Related papers: A generalized framework to construct third order W…
This work characterizes the structure of third and forth order WENO weights by deducing data bounded condition on third order polynomial approximations. Using these conditions, non-linear weights are defined for third and fourth order data…
A novel scheme, based on third-order Weighted Essentially Non-Oscillatory (WENO) reconstructions, is presented. It attains unconditionally optimal accuracy when the data is smooth enough, even in presence of critical points, and…
A modified Weighted Essentially Non-Oscillatory (WENO) reconstruction technique preventing accuracy loss near critical points (regardless of their order) of the underlying data is presented. This approach only uses local data from the…
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…
The advantage of WENO-JS5 scheme [ J. Comput. Phys. 1996] over the WENO-LOC scheme [J. Comput. Phys.1994] is that the WENO-LOC nonlinear weights do not achieve the desired order of convergence in smooth monotone regions and at critical…
A novel procedure is given for choosing smoothest stencil to construct less oscillatory ENO schemes. The procedure is further used to define smoothness parameter in the non-linear weights of new WENO schemes. The main significant features…
Weighted essentially non-oscillatory (WENO) and finite volume (FV) methods employ different philosophies in their way to perform limiting. We show that a generalized view on limiter functions, which considers a two-dimensional, rather than…
In this paper we develop a new sixth-order finite difference central weighted essentially non-oscillatory (WENO) scheme with Z-type nonlinear weights for nonlinear degenerate parabolic equations. The centered polynomial is introduced for…
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…
To address the order degradation at critical points in the WENO3-Z scheme, some improvements have been proposed , but these approaches generally fail to consider the occurrence of critical points at arbitrary positions within grid…
In this paper we propose new Z-type nonlinear weights of the fifth-order weighted essentially non-oscillatory (WENO) finite difference scheme for hyperbolic conservation laws. Instead of employing the classical smoothness indicators for the…
In this paper, we introduce the finite difference weighted essentially non-oscillatory (WENO) scheme based on the neural network for hyperbolic conservation laws. We employ the supervised learning and design two loss functions, one with the…
Conventional WENO3 methods are known to be highly dissipative at lower resolutions, introducing significant errors in the pre-asymptotic regime. In this paper, we employ a rational neural network to accurately estimate the local smoothness…
Common smoothness indicators used in Weighted Essentially Non\--Os\-cil\-la\-to\-ry (WENO) reconstructions [Jiang, G.S., Shu, C.W.: Efficient implementation of {Weighted} {ENO} schemes, J.\ Comput.\ Phys. \textbf{126}, 202--228 (1996)] have…
In this work we present a new WENO b-spline based quasi-interpolation algorithm. The novelty of this construction resides in the application of the WENO weights to the b-spline functions, that are a partition of unity, instead to the…
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…
A novel method for constructing robust and high-order accurate weighted essentially non-oscillatory (WENO) scheme is proposed in this paper. The method is mainly based on the WENO-Z type scheme, in which, an eighth-order global smoothness…
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, novel smoothness indicators are presented for calculating the nonlinear weights of weighted essentially non-oscillatory scheme to approximate the viscosity numerical solutions of Hamilton-Jacobi equations. These novel…
The weighted essentially non-oscillatory (WENO) schemes are a popular class of high order accurate numerical methods for solving hyperbolic partial differential equations (PDEs). The computational cost of such schemes increases…