A family of fourth-order entropy stable nonoscillatory spectral collocation schemes for the 1-D Navier-Stokes equations

DOI10.1016/j.jcp.2016.11.039zbMath1378.76079OpenAlexW2558500297MaRDI QIDQ680199

Nail K. Yamaleev, Mark H. Carpenter

Publication date: 22 January 2018

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2016.11.039

zbMATH Keywords

Navier-Stokes equationsweighted essentially nonoscillatory schemesspectral collocation methodsentropy stabilityWENO schemessummation-by-parts operatorsSBP operators

Mathematics Subject Classification ID

Spectral methods applied to problems in fluid mechanics (76M22) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items

On the robustness and performance of entropy stable collocated discontinuous Galerkin methods, Generalised summation-by-parts operators and variable coefficients, 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, Provably stable flux reconstruction high-order methods on curvilinear elements, A provably stable and high-order accurate finite difference approximation for the incompressible boundary layer equations, High-order positivity-preserving entropy stable schemes for the 3-D compressible Navier-Stokes equations, Entropy stable artificial dissipation based on Brenner regularization of the Navier-Stokes equations, Entropy stable spectral collocation schemes for the 3-D Navier-Stokes equations on dynamic unstructured grids, Extension of tensor-product generalized and dense-norm summation-by-parts operators to curvilinear coordinates, First-order positivity-preserving entropy stable scheme for the 3-D compressible Navier-Stokes equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes
• High-order entropy stable finite difference schemes for nonlinear conservation laws: finite domains
• Entropy stable discontinuous interfaces coupling for the three-dimensional compressible Navier-Stokes equations
• Boundary closures for fourth-order energy stable weighted essentially non-oscillatory finite-difference schemes
• On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes
• A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
• Affordable, entropy-consistent Euler flux functions. II: Entropy production at shocks
• Third-order energy stable WENO scheme
• A systematic methodology for constructing high-order energy stable WENO schemes
• 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
• Uniformly high order accurate essentially non-oscillatory schemes. III
• On the symmetric form of systems of conservation laws with entropy
• Weighted essentially non-oscillatory schemes
• Low-storage, explicit Runge-Kutta schemes for the compressible Navier-Stokes equations
• Efficient implementation of weighted ENO schemes
• Entropy stable shock capturing space-time discontinuous Galerkin schemes for systems of conservation laws
• Discretely conservative finite-difference formulations for nonlinear conservation laws in split form: theory and boundary conditions
• Spectral methods on arbitrary grids
• Solutions of multi-dimensional hyperbolic systems of conservation laws by square entropy condition satisfying discontinuous Galerkin method
• Arbitrarily High-order Accurate Entropy Stable Essentially Nonoscillatory Schemes for Systems of Conservation Laws
• Entropy Stable Spectral Collocation Schemes for the Navier--Stokes Equations: Discontinuous Interfaces
• Convergence of Godunov-Type Schemes for Scalar Conservation Laws under Large Time Steps
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• On a Cell Entropy Inequality for Discontinuous Galerkin Methods
• Convergence of Semi-Lagrangian Approximations to Convex Hamilton--Jacobi Equations under (Very) Large Courant Numbers
• Entropy stability theory for difference approximations of nonlinear conservation laws and related time-dependent problems
• Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters
• Numerical Methods for High-Speed Flows
• Systems of conservation laws
• A technique of treating negative weights in WENO schemes