On entropy-stable discretizations and the entropy adjoint
type: Item
instance of: scholarly article
title: On entropy-stable discretizations and the entropy adjoint
zbMATH Open document ID: 1475.65144
author: J. E. Hicken
published in: Journal of Scientific Computing
publication date: 2021-05-28T00:00:00Z
review text: For symmetrizable conservation laws, the entropy variables are adjoints for a functional that balances entropy flux into the domain with sources of entropy inside the domain. In this paper, it was shown that entropy-stable summation by parts (SBP) discretizations mimic an additional property of the continuous equations: the entropy adjoint. The entropy variables satisfy the discrete adjoint equation for a discretized entropy-balance functional if they are evaluated from the discrete solution. They are identical to the discrete adjoint variables up to machine accuracy. The theoretical results are verified for steady inviscid (Euler equation) and viscous flows (Navier-Stokes equation) over an airfoil.
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 76N15
Mathematics Subject Classification ID: 76B10
Mathematics Subject Classification ID: 35Q31
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 7352181
zbMATH Keywords: entropy variables
zbMATH Keywords: adjoint
zbMATH Keywords: summation-by-parts
zbMATH Keywords: entropy stable
reviewed by: Bülent Karasözen
MaRDI profile type: Publication
full work available at URL: s10915-020-01395-7
OpenAlex ID: W3124233850
cites work: A finite element pressure gradient stabilization for the Stokes equations based on local projections
cites work: Entropy Stable Spectral Collocation Schemes for the Navier--Stokes Equations: Discontinuous Interfaces
cites work: On discretely entropy conservative and entropy stable discontinuous Galerkin methods
cites work: Kinetic Energy Preserving and Entropy Stable Finite Volume Schemes for Compressible Euler and Navier-Stokes Equations
cites work: Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws
cites work: Entropy-stable summation-by-parts discretization of the Euler equations on general curved elements
cites work: Staggered-grid entropy-stable multidimensional summation-by-parts discretizations on curvilinear coordinates
cites work: Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations
cites work: An Entropy Adjoint Approach to Mesh Refinement
cites work: High-order entropy stable finite difference schemes for nonlinear conservation laws: finite domains
cites work: Discretely conservative finite-difference formulations for nonlinear conservation laws in split form: theory and boundary conditions
cites work: Arbitrarily high-order accurate entropy stable essentially nonoscillatory schemes for systems of conservation laws
cites work: Entropy stable space-time discontinuous Galerkin schemes with summation-by-parts property for hyperbolic conservation laws
cites work: Entropy conservative schemes and the receding flow problem
cites work: On the symmetric form of systems of conservation laws with entropy
cites work: Entropy-stable, high-order summation-by-parts discretizations without interface penalties
cites work: A new finite element formulation for computational fluid dynamics. I: Symmetric forms of the compressible Euler and Navier-Stokes equations and the second law of thermodynamics
cites work: Affordable, entropy-consistent Euler flux functions. II: Entropy production at shocks
cites work: Q4127319
cites work: Q3848368
cites work: Systems of conservation laws of mixed type
cites work: Entropy stable staggered grid discontinuous spectral collocation methods of any order for the compressible Navier-Stokes equations
cites work: Entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations
cites work: Comparison of some entropy conservative numerical fluxes for the Euler equations
cites work: Relaxation Runge--Kutta Methods: Fully Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier--Stokes Equations
cites work: Review of summation-by-parts schemes for initial-boundary-value problems
cites work: Entropy-stable schemes for the Euler equations with far-field and wall boundary conditions
cites work: Skew-selfadjoint form for systems of conservation laws
cites work: The Numerical Viscosity of Entropy Stable Schemes for Systems of Conservation Laws. I
cites work: Entropy stability theory for difference approximations of nonlinear conservation laws and related time-dependent problems
DOI: 10.1007/S10915-020-01395-7
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description: scientific article; zbMATH DE number 7352181