In these lecture notes we describe the construction, analysis, and application of ENO
(Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes for …

Computational approaches are being developed to study a range of problems in
aeroacoustics. These aeroacoustic problems may be classified based on the physical …

Abstract Fisher and Carpenter (2013)[12] found a remarkable equivalence of general
diagonal norm high-order summation-by-parts operators to a subcell based high-order finite …

In this paper we further explore a class of high order TVD (total variation diminishing) Runge-
Kutta time discretization initialized in a paper by Shu and Osher, suitable for solving …

Mathematicsisplayinganevermoreimportant…-ical sciences, provoking a blurring of
boundaries between scienti? c disciplines and a resurgence of interest in the modern as …

In this paper we review and further develop a class of strong stability-preserving (SSP) high-
order time discretizations for semidiscrete method of lines approximations of partial …

We present the latest developments of our High-Order Spectral Element Solver (Image 1),
an open source high-order discontinuous Galerkin framework, capable of solving a variety of …

The objective of this book is to provide a comprehensive discussion of Fourier and
Chebyshev spectral methods for the computation of incom pressible viscous flows, based on …

Explicit numerical methods for spatial derivation, filtering and time integration are proposed.
They are developed with the aim of computing flow and noise with high accuracy and …

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