There have been growing research interests in high-order discontinuous schemes over
recent years. With established theoretical basis and framework, more efforts have recently …

As computational astrophysics comes under pressure to become a precision science, there
is an increasing need to move to high accuracy schemes for computational astrophysics …

In this paper, a new type of high-order finite difference and finite volume multi-resolution
weighted essentially non-oscillatory (WENO) schemes is presented for solving hyperbolic …

We introduce a new relativistic astrophysics code, SpECTRE, that combines a discontinuous
Galerkin method with a task-based parallelism model. SpECTRE's goal is to achieve more …

In this paper we develop a family of very high-order central (up to 6th-order) non-oscillatory
schemes for mixed-element unstructured meshes. The schemes are inherently compact in …

We present a novel, cell-local shock detector for use with discontinuous Galerkin (DG)
methods. The output of this detector is a reliably scaled, element-wise smoothness estimate …

Several computational problems in science and engineering are stringent enough that
maintaining positivity of density and pressure can become a problem. We build on the …

ADER (Arbitrary DERivative in space and time) methods for the time-evolution of hyperbolic
conservation laws have recently generated a fair bit of interest. The ADER time update can …

This study presents a new weighted compact nonlinear scheme (WCNS). In the WCNS
procedure, the linear difference scheme is modified to use the flux on the computational …

This paper presents the development and implementation of weighted-essentially-non-
oscillatory (WENO) schemes for viscous flows on arbitrary unstructured grids. WENO …