On the rotation and skew-symmetric forms for incompressible flow simulations
Applied Numerical Mathematics - Special issue: Transition to turbulence
Why nonconservative schemes converge to wrong solutions: error analysis
Mathematics of Computation
The effect of the formulation of nonlinear terms on aliasing errors in spectral methods
Applied Numerical Mathematics
Designing an efficient solution strategy for fluid flows
Journal of Computational Physics
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Fully conservative higher order finite difference schemes for incompressible flow
Journal of Computational Physics
A stable and conservative interface treatment of arbitrary spatial accuracy
Journal of Computational Physics
Journal of Computational Physics
Entropy splitting and numerical dissipation
Journal of Computational Physics
Summation by parts operators for finite difference approximations of second derivatives
Journal of Computational Physics
Higher entropy conservation and numerical stability of compressible turbulence simulations
Journal of Computational Physics
On the order of accuracy for difference approximations of initial-boundary value problems
Journal of Computational Physics
An artificial nonlinear diffusivity method for supersonic reacting flows with shocks
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
Localized artificial diffusivity scheme for discontinuity capturing on curvilinear meshes
Journal of Computational Physics
A fully discrete, kinetic energy consistent finite-volume scheme for compressible flows
Journal of Computational Physics
A systematic methodology for constructing high-order energy stable WENO schemes
Journal of Computational Physics
Journal of Computational Physics
Generalized conservative approximations of split convective derivative operators
Journal of Computational Physics
Stabilized non-dissipative approximations of Euler equations in generalized curvilinear coordinates
Journal of Computational Physics
Stable and Accurate Interpolation Operators for High-Order Multiblock Finite Difference Methods
SIAM Journal on Scientific Computing
Journal of Computational Physics
Journal of Scientific Computing
A conservative finite difference scheme for Poisson---Nernst---Planck equations
Journal of Computational Electronics
Hi-index | 31.45 |
The Lax-Wendroff theorem stipulates that a discretely conservative operator is necessary to accurately capture discontinuities. The discrete operator, however, need not be derived from the divergence form of the continuous equations. Indeed, conservation law equations that are split into linear combinations of the divergence and product rule form and then discretized using any diagonal-norm skew-symmetric summation-by-parts (SBP) spatial operator, yield discrete operators that are conservative. Furthermore, split-form, discretely conservation operators can be derived for periodic or finite-domain SBP spatial operators of any order. Examples are presented of a fourth-order, SBP finite-difference operator with second-order boundary closures. Sixth- and eighth-order constructions are derived, and are supplied in an accompanying text file.