A Convergent Numerical Scheme for the Compressible Navier--Stokes Equations

DOI10.1137/15M1010361zbMath1381.76243OpenAlexW2404040229MaRDI QIDQ2807286

Magnus Svärd

Publication date: 20 May 2016

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m1010361

zbMATH Keywords

convergenceexistenceNavier-Stokes equationsweak solutionsfinite difference scheme

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Finite difference methods applied to problems in fluid mechanics (76M20) Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10)

Related Items (10)

Large eddy simulations by approximate weak entropy solutions ⋮ A new Eulerian model for viscous and heat conducting compressible flows ⋮ Positivity-preserving entropy stable schemes for the 1-D compressible Navier-Stokes equations: high-order flux limiting ⋮ Positivity-preserving entropy stable schemes for the 1-D compressible Navier-Stokes equations: first-order approximation ⋮ A positivity preserving strategy for entropy stable discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations ⋮ High-order positivity-preserving entropy stable schemes for the 3-D compressible Navier-Stokes equations ⋮ Entropy Stability and the No-Slip Wall Boundary Condition ⋮ Entropy stable artificial dissipation based on Brenner regularization of the Navier-Stokes equations ⋮ Entropy stability for the compressible Navier-Stokes equations with strong imposition of the no-slip boundary condition ⋮ First-order positivity-preserving entropy stable scheme for the 3-D compressible Navier-Stokes equations

Cites Work

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• Review of summation-by-parts schemes for initial-boundary-value problems
• Entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations
• Weak solutions and convergent numerical schemes of modified compressible Navier-Stokes equations
• 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
• Systems of conservation laws of mixed type
• Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations
• Weak-strong uniqueness property for the full Navier-Stokes-Fourier system
• Entropy-stable schemes for the Euler equations with far-field and wall boundary conditions
• Generalized Korn's inequality and conformal Killing vectors
• Entropy stability theory for difference approximations of nonlinear conservation laws and related time-dependent problems
• Positivity-preserving analysis of explicit and implicit Lax-Friedrichs schemes for compressible Euler equations

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