Entropy-Adjoint p-Adaptive Discontinuous Galerkin Method for the Under-Resolved Simulation of Turbulent Flows

Bassi, Francesco; Colombo, Alessandro; Crivellini, Andrea; Fidkowski, Krzysztof J.; Franciolini, Matteo; Ghidoni, Antonio; Noventa, G.

doi:10.2514/1.j058847

Cited by 23 publications

(18 citation statements)

References 56 publications

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“…However, when applying the substep scaling (Fig. 1b), RK-CB3e allows scaled time steps ∆t s roughly 1.5 times larger than RK-ARS3 and 4 times larger than SDC-Eu (3,5). SDC-CB3e(3,3) and SDC-ARS3(3,3) resemble the latter and are omitted for clarity.…”

Section: Spectral Deferred Correctionmentioning

confidence: 96%

“…Figure 2 compares the scaled accuracy domains of the same methods for two different thresholds. For errors smaller than 10 −5 , RK-CB3e is clearly the most efficient method, followed by RK-CB4 and then RK-CB3c and SDC-Eu (3,5), with considerably smaller z s or, respectively, ∆t s . With increasing accuracy, the 6-th order SDC methods gain efficiency and become competitive with RK-CB3e for |ε| ≈ 10 −10 (Fig.…”

Section: Spectral Deferred Correctionmentioning

confidence: 97%

“…Using M = 3 subintervals and K = 5 corrections with Euler and K = 3 with RK yields a theoretical order of 6. The resulting methods are denoted as SDC-Eu (3,5), SDC-CB3e (3,3) and SDC-ARS3 (3,3), respectively. In all simulations, the pressure and diffusion problems are solved with a relative tolerance of 10 −12 of the RMS residual evaluated at the collocation points.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…High-order discretization methods enjoy increasing popularity because of their low dispersion errors and superior convergence properties [5,6,16,47,54,58]. However, many studies use high order (3 to 16) in space, whereas time integration is often conducted with schemes of order 2, only.…”

Section: Introductionmentioning

confidence: 99%

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Assessment of high-order IMEX methods for incompressible flow

Montadhar¹,

Grotteschi²,

Stiller³

2021

Preprint

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This paper investigates the competitiveness of semi-implicit Runge-Kutta (RK) and spectral deferred correction (SDC) time-integration methods up to order six for incompressible Navier-Stokes problems in conjunction with a high-order discontinuous Galerkin method for space discretization. It is proposed to harness the implicit and explicit RK parts as a partitioned scheme, which provides a natural basis for the underlying projection scheme and yields a straight-forward approach for accommodating nonlinear viscosity. Numerical experiments on laminar flow, variable viscosity and transition to turbulence are carried out to assess accuracy, convergence and computational efficiency. Although the methods of order 3 or higher are susceptible to order reduction due to time-dependent boundary conditions, two thirdorder RK methods are identified that perform well in all test cases and clearly surpass all second-order schemes including the popular extrapolated backward difference method. The considered SDC methods are more accurate than the RK methods, but become competitive only for relative errors smaller than ca 10 −5 .

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Section: Spectral Deferred Correctionmentioning

confidence: 96%

Section: Spectral Deferred Correctionmentioning

confidence: 97%

Section: Numerical Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Assessment of high-order IMEX methods for incompressible flow

Montadhar¹,

Grotteschi²,

Stiller³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…As a consequence, the order of accuracy can be varied locally by using a different degree of the polynomial representation (see Figure 1) according to some error indicator. In literature this approach is known as p-adaptation [32][33][34][35][36] and allows for the capture of the flow features by changing locally the solution accuracy.…”

Section: P-adaptation Strategymentioning

confidence: 99%

Assessment of a Discontinuous Galerkin Method for the Simulation of the Turbulent Flow around the DrivAer Car Model

et al. 2021

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The turbulent flow over the DrivAer fastback model is here investigated with an order-adaptive discontinuous Galerkin (DG) method. The growing need of high-fidelity flow simulations for the accurate determination of problems, e.g., vehicle aerodynamics, promoted research on models and methods to improve the computational efficiency and to bring the practice of Scale Resolving Simulations (SRS), like the large-eddy simulation (LES), to an industrial level. An appealing choice for SRS is the Implicit LES (ILES) via a high-order DG method, where the favourable numerical dissipation of the space discretization scheme plays directly the role of a subgrid-scale model. Implicit time integration and the p-adaptive algorithm reduce the computational cost allowing a high-fidelity description of the physical phenomenon with very coarse mesh and moderate number of degrees of freedom. Two different models have been considered: (i) a simplified DrivAer fastback model, without the rear-view mirrors and the wheels, and a smooth underbody; (ii) the DrivAer fastback model, without rear-view mirrors and a smooth underbody. The predicted results have been compared with experimental data and CFD reference results, showing a good agreement.

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An implicit p‐adaptive discontinuous Galerkin solver for CAA/CFD simulations

Colombo

Crivellini

Ghidoni

et al. 2022

Numerical Methods in Fluids

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In the last decades flow simulations have become a routine practice in many industrial fields for the aerodynamic and noise prediction. Moreover, the ever increasing interest in simulating off‐design operating conditions promoted the development of high‐fidelity simulation tools to overcome the modeling and accuracy limits of standard industrial codes in predicting turbulent separated flows. The discontinuous Galerkin (DG) method is well suited for this class of simulations, but today DG‐based CFD and CAA (Computational AeroAcoustics) solvers cannot yet reach the computational efficiency of well‐established commercial codes. As a consequence, the present paper aims at exploiting some attractive strategies, such as the adaptation of the elemental polynomial degree (p‐adaptation) and of the degree of exactness of quadrature rules, to enhance the computational efficiency of an implicit DG platform for CFD and CAA simulations. Moreover, a sponge layer non‐reflecting boundary treatment has been also implemented for CAA. The predicting capabilities of the method have been assessed on classical CAA and CFD test cases. The proposed adaptive strategy guarantees a significant reduction ( prefix≈-.27em50%) of the computational effort for both CFD and CAA simulations, compared to uniform‐order discretizations, while not spoiling the high accuracy requested to an high‐fidelity simulation tool.

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Entropy-Adjoint p-Adaptive Discontinuous Galerkin Method for the Under-Resolved Simulation of Turbulent Flows

Cited by 23 publications

References 56 publications

Assessment of high-order IMEX methods for incompressible flow

Assessment of high-order IMEX methods for incompressible flow

Assessment of a Discontinuous Galerkin Method for the Simulation of the Turbulent Flow around the DrivAer Car Model

An implicit p‐adaptive discontinuous Galerkin solver for CAA/CFD simulations

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