Local smoothness indicators are constructed based upon Lagrange's interpolation polynomial. We constructed a new high-order global smoothness indicator to guarantee the scheme achieves optimal order of accuracy at critical points. We investigated this scheme at critical points and verified its order of ...
accuracy, self-similarity, and a parameter-free nature. They are also highly robust with no oscillations near shock waves. Despite these benefits, there are still several areas in which the scheme can be improved. For example, the accuracy of the ENO scheme can be compromised due to changes ...
Another key feature of this method is that the cost of the computation of the smoothness indicators for a nonuniform stencil does not have a significant impact on the whole computational cost of the scheme, compared with the cost that the computation of the smoothness indicators has on the ...
The higher-order information presented for the classical WENO scheme is applied to construct a new global smoothness indicator, a composition of first derivatives of local smoothness indicators with their respective interpolation polynomials. The sufficient condition of nonlinear weights is satisfied by ...
In a few circumstances, we have also compared with the ‘ADER-Char’ scheme, namely a traditional ADER scheme in which, however, the spatial reconstruction is performed on the characteristic variables. In this Section we focus our attention on finite volume schemes, which, according to the ...
The aim of this paper is the presentation of a new modified weighted essentially non-oscillatory scheme with a seventh-order of accuracy, and, a novel nonlinear weighting method. Local smoothness indicators of this scheme constructed using Lagrange's interpolation polynomial. We developed a new high...
the final ALE one-step finite volume scheme uses moving triangular meshes with straight edges.This is possible in the ALE framework,which allows a local mesh velocity that is different from the local fluid velocity.We present numerical convergence rates for the schemes presented in this paper up ...
[20].In the Lagrangian framework considered here,the local space-time DG predictor is based on a weak formulation of the governing PDE on a moving space-time element.For the spacetime basis and test functions we use Lagrange interpolation polynomials defined by tensor-product Gauss-Legendre ...
Within the space–time predictor the physical element is mapped onto a reference element using a high order isoparametric approach, where the space–time basis and test functions are given by the Lagrange interpolation polynomials passing through a predefined set of space–time nodes. Since our ...
Then a new Mapped WENO scheme is proposed with a new smoothness indicator for both one and two dimensional H–J equations. 2.1. WENO We first briefly introduce the construction of the WENO scheme for solving H–J equations [18]. We assume a uniform grid in space with mesh size Δx such...