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 …

This paper shows that the discontinuous Galerkin collocation spectral element method with
Gauss--Lobatto points (DGSEM-GL) satisfies the discrete summation-by-parts (SBP) …

Nonlinear entropy stability is used to derive provably stable high-order finite difference
operators including boundary closure stencils, for the compressible Navier–Stokes …

High order (HO) schemes are attractive candidates for the numerical solution of multiscale
problems occurring in fluid dynamics and related disciplines. Among the HO discretization …

Nonlinear entropy stability and a summation-by-parts framework are used to derive provably
stable, polynomial-based spectral collocation element methods of arbitrary order for the …

Computational fluid dynamics (CFD) methods used for the numerical solution of the Euler
and Navier–Stokes equations have been sufficiently matured and enable to perform high …

A generalized framework is presented that extends the classical theory of finite-difference
summation-by-parts (SBP) operators to include a wide range of operators, where the main …

In this work, we present a rigorous derivation of the volume-filtered viscous compressible
Navier–Stokes equations for disperse two-phase flows. Compared to incompressible flows …

Finite difference operators approximating second derivatives with variable coefficients and
satisfying a summation-by-parts rule have been derived for the second-, fourth-and sixth …