Implicit summation by parts operators for finite difference approximations of first and second derivatives

DOI10.1016/j.jcp.2022.111743OpenAlexW4308514782MaRDI QIDQ2106961

Ylva Ljungberg Rydin, Ken Mattsson

Publication date: 29 November 2022

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

Full work available at URL: https://doi.org/10.1016/j.jcp.2022.111743

zbMATH Keywords

stabilityhigh-order accuracyboundary treatmentdispersion propertiesimplicit finite difference methods

Mathematics Subject Classification ID

Numerical approximation and computational geometry (primarily algorithms) (65Dxx) Basic methods in fluid mechanics (76Mxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx)

Cites Work

• Unnamed Item
• Unnamed Item
• A solution to the stability issues with block norm summation by parts operators
• Optimal diagonal-norm SBP operators
• 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 generalized framework for nodal first derivative summation-by-parts operators
• Output error estimation for summation-by-parts finite-difference schemes
• Summation by parts operators for finite difference approximations of second-derivatives with variable coefficients
• Stable boundary treatment for the wave equation on second-order form
• Dispersion-relation-preserving finite differene schemes for computational acoustics
• Stable and accurate artificial dissipation
• Diagonal-norm summation by parts operators for finite difference approximations of third and fourth derivatives
• Energy conservative SBP discretizations of the acoustic wave equation in covariant form on staggered curvilinear grids
• Conservative finite difference formulations, variable coefficients, energy estimates and artificial dissipation
• High-order accurate computations for unsteady aerodynamics
• Compact finite difference schemes with spectral-like resolution
• Summation by parts for finite difference approximations for \(d/dx\)
• The stability of numerical boundary treatments for compact high-order finite-difference schemes
• Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes
• Asymptotically stable fourth-order accurate schemes for the diffusion equation on complex shapes
• On coordinate transformations for summation-by-parts operators
• Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations
• Compatible diagonal-norm staggered and upwind SBP operators
• A high-order accurate embedded boundary method for first order hyperbolic equations
• Diagonal-norm upwind SBP operators
• Summation-by-parts operators with minimal dispersion error for coarse grid flow calculations
• Energy stable and high-order-accurate finite difference methods on staggered grids
• Stability of finite volume approximations for the Laplacian operator on quadrilateral and triangular grids
• Summation by parts operators for finite difference approximations of second derivatives
• Strict stability of high-order compact implicit finite-difference schemes: The role of boundary conditions for hyperbolic PDEs. I
• Strict stability of high-order compact implicit finite-difference schemes: The role of boundary conditions for hyperbolic PDEs. II
• An improved projection method
• Galerkin differences for acoustic and elastic wave equations in two space dimensions
• A residual-based artificial viscosity finite difference method for scalar conservation laws
• Continuous/discontinuous Galerkin difference discretizations of high-order differential operators
• Weak versus strong wall boundary conditions for the incompressible Navier-Stokes equations
• Robust approaches to handling complex geometries with Galerkin difference methods
• On the convergence rates of energy-stable finite-difference schemes
• Boundary optimized diagonal-norm SBP operators
• Uniformly best wavenumber approximations by spatial central difference operators
• On Galerkin difference methods
• Entropy-stable schemes for the Euler equations with far-field and wall boundary conditions
• Spectral methods on arbitrary grids
• Steady-state computations using summation-by-parts operators
• Skew-symmetric form of convective terms and fully conservative finite difference schemes for variable density low-Mach number flows
• Entropy Stable Spectral Collocation Schemes for the Navier--Stokes Equations: Discontinuous Interfaces
• High-Order Finite Differences and the Pseudospectral Method on Staggered Grids
• 10.1007/s11470-008-3006-y
• A Stable Penalty Method for the Compressible Navier--Stokes Equations: III. Multidimensional Domain Decomposition Schemes
• HIGH-ORDER-ACCURATE SCHEMES FOR INCOMPRESSIBLE VISCOUS FLOW
• Spatial Finite Difference Approximations for Wave-Type Equations
• Summation by Parts, Projections, and Stability. I
• Summation by Parts, Projections, and Stability. II

This page was built for publication: Implicit summation by parts operators for finite difference approximations of first and second derivatives