It is a notoriously challenge problem for Lagrangian particle methods to solve compressible
flows with strong discontinuities and large volume variations. To overcome the problems of …

The finite difference multi-resolution alternative weighted essentially non-oscillatory (MR-
AWENO) scheme has been designed to solve hyperbolic conservation laws (Wang et al. in …

A hybrid finite difference fifth-order multi-resolution weighted compact nonlinear scheme
(WCNS) is presented for simulating the inviscid and viscous compressible flows in this …

Numerical study on compressible two-medium flows has been a hot issue in recent
decades. In this study, we design quasi-conservative finite difference alternative weighted …

In this paper, a hybrid unequal-sized weighted essentially non-oscillatory (US-WENO)
scheme is developed to reduce the computational cost caused by the computation of …

In this paper, the new fifth-order, seventh-order, and ninth-order finite difference and finite
volume multi-resolution weighted essentially non-oscillatory (MR-WENO) schemes with …

The weighted essentially non-oscillatory (WENO) scheme is a famous shock-capturing
scheme, but for high-precision numerical simulation, the classical WENO scheme is always …

In this paper, two unequal-sized weighted essentially non-oscillatory (US-WENO) schemes
are proposed for solving hyperbolic conservation laws. First, an alternative US-WENO (AUS …

In this paper, we develop a simple, efficient, and fifth-order finite difference interpolation-
based Hermite WENO (HWENO-I) scheme for one-and two-dimensional hyperbolic …

The coexistence and interaction of shock waves and turbulence occur in various
applications, such as inertial confinement fusion, scramjet propulsion, and supernova …