Very High-Order Accurate Discontinuous Galerkin Computation of Transonic Turbulent Flows on Aeronautical Configurations

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

doi:10.1007/978-3-642-03707-8_3

Cited by 36 publications

(37 citation statements)

References 6 publications

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“…In this work we employ the shock-capturing technique presented in [16], originally inspired by [29] which is based on the explicit introduction of artificial viscosity into the governing equations. The following element-wise artificial dissipation contribution is thereby added to the system (19):…”

Section: Shock-capturing Techniquementioning

confidence: 99%

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: Shock-capturing Techniquementioning

confidence: 99%

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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“…In this section, we give details on the shock‐capturing scheme used to stabilize the discretization in non‐smooth parts of the flow solution such as near shocks. In particular, we augment the discretization with a stabilization term based on artificial viscosity that in general is given by

{scriptN}_{normalsc} ({bold-italicu}_{h} MathClass-punc, bold-italicv) MathClass-rel\equiv {MathClass-op\sum}_{κ MathClass-rel\in {scriptT}_{h}} {MathClass-op\int}_{κ} ϵ ({bold-italicu}_{h}) MathClass-rel\nabla {bold-italicu}_{h} MathClass-punc: MathClass-rel\nabla bold-italicv normald bold-italicx MathClass-rel\equiv {MathClass-op\sum}_{κ MathClass-rel\in {scriptT}_{h}} {MathClass-op\int}_{κ} ϵ_{klm} ({bold-italicu}_{h}) \partial_{x_{l}} u_{h}^{m} \partial_{x_{k}} v^{m} normald bold-italicx MathClass-punc.

Many stabilization schemes based on artificial viscosity have been proposed, first by Hughes and Johnson in the context of SUPG and SD finite element methods, by Jaffre et al in DG methods for scalar hyperbolic conservation laws, later by Hartmann for DG discretizations of laminar compressible flows and by Bassi et al for DG discretizations of turbulent flows. The artificial viscosity schemes in references are of the form ; they only differ in the specific definition of the viscosity term ϵ ( u h ).…”

Section: Shock‐capturing Based On Artificial Viscositymentioning

confidence: 99%

“…In this article, we devise a new shock‐capturing scheme based on artificial viscosity for the Reynolds‐averaged Navier–Stokes and k ‐ ω turbulence model (RANS‐ kω ) equations. The proposed artificial viscosity term is a combination of the shock‐capturing scheme developed in for the laminar compressible Navier–Stokes equations and the shock‐capturing scheme developed by Bassi et al for the RANS‐ kω equations. In particular, the proposed artificial viscosity term includes the element residual of the governing equations in strong form.…”

Section: Introductionmentioning

confidence: 99%

“…Both ingredients are generalizations of the scheme in from laminar to turbulent flows. In , a so‐called pressure‐switch is included to decrease the effect of the scheme in smooth parts of the flow solution with steep gradients. Furthermore, residual components are linearly combined with derivatives of the pressure and scaled with the pressure to form a scalar residual value that serves as a factor of the artificial viscosity.…”

Section: Introductionmentioning

confidence: 99%

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Higher‐order and adaptive discontinuous Galerkin methods with shock‐capturing applied to transonic turbulent delta wing flow

Hartmann¹

2013

Numerical Methods in Fluids

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SUMMARYDiscontinuous Galerkin (DG) methods allow high‐order flow solutions on unstructured or locally refined meshes by increasing the polynomial degree and using curved instead of straight‐sided elements. DG discretizations with higher polynomial degrees must, however, be stabilized in the vicinity of discontinuities of flow solutions such as shocks.In this article, we device a consistent shock‐capturing method for the Reynolds‐averaged Navier–Stokes and k‐ ω turbulence model equations based on an artificial viscosity term that depends on element residual terms. Furthermore, the DG method is combined with a residual‐based adaptation algorithm that targets at resolving all flow features. The higher‐order and adaptive DG method is applied to a fully turbulent transonic flow around the second Vortex Flow Experiment (VFE‐2) configuration with a good resolution of the vortex system.Copyright © 2013 John Wiley & Sons, Ltd.

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“…The technique is widely employed for the computation of steady-state solutions of non-linear differential equations, see e.g. [3,6,8,9,17,25] for some recently published applications.…”

Section: Introductionmentioning

confidence: 99%

A choice of forcing terms in inexact Newton iterations with application to pseudo-transient continuation for incompressible fluid flow computations

Botti

2015

Applied Mathematics and Computation

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a b s t r a c tA strategy for choosing the forcing terms in inexact Newton iterations is presented. The final goal is to obtain fast steady state marching strategies for the solution of PDEs. The new approach is analyzed and tested in the context of inexact Newton methods but is also well suited to be applied in the pseudo-transient continuation framework. To validate the strategy and assess its gains in terms of computational costs we seek approximate solutions of the incompressible Navier-Stokes equations at high-Reynolds numbers. In particular we consider the well known 2D lid-driven cavity flow and backward-facing step problem focusing on the efficiency of the time marching strategy. Residual history and computation time are monitored and compared with many fixed and adaptive forcing term choices of reference.

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Very High-Order Accurate Discontinuous Galerkin Computation of Transonic Turbulent Flows on Aeronautical Configurations

Cited by 36 publications

References 6 publications

Discontinuous Galerkin Computation of Gaseous Mixture Coaxial Jets

Discontinuous Galerkin Computation of Gaseous Mixture Coaxial Jets

Higher‐order and adaptive discontinuous Galerkin methods with shock‐capturing applied to transonic turbulent delta wing flow

A choice of forcing terms in inexact Newton iterations with application to pseudo-transient continuation for incompressible fluid flow computations

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