Provably stable flux reconstruction high-order methods on curvilinear elements

DOI10.1016/j.jcp.2022.111259OpenAlexW3202480948MaRDI QIDQ2671373

David C. Del Rey Fernández, Alexander Cicchino, Jesse Chan, Mark H. Carpenter, Siva K. Nadarajah

Publication date: 3 June 2022

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

Full work available at URL: https://arxiv.org/abs/2109.11617

zbMATH Keywords

discontinuous Galerkinflux reconstructionhigh-ordersummation-by-parts

Mathematics Subject Classification ID

Basic methods in fluid mechanics (76Mxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Hyperbolic equations and hyperbolic systems (35Lxx)

Uses Software

• PyFR

Cites Work

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• On the stability of the flux reconstruction schemes on quadrilateral elements for the linear advection equation
• PyFR: an open source framework for solving advection-diffusion type problems on streaming architectures using the flux reconstruction approach
• High-order entropy stable finite difference schemes for nonlinear conservation laws: finite domains
• On the accuracy and efficiency of discontinuous Galerkin, spectral difference and correction procedure via reconstruction methods
• Review of summation-by-parts schemes for initial-boundary-value problems
• Entropy stable discontinuous interfaces coupling for the three-dimensional compressible Navier-Stokes equations
• Entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations
• A high-order spectral difference method for unstructured dynamic grids
• A generalized framework for nodal first derivative summation-by-parts operators
• On the non-linear stability of flux reconstruction schemes
• Connections between the filtered discontinuous Galerkin method and the flux reconstruction approach to high order discretizations
• A new class of high-order energy stable flux reconstruction schemes for triangular elements
• Energy stable flux reconstruction schemes for advection-diffusion problems on tetrahedra
• An analysis of solution point coordinates for flux reconstruction schemes on triangular elements
• Revisiting and extending interface penalties for multi-domain summation-by-parts operators
• A proof of the stability of the spectral difference method for all orders of accuracy
• A new class of high-order energy stable flux reconstruction schemes
• Insights from von Neumann analysis of high-order flux reconstruction schemes
• A family of fourth-order entropy stable nonoscillatory spectral collocation schemes for the 1-D Navier-Stokes equations
• On the freestream preservation of high-order conservative flux-reconstruction schemes
• Equivalence between the energy stable flux reconstruction and filtered discontinuous Galerkin schemes
• Formulation of discontinuous Galerkin methods for relativistic astrophysics
• A unifying lifting collocation penalty formulation including the discontinuous Galerkin, spectral volume/difference methods for conservation laws on mixed grids
• A stable and conservative interface treatment of arbitrary spatial accuracy
• Boundary and interface conditions for high-order finite-difference methods applied to the Euler and Navier-Stokes equations
• Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes
• On coordinate transformations for summation-by-parts operators
• The BR1 scheme is stable for the compressible Navier-Stokes equations
• On discretely entropy conservative and entropy stable discontinuous Galerkin methods
• Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations
• High-order methods for computational fluid dynamics: a brief review of compact differential formulations on unstructured grids
• An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry
• Extended skew-symmetric form for summation-by-parts operators and varying Jacobians
• Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws
• Entropy-stable summation-by-parts discretization of the Euler equations on general curved elements
• Stable, non-dissipative, and conservative flux-reconstruction schemes in split forms
• Influence of reference-to-physical frame mappings on approximation properties of discontinuous piecewise polynomial spaces
• On the connection between the correction and weighting functions in the correction procedure via reconstruction method
• A general framework to construct schemes satisfying additional conservation relations. Application to entropy conservative and entropy dissipative schemes
• A new norm and stability condition for tensor product flux reconstruction schemes
• Entropy-stable discontinuous Galerkin approximation with summation-by-parts property for the incompressible Navier-Stokes/Cahn-Hilliard system
• A provably entropy stable subcell shock capturing approach for high order split form DG for the compressible Euler equations
• Nonlinearly stable flux reconstruction high-order methods in split form
• Encapsulated high order difference operators on curvilinear non-conforming grids
• Entropy stable \(h/p\)-nonconforming discretization with the summation-by-parts property for the compressible Euler and Navier-Stokes equations
• Staggered-grid entropy-stable multidimensional summation-by-parts discretizations on curvilinear coordinates
• High-order entropy stable discontinuous Galerkin methods for the shallow water equations: curved triangular meshes and GPU acceleration
• Full-space approach to aerodynamic shape optimization
• On discretely entropy stable weight-adjusted discontinuous Galerkin methods: curvilinear meshes
• Free-stream preservation for curved geometrically non-conforming discontinuous Galerkin spectral elements
• Entropy stable space-time discontinuous Galerkin schemes with summation-by-parts property for hyperbolic conservation laws
• Extension of tensor-product generalized and dense-norm summation-by-parts operators to curvilinear coordinates
• Skew-symmetric entropy stable modal discontinuous Galerkin formulations
• Summation-by-parts operators for correction procedure via reconstruction
• Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations
• Interpolation error bounds for curvilinear finite elements and their implications on adaptive mesh refinement
• Entropy-stable schemes for the Euler equations with far-field and wall boundary conditions
• Discretely conservative finite-difference formulations for nonlinear conservation laws in split form: theory and boundary conditions
• Energy stable flux reconstruction schemes for advection-diffusion problems
• Metric identities and the discontinuous spectral element method on curvilinear meshes
• On the connections between discontinuous Galerkin and flux reconstruction schemes: extension to curvilinear meshes
• An extended range of stable-symmetric-conservative flux reconstruction correction functions
• Entropy Stable Staggered Grid Discontinuous Spectral Collocation Methods of any Order for the Compressible Navier--Stokes Equations
• Entropy Stable Spectral Collocation Schemes for the Navier--Stokes Equations: Discontinuous Interfaces
• A High-Order Unifying Discontinuous Formulation for the Navier-Stokes Equations on 3D Mixed Grids
• Geometric Conservation Law and Its Application to Flow Computations on Moving Grids
• Connections between the discontinuous Galerkin method and high‐order flux reconstruction schemes
• High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates

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