Related papers: High order finite difference Hermite WENO fixed-po…
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…
Fixed-point iterative sweeping methods were developed in the literature to efficiently solve steady state solutions of Hamilton-Jacobi equations and hyperbolic conservation laws. Similar as other fast sweeping schemes, the key components of…
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…
In this paper, we extend the previous work on absolutely convergent fixed-point fast sweeping WENO methods by Li et al. (J. Comput. Phys. 443: 110516, 2021) and design a fifth-order hybrid fast sweeping scheme for solving steady state…
In this paper, we propose a well-balanced fifth-order finite difference Hermite WENO (HWENO) scheme for the shallow water equations with non-flat bottom topography in pre-balanced form. For achieving the well-balance property, we adopt the…
Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady state solutions of hyperbolic partial differential equations (PDEs). As other types of fast sweeping…
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 to combine the fifth order Hermite weighted essentially non-oscillatory (HWENO) scheme and fast sweeping method (FSM) for the solution of the steady-state $S_{N}$ transport equation in the finite volume framework.…
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…
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…
High order fast sweeping methods for efficiently solving steady state solutions of hyperbolic PDEs were not available yet on unstructured meshes. In this paper, we extend high order fast sweeping methods to unstructured triangular meshes by…
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…
Higher order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes for conservation laws are extremely popular because, for multidimensional problems, they offer high order accuracy at a fraction of the cost of finite volume…
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.…
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…
Higher order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes for conservation laws represent a technology that has been reasonably consolidated. They are extremely popular because, when applied to multidimensional…
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…
In \cite{christlieb2019kernel}, the authors developed a class of high-order numerical schemes for the Hamilton-Jacobi (H-J) equations, which are unconditionally stable, yet take the form of an explicit scheme. This paper extends such…
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…