Abstract Summation-by-parts (SBP) operators have a number of properties that make them
an attractive option for higher-order spatial discretizations of partial differential equations. In …

High-order finite difference methods are efficient, easy to program, scale well in multiple
dimensions and can be modified locally for various reasons (such as shock treatment for …

We describe a method for computing time-dependent solutions to the compressible Navier–
Stokes equations on variable geometries. We introduce a continuous mapping between a …

We present and analyze an entropy-stable semi-discretization of the Euler equations based
on high-order summation-by-parts (SBP) operators. In particular, we consider general …

A stable wall boundary procedure is derived for the discretized compressible Navier–Stokes
equations. The procedure leads to an energy estimate for the linearized equations. We …

We develop a new high order accurate time-integration technique for initial value problems.
We focus on problems that originate from a space approximation using high order finite …

Block-to-block interface interpolation operators are constructed for several common high-
order finite difference discretizations. In contrast to conventional interpolation operators …

High-order accurate first derivative finite difference operators are derived that naturally
introduce artificial dissipation. The boundary closures are based on the diagonal-norm …

A high-order explicit finite difference scheme is derived solving the shallow water equations.
The boundary closures are based on the diagonal-norm summation-by-parts (SBP) …

A stable and accurate boundary treatment is derived for the second-order wave equation.
The domain is discretized using narrow-diagonal summation by parts operators and the …