相关论文: Well-balanced fifth-order finite difference Hermit…

In this paper, a simple fifth-order finite difference Hermite WENO (HWENO) scheme combined with limiter is proposed for one- and two- dimensional hyperbolic conservation laws. The fluxes in the governing equation are approximated by the…

In this paper, we propose a new well-balanced fifth-order finite volume WENO method for solving one- and two-dimensional shallow water equations with bottom topography. The well-balanced property is crucial to the ability of a scheme to…

In this paper, we are concerned with the shallow water flow model over non-flat bottom topography by high-order schemes. Most of the numerical schemes in the literature are developed from the original mathematical model of the shallow water…

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 conservation laws. We directly interpolate the solution and…

In this paper, we propose a novel Hermite weighted essentially non-oscillatory (HWENO) fast sweeping method to solve the static Hamilton-Jacobi equations efficiently. During the HWENO reconstruction procedure, the proposed method is built…

In this paper, we combine the nonlinear HWENO reconstruction in \cite{newhwenozq} and the fixed-point iteration with Gauss-Seidel fast sweeping strategy, to solve the static Hamilton-Jacobi equations in a novel HWENO framework recently…

In this paper, we propose a hybrid finite volume Hermite weighted essentially non-oscillatory (HWENO) scheme for solving one and two dimensional hyperbolic conservation laws. The zeroth-order and the first-order moments are used in the…

In this paper, a fifth-order moment-based Hermite weighted essentially non-oscillatory scheme with unified stencils (termed as HWENO-U) is proposed for hyperbolic conservation laws. The main idea of the HWENO-U scheme is to modify the…

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 conservation laws, where the zeroth-order and the first-order moments…

Higher order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes have been constructed for conservation laws. For multidimensional problems, they offer high order accuracy at a fraction of the cost of a finite volume WENO…

The blood flow model maintains the steady state solutions, in which the flux gradients are non-zero but exactly balanced by the source term. In this paper, we design high order finite difference weighted non-oscillatory (WENO) schemes to…

In this paper, we develop a high order residual distribution (RD) method for solving steady state conservation laws in a novel Hermite weighted essentially non-oscillatory (HWENO) framework recently developed in [24]. In particular, we…

This paper develops a new fifth order accurate Hermite WENO (HWENO) reconstruction method for hyperbolic conservation schemes in the framework of the two-stage fourth order accurate temporal discretization in [{\em J. Li and Z. Du, A…

In this paper, a high-order moment-based multi-resolution Hermite weighted essentially non-oscillatory (HWENO) scheme is designed for hyperbolic conservation laws. The main idea of this scheme is derived from our previous work [J. Comput.…

In this paper, high order semi-implicit well-balanced and asymptotic preserving finite difference WENO schemes are proposed for the shallow water equations with a non-flat bottom topography. We consider the Froude number ranging from O(1)…

High order finite volume schemes for conservation laws are very useful in applications, due to their ability to compute accurate solutions on quite coarse meshes and with very few restrictions on the kind of cells employed in the…

This paper deals with a new fifth-order weighted essentially non-oscillatory (WENO) scheme improving the WENO-NS and WENO-P methods which are introduced in Ha et al. J. Comput. Phys. (2013) and Kim et al., J. Sci. Comput. (2016)…

In this paper, A new sixth-order weighted essentially non-oscillatory (WENO) scheme, refered as the WENO-6, is proposed in the finite volume framework for the hyperbolic conservation laws. Instead of selecting one stencil for each cell in…

In this paper, we develop two finite difference weighted essentially non-oscillatory (WENO) schemes with unequal-sized sub-stencils for solving the Degasperis-Procesi (DP) and $\mu$-Degasperis-Procesi ($\mu$DP) equations, which contain…

This paper proposes high-order accurate, oscillation-eliminating Hermite weighted essentially non-oscillatory (OE-HWENO) finite volume schemes for hyperbolic conservation laws. The OE-HWENO schemes apply an OE procedure after each…