Nonlinear boundary conditions for initial boundary value problems with applications in computational fluid dynamics

DOI10.1016/j.jcp.2023.112685arXiv2306.01297MaRDI QIDQ6187662

Publication date: 31 January 2024

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

Full work available at URL: https://arxiv.org/abs/2306.01297

zbMATH Keywords

Navier-Stokes equations shallow water equations Euler equations nonlinear boundary conditions summation-by-parts energy and entropy stability

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)

Cites Work

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Exactly well-balanced discontinuous Galerkin methods for the shallow water equations with moving water equilibrium
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 and strong wall boundary procedures and convergence to steady-state of the Navier-Stokes equations
A stable high-order finite difference scheme for the compressible Navier-Stokes equations: No-slip wall boundary conditions
A stable and conservative high order multi-block method for the compressible Navier-Stokes equations
Skew-selfadjoint form for systems of conservation laws
Boundary conditions for nonlinear hyperbolic systems of conservation laws
On the symmetric form of systems of conservation laws with entropy
Balancing source terms and flux gradients in high-resolution Godunov methods: The quasi-steady wave-propagation algorithm
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
The numerical interface coupling of nonlinear hyperbolic systems of conservation laws. I: The scalar case
A hybrid framework for coupling arbitrary summation-by-parts schemes on general meshes
Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations
A conservative, skew-symmetric finite difference scheme for the compressible Navier-Stokes equations
An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry
A roadmap to well posed and stable problems in computational physics
Finite volume methods, unstructured meshes and strict stability for hyperbolic problems
The use of characteristic boundary conditions for the Navier-Stokes equations
Entropy stable schemes for initial-boundary-value conservation laws
Stability of discontinuous Galerkin spectral element schemes for wave propagation when the coefficient matrices have jumps
Entropy stability for the compressible Navier-Stokes equations with strong imposition of the no-slip boundary condition
A skew-symmetric energy and entropy stable formulation of the compressible Euler equations
Entropy stable boundary conditions for the Euler equations
Nonlinear and linearised primal and dual initial boundary value problems: when are they bounded? How are they connected?
Entropy stable modal discontinuous Galerkin schemes and wall boundary conditions for the compressible Navier-Stokes equations
Entropy stable numerical approximations for the isothermal and polytropic Euler equations
Analysis of the SBP-SAT stabilization for finite element methods. I: Linear problems
Conservative and entropy stable solid wall boundary conditions for the compressible Navier-Stokes equations: adiabatic wall and heat entropy transfer
The spatial operator in the incompressible Navier-Stokes, Oseen and Stokes equations
A stable high-order finite difference scheme for the compressible Navier-Stokes equations, far-field boundary conditions
Entropy-stable schemes for the Euler equations with far-field and wall boundary conditions
Energy stable flux reconstruction schemes for advection-diffusion problems
The entropy rate admissibility criterion for solutions of hyperbolic conservation laws
Spectral methods on arbitrary grids
A linear and nonlinear analysis of the shallow water equations and its impact on boundary conditions
A Skew-Symmetric Discontinuous Galerkin Spectral Element Discretization and Its Relation to SBP-SAT Finite Difference Methods
Entropy Stable Spectral Collocation Schemes for the Navier--Stokes Equations: Discontinuous Interfaces
The Numerical Viscosity of Entropy Stable Schemes for Systems of Conservation Laws. I
Initial boundary value problems for incompletely parabolic systems
Absorbing Boundary Conditions for the Numerical Simulation of Waves
Incompletely Parabolic Problems in Fluid Dynamics
Theoretical and Practical Aspects of Some Initial Boundary Value Problems in Fluid Dynamics
Entropy stability theory for difference approximations of nonlinear conservation laws and related time-dependent problems
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
Energy stable boundary conditions for the nonlinear incompressible Navier–Stokes equations
Entropy Stability and the No-Slip Wall Boundary Condition
A Stable Penalty Method for the Compressible Navier–Stokes Equations: I. Open Boundary Conditions
The Number of Boundary Conditions for Initial Boundary Value Problems
Initial boundary value problems for hyperbolic systems
FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES
Well-Posed Boundary Conditions for the Navier--Stokes Equations
Analysis of the SBP-SAT stabilization for finite element methods. II: Entropy stability

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