Review of summation-by-parts schemes for initial-boundary-value problems (Q349036)

scientific article; zbMATH DE number 6660200

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English	Review of summation-by-parts schemes for initial-boundary-value problems	scientific article; zbMATH DE number 6660200

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instance of

scholarly article

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title

Review of summation-by-parts schemes for initial-boundary-value problems (English)

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Journal of Computational Physics

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publication date

5 December 2016

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full work available at URL

https://arxiv.org/abs/1311.4984

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zbMATH Keywords

summation-by-parts schemes

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simultaneous approximation terms

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Summation by parts for finite difference approximations for \(d/dx\)

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Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes

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Q4875410

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On the stability definition of difference approximations for the initial boundary value problem

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From Semidiscrete to Fully Discrete: Stability of Runge--Kutta Schemes by The Energy Method

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Summation-by-parts in time

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Entropy stable schemes for initial-boundary-value conservation laws

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Weak and strong wall boundary procedures and convergence to steady-state of the Navier-Stokes equations

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Fluid Structure Interaction Problems: the Necessity of a Well Posed, Stable and Accurate Formulation

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Finite volume methods, unstructured meshes and strict stability for hyperbolic problems

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Strict stability of high-order compact implicit finite-difference schemes: The role of boundary conditions for hyperbolic PDEs. I

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Strict stability of high-order compact implicit finite-difference schemes: The role of boundary conditions for hyperbolic PDEs. II

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The use of characteristic boundary conditions for the Navier-Stokes equations

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Boundary and interface conditions for high-order finite-difference methods applied to the Euler and Navier-Stokes equations

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A stable and conservative interface treatment of arbitrary spatial accuracy

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A stable high-order finite difference scheme for the compressible Navier-Stokes equations: No-slip wall boundary conditions

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Interface procedures for finite difference approximations of the advection-diffusion equation

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Spectral analysis of the continuous and discretized heat and advection equation on single and multiple domains

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A stable and conservative method for locally adapting the design order of finite difference schemes

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Revisiting and extending interface penalties for multi-domain summation-by-parts operators

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Stability at nonconforming grid interfaces for a high order discretization of the Schrödinger equation

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Stable and Accurate Interpolation Operators for High-Order Multiblock Finite Difference Methods

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A stable and conservative high order multi-block method for the compressible Navier-Stokes equations

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Discretely conservative finite-difference formulations for nonlinear conservation laws in split form: theory and boundary conditions

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Entropy-stable schemes for the Euler equations with far-field and wall boundary conditions

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Summation by parts operators for finite difference approximations of second derivatives

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Stable and accurate schemes for the compressible Navier-Stokes equations

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Asymptotically stable fourth-order accurate schemes for the diffusion equation on complex shapes

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Multi-dimensional asymptotically stable finite difference schemes for the advection-diffusion equation

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Survey of the stability of linear finite difference equations

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The Convergence Rate for Difference Approximations to Mixed Initial Boundary Value Problems

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The Convergence Rate for Difference Approximations to General Mixed Initial-Boundary Value Problems

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On error bounds of finite difference approximations to partial differential equations. -- Temporal behavior and rate of convergence

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On the order of accuracy for difference approximations of initial-boundary value problems

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High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates

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Summation by Parts, Projections, and Stability. I

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Summation by Parts, Projections, and Stability. II

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Designing an efficient solution strategy for fluid flows. I: A stable high order finite difference scheme and sharp shock resolution for the Euler equations

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Designing an efficient solution strategy for fluid flows. II: Stable high-order central finite difference schemes on composite adaptive grids with sharp shock resolution

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High Order Difference Methods for Time Dependent PDE

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Boundary procedures for summation-by-parts operators

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Accuracy of the simultaneous-approximation-term boundary condition for time-dependent problems

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Stable Robin solid wall boundary conditions for the Navier-Stokes equations

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A computational study of vortex-airfoil interaction using high-order finite difference methods

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Boundary conditions for nonlinear hyperbolic systems of conservation laws

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A stable high-order finite difference scheme for the compressible Navier-Stokes equations, far-field boundary conditions

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Conservative finite difference formulations, variable coefficients, energy estimates and artificial dissipation

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Error Bounded Schemes for Time-dependent Hyperbolic Problems

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Simulation of dynamic earthquake ruptures in complex geometries using high-order finite difference methods

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Interaction of waves with frictional interfaces using summation-by-parts difference operators: weak enforcement of nonlinear boundary conditions

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On coordinate transformations for summation-by-parts operators

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Steady-state computations using summation-by-parts operators

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Superconvergent Functional Estimates from Summation-By-Parts Finite-Difference Discretizations

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Output error estimation for summation-by-parts finite-difference schemes

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Summation-by-parts operators and high-order quadrature

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Superconvergent functional output for time-dependent problems using finite differences on summation-by-parts form

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Dual consistency and functional accuracy: a finite-difference perspective

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On the impact of boundary conditions on dual consistent finite difference discretizations

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Duality based boundary conditions and dual consistent finite difference discretizations of the Navier-Stokes and Euler equations

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Finite volume approximations and strict stability for hyperbolic problems

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Stability of finite volume approximations for the Laplacian operator on quadrilateral and triangular grids

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Stable artificial dissipation operators for finite volume schemes on unstructured grids

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An adaptive implicit-explicit scheme for the DNS and LES of compressible flows on unstructured grids

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A stable hybrid method for hyperbolic problems

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A stable and efficient hybrid scheme for viscous problems in complex geometries

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A hybrid method for unsteady inviscid fluid flow

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A skew-symmetric discontinuous Galerkin spectral element discretization and its relation to SBP-SAT finite difference methods

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Energy stable flux reconstruction schemes for advection-diffusion problems on triangles

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Optimal time splitting for two- and three-dimensional Navier-Stokes equations with mixed derivatives

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A diagonal form of an implicit approximate-factorization algorithm

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Stable and accurate artificial dissipation

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Optimized high-order derivative and dissipation operators satisfying summation by parts, and applications in three-dimensional multi-block evolutions

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Low-storage, explicit Runge-Kutta schemes for the compressible Navier-Stokes equations

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Additive Runge-Kutta schemes for convection-diffusion-reaction equations

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Implicit time integration schemes for the unsteady compressible Navier-Stokes equations: Laminar flow

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Fourth-order Runge-Kutta schemes for fluid mechanics applications

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High-order accurate computations for unsteady aerodynamics

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Scattering of an entropy disturbance into sound by a symmetric thin body

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Boundary conditions for a divergence-free velocity-pressure formulation of the Navier-Stokes equations

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Towards Time-Stable and Accurate LES on Unstructured Grids

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High order numerical simulation of aeolian tones

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Entropy splitting for high-order numerical simulation of vortex sound at low Mach numbers

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Numerical simulation of confined pulsating jets in human phonation

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Conjugate heat transfer for the unsteady compressible Navier-Stokes equations using a multi-block coupling

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High order finite difference methods for wave propagation in discontinuous media

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Stable boundary treatment for the wave equation on second-order form

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Stable and Accurate Second-order Formulation of the Shifted Wave Equation

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Higher order finite difference schemes for the magnetic induction equations

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Higher-order finite difference schemes for the magnetic induction equations with resistivity

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Numerical analysis of the Burgers' equation in the presence of uncertainty

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On stability and monotonicity requirements of finite difference approximations of stochastic conservation laws with random viscosity

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An intrusive hybrid method for discontinuous two-phase flow under uncertainty

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A stochastic Galerkin method for the Euler equations with roe variable transformation

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Accurate partial difference methods. II: Non-linear problems

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Q4692703

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Stability Theory of Difference Approximations for Multidimensional Initial-Boundary Value Problems

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Convergence Theorem for Difference Approximations of Hyperbolic Quasi- Initial-Boundary Value Problems

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Symmetrizable Finite Difference Operators

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Linear Instability of the Fifth-Order WENO Method

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On the linear stability of the fifth-order WENO discretization

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Boundary closures for fourth-order energy stable weighted essentially non-oscillatory finite-difference schemes

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Entropy stability theory for difference approximations of nonlinear conservation laws and related time-dependent problems

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Third-order accurate entropy-stable schemes for initial-boundary-value conservation laws

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High-order entropy stable finite difference schemes for nonlinear conservation laws: finite domains

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Identifiers

zbMATH Open document ID

1349.65336

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Mathematics Subject Classification ID

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10.1016/J.JCP.2014.02.031

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Sitelinks

Mathematics(1 entry)

mardi Publication:349036