The stability of numerical boundary treatments for compact high-order finite-difference schemes
Journal of Computational Physics
Summation by parts for finite difference approximations for d/dx
Journal of Computational Physics
Fourth-order difference methods for hyperbolic IBVPs
Journal of Computational Physics
Spectral methods on arbitrary grids
Journal of Computational Physics
Asymptotically stable fourth-order accurate schemes for the diffusion equation on complex shapes
Journal of Computational Physics
Spectral simulations of electromagnetic wave scattering
Journal of Computational Physics
SIAM Journal on Scientific Computing
A stable and conservative interface treatment of arbitrary spatial accuracy
Journal of Computational Physics
Journal of Computational Physics
High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates
Journal of Computational Physics
On Coordinate Transformations for Summation-by-Parts Operators
Journal of Scientific Computing
Applied Numerical Mathematics
Summation by parts operators for finite difference approximations of second derivatives
Journal of Computational Physics
Steady-State Computations Using Summation-by-Parts Operators
Journal of Scientific Computing
A stable hybrid method for hyperbolic problems
Journal of Computational Physics
Journal of Scientific Computing
On the order of accuracy for difference approximations of initial-boundary value problems
Journal of Computational Physics
Journal of Computational Physics
Stable and accurate schemes for the compressible Navier-Stokes equations
Journal of Computational Physics
A stable high-order finite difference scheme for the compressible Navier-Stokes equations
Journal of Computational Physics
Stable and accurate wave-propagation in discontinuous media
Journal of Computational Physics
Stable and Accurate Interpolation Operators for High-Order Multiblock Finite Difference Methods
SIAM Journal on Scientific Computing
Superconvergent Functional Estimates from Summation-By-Parts Finite-Difference Discretizations
SIAM Journal on Scientific Computing
Output error estimation for summation-by-parts finite-difference schemes
Journal of Computational Physics
Journal of Scientific Computing
High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains
Journal of Computational Physics
Hi-index | 31.45 |
Optimal boundary closures are derived for first derivative, finite difference operators of order 2, 4, 6 and 8. The closures are based on a diagonal-norm summation-by-parts (SBP) framework, thereby guaranteeing linear stability on piecewise curvilinear multi-block grids and entropy stability for nonlinear equations that support a convex extension. The new closures are developed by enriching conventional approaches with additional boundary closure stencils and non-equidistant grid distributions at the domain boundaries. Greatly improved accuracy is achieved near the boundaries, as compared with traditional diagonal-norm operators of the same order. The superior accuracy of the new optimal diagonal-norm SBP operators is demonstrated for linear hyperbolic systems in one dimension and for the nonlinear compressible Euler equations in two dimensions.