Galerkin method for turbomachinery flows

Bassi, Francesco; Botti, Lorenzo Alessio; Colombo, Alessandro; Crivellini, Andrea; Franchina, Nicoletta; Ghidoni, Antonio

doi:10.1080/10618562.2016.1198783

Cited by 38 publications

(41 citation statements)

References 41 publications

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“…The new multicomponent DG solver here presented closely follows the implementation of the monocomponent DG MIGALE code [1,2,3,4]. A fully implicit discretization is employed with Jacobian matrices analytically computed to account in exact manner for the dependence of residuals on the values of variables and gradients, also including the treatment of lifting operators and boundary conditions.…”

Section: Discontinuous Galerkin Discretizationmentioning

confidence: 99%

“…used by the BR2 scheme [1] to define a DG discretization of the viscous part of the governing equations. The jump [[·]] and average {·} trace operators are defined as usual in the DG context to conveniently deal with discontinuities at elements interface as…”

Section: Discontinuous Galerkin Discretizationmentioning

confidence: 99%

“…In the current work, the development of the DG code MIGALE [1,2,3,4] for the computation of multicomponent flows, is presented. The solver is considered as one of our preliminary steps to deal with homogeneous (gas phase) combustion problems by means of a high-order CFD-DG tool and at present it neglects the modeling of chemical reactions.…”

Section: Introductionmentioning

confidence: 99%

“…The adopted DG solver is based on the "exact" Riemann solver [13] and on the BR2 scheme [1] for the computation of the interface convective and diffusive flux vector, respectively. It is well-known that the discretization of multicomponent flow fields has to cope with numerical oscillations that are not encountered with single component flows.…”

Section: Introductionmentioning

confidence: 99%

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Discontinuous Galerkin Computation of Gaseous Mixture Coaxial Jets

Franchina¹,

Savini²,

Bassi³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. A novel approach based upon Discontinuous Galerkin (DG) discretization, applied to the divergence form of the multicomponent Navier-Stokes equations, is here presented and used to compute non reactive turbulent axisymmetric gaseous jets. The original key feature is the use of L 2 -projection form of the (perfect gas) equation of state. This choice mitigates problems typically encountered by the front-capturing schemes in computing multicomponent flow fields, i.e. spurious oscillations across material and contact surfaces where the mixture composition is changing. The solver makes also use of a shock-capturing technique based on artificial dissipation selectively added into the equations and tuned in connection with the magnitude of inviscid residuals of the equations and on suitable coefficients accounting for the variation of the unknown variables within and across grid elements. A simple limiting procedure is introduced in order to avoid the occurrence of unphysical gas properties due to negative and/or greater that one mass fractions values within the domain. The DG code based on the proposed novel technique for multicomponent flow computation is here employed to study the mixing mode and the preferential diffusion mechanism of a mixture jet of helium and carbon dioxide in a surrounding flow of air, both in laminar and turbulent flow regimes. Mass diffusion is modelled by means of Fick's first law and use is made of constant Prandtl and Schmidt numbers in Wilcox's (2008) k − ω model. Third-order accurate results are presented, discussed and compared with the available experimental data. They confirm the possible existence in coaxial jets of different periodic flow structures, greatly affecting mixing rates, and different species diffusive mass fluxes. The relative importance of both phenomena depends on the flow regime and its characteristics. The tests carried out give at the same time indications about the accuracy of the proposed method and its effectiveness in computing complex unsteady flow fields.

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Section: Discontinuous Galerkin Discretizationmentioning

confidence: 99%

Section: Discontinuous Galerkin Discretizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Discontinuous Galerkin Computation of Gaseous Mixture Coaxial Jets

Franchina¹,

Savini²,

Bassi³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…Otherwise, implicit schemes, although memory consuming due to the need of the Jacobian matrix, can be A-stable and Lstable even for high order of accuracy. Most popular implicit schemes are Backward Differentiation Formulae (BDF) [9], which are only A-stable up to the second-order, and their low accuracy is not well suited to match the spatial accuracy of DG methods. In the attempt to couple a high-order discretization both in space and time, several temporal schemes have been used to advance in time the DG space discretized equations [6,26,25,5].…”

Section: Introductionmentioning

confidence: 99%

High-Order Linearly Implicit Two-Step Peer Methods for the Discontinuous Galerkin Solution of the Incompressible Rans Equations

Massa¹,

Noventa²,

Bassi³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. In recent years the increasing attention to high-order Finite Volume (FV), Finite Element (FE) and spectral methods and the growth of computing power promote the development of high-order temporal schemes to perform robust, accurate and efficient unsteady long-time simulations. In this context, some features of the Discontinuous Galerkin finite element (DG) methods, e.g. compactness and flexibility, can be advantageous both for explicit and implicit time integration approaches. Explicit schemes can achieve very high accuracy, but are limited by time-step restrictions, while implicit schemes, even if memory consuming, can overcome time-step limitations, thus improving the time integration efficiency. During last decades several high order implicit temporal schemes have been developed, and some of them have been successfully coupled with DG methods. However these schemes can show the order reduction if applied to very stiff problems or problems with time-dependent boundary conditions. To overcome these limitations, high-order linearly implicit two-step peer methods have been proposed and successfully applied to the numerical solution of differential-algebraic equations. The aim of the present work is to implement high-order two-step peer methods in a DG code and assess their performance for the unsteady solution of the incompressible Navier-Stokes (INS) and Reynolds Averaged Navier-Stokes equations (RANS) equations.

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An oscillation free local discontinuous Galerkin method for nonlinear degenerate parabolic equations

Liu

Jiang

et al. 2023

Numerical Methods Partial

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An oscillation free local discontinuous Galerkin (OFLDG) method is proposed for solving nonlinear degenerate parabolic equations. The damping terms are added to the original LDG scheme to control the spurious oscillations when solutions have a large gradient. The L2‐stability and optimal priori error estimates for the semi‐discrete scheme in one‐ and multi‐dimensions are established. The numerical experiments demonstrate that the proposed method maintains the high order accuracy and controls the spurious oscillations well.

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Assessment of a high-order accurate Discontinuous Galerkin method for turbomachinery flows

Cited by 38 publications

References 41 publications

Discontinuous Galerkin Computation of Gaseous Mixture Coaxial Jets

Discontinuous Galerkin Computation of Gaseous Mixture Coaxial Jets

High-Order Linearly Implicit Two-Step Peer Methods for the Discontinuous Galerkin Solution of the Incompressible Rans Equations

An oscillation free local discontinuous Galerkin method for nonlinear degenerate parabolic equations

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