For compressible flow simulations involving both turbulence and shockwaves, the
competing requirements render it challenging to develop high-order numerical methods …

For solving time-dependent convection-dominated partial differential equations (PDEs),
which arise frequently in computational physics, high order numerical methods, including …

In this paper, a new type of multi-resolution weighted essentially non-oscillatory (WENO)
limiters for high-order Runge-Kutta discontinuous Galerkin (RKDG) methods is designed …

We present a new perspective on the use of weighted essentially nonoscillatory (WENO)
reconstructions in high-order methods for scalar hyperbolic conservation laws. The main …

We introduce a new troubled-cell indicator for the discontinuous Galerkin (DG) methods for
solving hyperbolic conservation laws. This indicator can be defined on unstructured meshes …

Abstract Runge–Kutta discontinuous Galerkin (RKDG) methods are widely used for solving
hyperbolic conservation laws, supplemented with troubled cell indicators and limiters to …

In the realm of steady-state solutions of Euler equations, the challenge of achieving
convergence of residue close to machine zero has long plagued high-order shock-capturing …

In this paper we generalize a new type of compact Hermite weighted essentially non-
oscillatory (HWENO) limiter for the Runge-Kutta discontinuous Galerkin (RKDG) method …

In this paper, we construct a positivity-preserving high order accurate finite volume hybrid
Hermite Weighted Essentially Non-oscillatory (HWENO) scheme for compressible Navier …

In this paper, a fifth-order Hermite weighted essentially non-oscillatory (HWENO) scheme
with artificial linear weights is proposed for one and two dimensional hyperbolic …