Debris flows are among the most catastrophic natural phenomena, attracting the interest of
researchers, engineers and government agencies. The complexity of the physical process …

Very high order weighted essentially non-oscillatory (WENO) schemes can obtain more
accurate results than those relatively low order WENO schemes for many problems …

This paper presents a gradient-based reconstruction approach for simulations of
compressible single and multi-species Navier–Stokes equations. The novel feature of the …

We present a systematic framework for the evaluation of shock sensors in high-resolution
hybrid compact/WENO algorithms, with the goals of testing robustness and establishing …

Smoothness indicator is an essential part of weighted essentially non-oscillatory (WENO)
scheme, whose target is to distinguish discontinuous profiles and continuous profiles …

This paper presents a weighted compact nonlinear scheme (WCNS) with high-order
accuracy. The WCNS has the flexibility to select a numerical flux and is easily applied to …

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 …

In this paper, we present a novel hybrid nonlinear explicit-compact scheme for shock-
capturing based on a boundary variation diminishing (BVD) reconstruction. In our approach …

Weighted compact nonlinear schemes (WCNSs)[1] are a popular family of high resolution
shock-capturing methods, of which the nonlinear interpolation procedure is essential for non …

In this paper, a new five-point targeted essentially non-oscillatory (TENO) scheme with
adaptive dissipation is proposed. With the standard TENO weighting strategy, the cut-off …