Accuracy-preserving and non-oscillatory shock-capturing technique is the bottle neck in the development of discontinuous Galerkin method. Inspired by the success of the k-exact WENO limiters for high order finite volume methods, this paper generalize the k-exact WENO limiter to discontinuous Galerkin methods. Also several improvements are put forward to keep the compactness and high-order accur...

A reconstructed discontinuous Galerkin (RDG) method based on a Hierarchical WENO reconstruction, termed HWENO(P1P2) in this work, designed not only to enhance the accuracy of discontinuous Galerkin method but also to ensure the nonlinear stability of the RDG method, is presented for solving the compressible Euler equations on tetrahedral grids. In this HWENO(P1P2) method, a quadratic polynomial...

In this paper, we develop a new sixth-order finite difference central weighted essentially non-oscillatory (WENO) scheme with Z-type nonlinear weights for degenerate parabolic equations. The centered polynomial is introduced the WENO reconstruction to avoid negative linear weights. We choose based on $$L^2$$ -norm smoothness indicators, yielding less computational cost. It also confirmed that p...

Implicit variant WENO schemes with anti-diffusive flux for compressible flow computations are presented. These variant WENO schemes include the antis for the preconditioned compressible Euler/Navier-Stokes equations are also considered. The numerical flux of the variant WENO scdiffusive flux corrections, the mapped WENO scheme, and modified smoothness indicator. Implicit WENO schemeheme is cons...

The weighted essentially nonoscillatory (WENO) schemes, based on the successful essentially nonoscillatory (ENO) schemes with additional advantages, are a popular class of high-order accurate numerical methods for hyperbolic partial differential equations (PDEs) and other convection-dominated problems. The main advantage of such schemes is their capability to achieve arbitrarily high-order form...

Abstract Adaptive mesh refinement (AMR) is the art of solving PDEs on a hierarchy with increasing at each level hierarchy. Accurate treatment AMR hierarchies requires accurate prolongation solution from coarse to newly defined finer mesh. For scalar variables, suitably high-order finite volume WENO methods can carry out such prolongation. However, classes PDEs, as computational electrodynamics ...

This paper compares LES results of a cylinder flow with two sets of numerical schemes, two span lengths, and a coarse and refined mesh. One set of the numerical scheme is the 7th order WENO scheme for the inviscid fluxes and 6th order central differencing for the viscous terms (7-6), the other set is a 5th order WENO scheme with a 4th order central differencing(5-4). For this purpose, a fully c...

The simulation of turbulent compressible flows requires an algorithm with high accuracy and spectral resolution to capture different length scales, as well as nonoscillatory behavior across discontinuities like shock waves. Compact schemes have the desired resolution properties and thus, coupled with a nonoscillatory limiter, are ideal candidates for the numerical solution of such flows. A clas...

In this paper, we propose a high order residual distribution conservative finite difference scheme for solving convection– diffusion equations on non-smooth Cartesian meshes. WENO (weighted essentially non-oscillatory) integration and linear interpolation for the derivatives are used to compute the numerical fluxes based on the point values of the solution. The objective is to obtain a high ord...