Spectral methods yield numerical solutions of the Galerkin-truncated versions of nonlinear
partial differential equations (PDEs) involved especially in fluid dynamics. In the presence of …

The Roe scheme is known to have high resolution but to be afflicted by the notorious shock
anomalies (such as the carbuncle phenomena) and the unphysical expansion shocks. This …

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 classical third‐order weighted essentially nonoscillatory (WENO) scheme is notoriously
dissipative as it loses the optimal order of accuracy at critical points and its two‐point finite …

In this paper we proposed the kinetic framework based fifth-order adaptive finite difference
WENO schemes abbreviated as WENO-AO-K schemes to solve the compressible Euler …

Abstract The Weighted Essentially Non-Oscillatory (WENO) scheme is an accurate and
robust reconstruction procedure to simulate compressible flows, especially in the presence …

We develop a positivity-preserving finite difference WENO scheme for the Ten-Moment
equations with body forces acting as a source in the momentum and energy equations. A …

In high-resolution numerical simulations of flows characterized by both multiscale turbulence
and discontinuities, the conflict between spectral characteristics and stability becomes …

In this paper, a free surface flow solver based on an improved coupling method for practical,
highly nonlinear, complex free-surface flows is presented. The coupling method which is …

The FORCE-type centred schemes are simple and efficient and do not explicitly require the
wave propagation information of the system to calculate the numerical flux. However, their …