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

We review numerical methods for direct numerical simulation (DNS) and large-eddy
simulation (LES) of turbulent compressible flow in the presence of shock waves. Ideal …

Although classical WENO schemes have achieved great success and are widely accepted,
they exhibit several shortcomings. They are too dissipative for direct simulations of …

In 1917, the British scientist LF Richardson made the first reported attempt to predict the
weather by solving partial differential equations numerically, by hand! It is generally …

High order accurate weighted essentially nonoscillatory (WENO) schemes are relatively new
but have gained rapid popularity in numerical solutions of hyperbolic partial differential …

In this article, we show that for a WENO scheme to improve the numerical resolution of
smooth waves, increasing to some extent the contribution of the substencils where the …

UCNS3D is an open-source computational solver for compressible flows on unstructured
meshes. State-of-the-art high-order methods and their associated benefits can now be …

High-order accurate shock-capturing schemes are capable of properly resolving
discontinuities with correct wave speeds in single-fluid Riemann problems. However, when …

We develop a shock-and interface-capturing numerical method that is suitable for the
simulation of multicomponent flows governed by the compressible Navier–Stokes equations …

The framework of inner product norm preserving relaxation Runge--Kutta methods [DI
Ketcheson, SIAM J. Numer. Anal., 57 (2019), pp. 2850--2870] is extended to general convex …