High-order accurate entropy-stable discontinuous collocated Galerkin methods with the summation-by-parts property for compressible CFD frameworks: Scalable SSDC algorithms and flow solver

Parsani, Matteo; Boukharfane, Radouan; Nolasco, Irving Reyna; Fernández, David C. Del Rey; Zampini, Stefano; Hadri, Bilel; Dalcín, Lisandro

doi:10.1016/j.jcp.2020.109844

Cited by 33 publications

(52 citation statements)

References 89 publications

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“…The curvilinear, unstructured grid SSDC solver developed in the Advanced Algorithms and Numerical Simulations Laboratory (AANSLab) [40] is used to perform the numerical simulations. The SSDC solver is built on top of the Portable and Extensible Toolkit for Scientific computing (PETSc) [41], its mesh topology abstraction (DMPLEX) [42], and scalable ordinary differential equation (ODE)/differential algebraic equations (DAE) solver library [43].…”

Section: Numerical Resultsmentioning

confidence: 99%

Simulation of Turbulent Flows Using a Fully Discrete Explicit hp-nonconforming Entropy Stable Solver of Any Order on Unstructured Grids

Parsani

Boukharfane²,

Nolasco

et al. 2021

AIAA Scitech 2021 Forum

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We report the numerical solution of two challenging turbulent flow test cases simulated with the SSDC framework, a compressible, fully discrete hp-nonconforming entropy stable solver based on the summation-by-parts discontinuous collocation Galerkin discretizations and the relaxation Runge-Kutta methods. The algorithms at the core of the solver are systematically designed with mimetic and structure-preserving techniques that transfer fundamental properties from the continuous level to the discrete one. We aim at providing numerical evidence of the robustness and maturity of these entropy stable scale-resolving methods for the new generation of adaptive unstructured computational fluid dynamics tools. The two selected turbulent flows are i) the flow past two spheres in tandem at a Reynolds number based on the sphere diameter of Re D = 3.9 × 10 3 and 10 4 , and a Mach number of Ma ∞ = 0.1, and ii) the NASA junction flow experiment at a Reynolds number based on the crank chord length of Re = 2.4 × 10 6 and Ma ∞ = 0.189.

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Section: Numerical Resultsmentioning

confidence: 99%

Simulation of Turbulent Flows Using a Fully Discrete Explicit hp-nonconforming Entropy Stable Solver of Any Order on Unstructured Grids

Parsani

Boukharfane²,

Nolasco

et al. 2021

AIAA Scitech 2021 Forum

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“…where the vector is the discrete solution at the collocated nodes, and the vectors diss is added interface dissipation (the construction of this is detailed in [13,24]). The SAT I and SAT BC are utilized to weakly couple neighboring elements and impose boundary conditions, respectively.…”

Section: A Spatial Discretization Of Hyperbolic Conservation Lawsmentioning

confidence: 99%

“…The extension of Tadmor [10] and LeFloch ideas [11] to general high-order accurate discretizations has led to the development of a wide range of spatial discretizations [11][12][13][14][15][16][17][18][19][20][21] that can be proved to be nonlinearly stable (entropy stable) as long as positivity of the thermodynamic variables is preserved. Noticeably, high-order entropy stable algorithms offer a high level of robustness [22,23] and, when carefully implemented, scale well on large supercomputers [24].…”

Section: Introductionmentioning

confidence: 99%

“…The focus of this work is on the design of optimized explicit Runge-Kutta (ERK) schemes for the integration of systems of ordinary differential equations that arise from the spatial discretization with entropy stable high-order collocated discontinuous Galerkin methods on tensor product elements. Summation-by-part (SBP) operators constructed on the Legendre-Gauss-Lobatto (LGL) points [13,14,[33][34][35][36] are at the core of the spatial discretizations implemented in the scalable SSDC framework [37].…”

Section: Introductionmentioning

confidence: 99%

“…, is a two-point flux function matrix (the construction of this matrix is detailed in [24]), and 1 is a vector of ones. Approximation (3) enables us to mimic the continuous nonlinear (entropy) stability analysis at the semi-discrete level [36].…”

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confidence: 99%

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Optimized Explicit Runge-Kutta Schemes for Entropy Stable Discontinuous Collocated Methods Applied to the Euler and Navier–Stokes equations

Jahdali

Boukharfane²,

Dalcín³

et al. 2021

AIAA Scitech 2021 Forum

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In this work, we design a new set of optimized explicit Runge-Kutta schemes for the integration of systems of ordinary differential equations arising from the spatial discretization of wave propagation problems with entropy stable collocated discontinuous Galerkin methods. The optimization of the new time integration schemes is based on the spectrum of the discrete spatial operator for the advection equation. To demonstrate the efficiency and accuracy of the new schemes compared to some widely used classic explicit Runge-Kutta methods, we report the wall-clock time versus the error for the simulation of the two-dimensional advection equation and the propagation of an isentropic vortex with the compressible Euler equations. The efficiency and robustness of the proposed optimized schemes for more complex flow problems are presented for the three-dimensional Taylor-Green vortex at a Reynolds number of Re = 1.6 × 10 3 and Mach number Ma = 0.1, and the flow past two identical spheres in tandem at a Reynolds number of Re = 3.9 × 10 3 and Mach number Ma = 0.1.

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Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics

Ranocha

Dalcín

Parsani

et al. 2021

Commun. Appl. Math. Comput.

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We develop error-control based time integration algorithms for compressible fluid dynamics (CFD) applications and show that they are efficient and robust in both the accuracy-limited and stability-limited regime. Focusing on discontinuous spectral element semidiscretizations, we design new controllers for existing methods and for some new embedded Runge-Kutta pairs. We demonstrate the importance of choosing adequate controller parameters and provide a means to obtain these in practice. We compare a wide range of error-control-based methods, along with the common approach in which step size control is based on the Courant-Friedrichs-Lewy (CFL) number. The optimized methods give improved performance and naturally adopt a step size close to the maximum stable CFL number at loose tolerances, while additionally providing control of the temporal error at tighter tolerances. The numerical examples include challenging industrial CFD applications.

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High-order accurate entropy-stable discontinuous collocated Galerkin methods with the summation-by-parts property for compressible CFD frameworks: Scalable SSDC algorithms and flow solver

Cited by 33 publications

References 89 publications

Simulation of Turbulent Flows Using a Fully Discrete Explicit hp-nonconforming Entropy Stable Solver of Any Order on Unstructured Grids

Simulation of Turbulent Flows Using a Fully Discrete Explicit hp-nonconforming Entropy Stable Solver of Any Order on Unstructured Grids

Optimized Explicit Runge-Kutta Schemes for Entropy Stable Discontinuous Collocated Methods Applied to the Euler and Navier–Stokes equations

Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics

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