Affordable, entropy-consistent Euler flux functions II: Entropy production at shocks

Ismail, Farzad; Roe, Philip L.

doi:10.1016/j.jcp.2009.04.021

Cited by 330 publications

(298 citation statements)

References 15 publications

Supporting

Mentioning

292

Contrasting

Unclassified

Order By: Relevance

“…The study provides evidence that the the non-dissipative Euler fluxes of Ismail and Roe [8] do not degrade the formal accuracy of the high-order entropy consistent fluxes.…”

Section: Optimal Accuracy: a Periodic Cartesian Grid Test Casementioning

confidence: 76%

“…The inviscid terms in the discretization of the Navier-Stokes equations are calculated according to 3.42, 3.9, and 3.10, where the two-point entropy consistent flux was derived by Ismail and Roe [8],…”

Section: Entropy Stable Spatial Discretizationmentioning

confidence: 99%

“…A critical assumption used in the proof is that the two-point non-dissipative fluxes satisfy Tadmor's integral relation given in equation 3.10. Herein, the non-dissipative Euler fluxes of Ismail and Roe [8] are used, which to our knowledge have not been shown to satisfy Tadmor's integral relation. The first study is designed to detect the presence of order reduction resulting from the use of the Ismail and Roe fluxes in the entropy consistent formulation.…”

Section: Optimal Accuracy: a Periodic Cartesian Grid Test Casementioning

confidence: 99%

“…Tadmor constructed entropy consistent second-order finite volume schemes that conserve discrete entropy [5,6], while LeFloch and Rode [7] extended these schemes to highorder periodic domains. These schemes have been made computationally tractable for the Navier-Stokes equations through the work of Ismail and Roe [8]. A methodology for constructing entropy stable schemes satisfying a cell entropy inequality and capable of simulating flows with shocks in periodic domains has been developed by Fjordholm et al [9] Herein, an alternative approach is developed based on a finitedomain entropy stability proof, which yields entropy stable methods with formal boundary closures.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains

Fisher

Carpenter

2013

Journal of Computational Physics

288

265

View full text Add to dashboard Cite

“…The study provides evidence that the the non-dissipative Euler fluxes of Ismail and Roe [8] do not degrade the formal accuracy of the high-order entropy consistent fluxes.…”

Section: Optimal Accuracy: a Periodic Cartesian Grid Test Casementioning

confidence: 76%

Section: Entropy Stable Spatial Discretizationmentioning

confidence: 99%

Section: Optimal Accuracy: a Periodic Cartesian Grid Test Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains

Fisher

Carpenter

2013

Journal of Computational Physics

288

265

View full text Add to dashboard Cite

“…25,28 The following theorem summarizes the work given in reference 22, and provides the general formula for constructing f …”

Section: Iiic1 Entropy Consistent Inviscid Fluxesmentioning

confidence: 99%

Towards an Entropy Stable Spectral Element Framework for Computational Fluid Dynamics

Carpenter

Parsani

Nielsen

et al. 2016

54th AIAA Aerospace Sciences Meeting

View full text Add to dashboard Cite

Boundary variation diminishing algorithm for high‐order local polynomial‐based schemes

Sun

Xiao

2020

Numerical Methods in Fluids

View full text Add to dashboard Cite

Summary A novel approach for selecting appropriate reconstructions is implemented to the hyperbolic conservation laws in the high‐order local polynomial‐based framework, for example, the discontinuous Galerkin (DG) and flux reconstruction (FR) schemes. The high‐order polynomial approximation generally fails to correctly capture a strong discontinuity inside a cell due to the Gibbs phenomenon, which is replaced by more stable approximation on the basis of a troubled‐cell indicator such as that used with the total variation bounded (TVB) limiter. This paper examines the applicability of a new algorithm, so‐called boundary variation diminishing (BVD) reconstruction, to the weighted essentially nonoscillatory methodology in the FR framework including the nodal type DG method. The BVD reconstruction adaptively chooses a proper approximation for the solution function so as to minimize the jump between values at the left and right side of cell boundaries. The results of the BVD algorithm are comparable to those with the conventional TVB limiter in terms of oscillation suppression and numerical dissipation in one‐dimensional linear advection and nonlinear system equations, while the TVB limiter performs better in the case with strong discontinuities (the blast wave problem in the Euler equations). Overall, since the present BVD algorithm does not need any ad hoc constant such as the TVB parameter, it could be more reliable than the conventional TVB limiter that is often used in the DG and FR communities for shocks and other discontinuities. The proposed method would lead to a parameter‐free robust algorithm for the local polynomial‐based high‐order schemes.

show abstract

Affordable, entropy-consistent Euler flux functions II: Entropy production at shocks

Cited by 330 publications

References 15 publications

High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains

High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains

Towards an Entropy Stable Spectral Element Framework for Computational Fluid Dynamics

Boundary variation diminishing algorithm for high‐order local polynomial‐based schemes

Contact Info

Product

Resources

About