Related papers: An extending strategy based on TENO framework for …
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…
Entropy conditions play a crucial role in the extraction of a physically relevant solution for systems of conservation laws, thus motivating the construction of entropy stable schemes that satisfy a discrete analogue of such conditions.…
In this study, we establish a hybrid high-order smoothed particle hydrodynamics (SPH) framework (MLS-TENO-SPH) for compressible flows with discontinuities, which is able to achieve genuine high-order convergence in smooth regions and also…
In the present work, we propose two new variants of fifth order finite difference WENO schemes of adaptive order. We compare our proposed schemes with other variants of WENO schemes with special emphasize on WENO-AO(5,3) scheme [Balsara,…
The weighted essentially non-oscillatory (WENO) methods are popular and effective spatial discretization methods for nonlinear hyperbolic partial differential equations. Although these methods are formally first-order accurate when a shock…
In this article, the construction and implementation of a seventh order weighted essentially non-oscillatory scheme is reported for hyperbolic conservation laws. Local smoothness indicators are constructed based on $L_{1}$-norm, where a…
We present a novel arbitrary high order accurate central WENO spatial reconstruction procedure (CWENO) for the solution of nonlinear systems of hyperbolic conservation laws on fixed and moving unstructured simplex meshes in two and three…
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…
We present a new third-order central scheme for approximating solutions of systems of conservation laws in one and two space dimensions. In the spirit of Godunov-type schemes,our method is based on reconstructing a piecewise-polynomial…
A novel central weighted essentially non-oscillatory (central WENO; CWENO)-type scheme for the construction of high-resolution approximations to discontinuous solutions to hyperbolic systems of conservation laws is presented. This procedure…
In this paper, a maximum-principle-satisfying finite volume compact scheme is proposed for solving scalar hyperbolic conservation laws. The scheme combines WENO schemes (Weighted Essentially Non-Oscillatory) with a class of compact schemes…
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, a third-order weighted essentially non-oscillatory (WENO) scheme is developed for hyperbolic conservation laws on unstructured quadrilateral and triangular meshes. As a starting point, a general stencil is selected for the…
We present a new perspective on the use of weighted essentially nonoscillatory (WENO) reconstructions in high-order methods for scalar hyperbolic conservation laws. The main focus of this work is on nonlinear stabilization of continuous…
A set of arbitrarily high-order WENO schemes for reconstructions on nonuniform grids is presented. These non-linear interpolation methods use simple smoothness indicators with a linear cost with respect to the order, making them easy to…
In this paper, we propose a high order residual distribution conservative finite difference scheme for solving steady state conservation laws. A new type of WENO (weighted essentially non-oscillatory) termed as WENO-ZQ integration is used…
Different ways of implementing dimension-by-dimension CWENO reconstruction are discussed and the most efficient method is applied to develop a fourth order central scheme for multi-dimensional hyperbolic problems. Fourth order accuracy and…
In this work, we provide a deep investigation of a family of arbitrary high order numerical methods for hyperbolic partial differential equations (PDEs), with particular emphasis on very high order versions, i.e., with order higher than 5.…
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…
We consider implementations of high-order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes for the Euler equations in cylindrical and spherical coordinate systems with radial dependence only. The main concern of this…