High-Order Fluxes for Conservative Skew-Symmetric-like Schemes in Structured Meshes

By F. Ducros, F. Laporte, T. Soulères, V. Guinot, P. Moinat, B. Caruelle. 2000

363 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/baec41f5c017a78ca18031934b39673a4bf3c0ed

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In Aerospace Engineering

In Computational Mechanics

Citations in the corpus

Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations (2016, background): “[10] proposed the following form, where only the split form (α = 1/2) of the quadratic product (1.”
Large-eddy simulation and multiscale modelling of a Richtmyer–Meshkov instability with reshock (2006, background): “Moreover, it is possible to show that this skew-symmetric form can also be written in flux form ( Ducros et al. 2000 ).”
Theoretical predictions for the elliptical instability in a two-vortex flow (2002, methodology): “The advective terms are discretized with a fourth-order centred scheme developed at CERFACS (Ducros et al. 2000).”
Numerical Methods for High-Speed Flows (2011, background): “Ducros et al. (2000) showed that the skew-symmetric forms (18) and (19) give rise to locally conservative schemes, when the derivative operators are discretized with explicit central formulas (with order up to six).”
Direct numerical simulations of canonical shock/turbulence interaction (2008, methodology): “Near shocks, a fifth-order accurate weighted essentially non-oscillatory (WENO) scheme is used to approximate the inviscid fluxes, whereas a sixth-order accurate central difference scheme on the split form by Ducros et al. (2000) is used in the remainder of the domain.”
Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves (2010, methodology): “In smooth regions, a sixth-order accurate central differencing scheme is applied in split (or ‘skew-symmetric’) form for improved nonlinear stability [12].”
Generalized conservative approximations of split convective derivative operators (2010, background): “…conservative finite-difference approximations of convective derivatives for shock-free compressible flows with arbitrary order of accuracy, that generalizes the approach of Ducros et al. (2000) [1], and that can be applied as a building block of low-dissipative, hybrid shock-capturing methods.”
Reynolds- and Mach-number effects in canonical shock–turbulence interaction (2013, methodology): “Narrow regions around shock waves are treated with a fifth-order accurate weighted essentially non-oscillatory (WENO) scheme with Roe flux splitting, whereas a sixth-order accurate central difference scheme in the split form by Ducros et al. (2000) is used in the remainder of the domain.”
Partially premixed flamelets in LES of nonpremixed turbulent combustion (2002, methodology): “Navier–Stokes equations together with the balance equations for Z̃ (equation (29)) and c̃ (equation (33)) are solved using a fourth order finite volume skew-symmetric-like scheme proposed by Ducros et al [61] for the spatial derivatives.”