CWENO: uniformly accurate reconstructions for balance laws

Abstract

In this paper we introduce a general framework for defining and studying essentially non-oscillatory reconstruction procedures of arbitrarily high order accuracy, interpolating data in a central stencil around a given computational cell ($\CWENO$). This technique relies on the same selection mechanism of smooth stencils adopted in $\WENO$, but here the pool of candidates for the selection includes polynomials of different degrees. This seemingly minor difference allows to compute an analytic expression of a polynomial interpolant, approximating the unknown function uniformly within a cell, instead of only at one point at a time. For this reason this technique is particularly suited for balance laws for finite volume schemes, when averages of source terms require high order quadrature rules based on several points; in the computation of local averages, during refinement in h-adaptive schemes; or in the transfer of the solution between grids in moving mesh techniques, and in general when a globally defined reconstruction is needed. Previously, these needs have been satisfied mostly by ENO reconstruction techniques, which, however, require a much wider stencil then the $\CWENO$ reconstruction studied here, for the same accuracy.

References in corpus (4)

• On the accuracy of WENO and CWENO reconstructions of third order on nonuniform meshes
• Adaptive Mesh Refinement for Hyperbolic Systems based on Third-Order Compact WENO Reconstruction
• Well-balanced high order schemes on non-uniform grids and entropy residuals
• Representation of the Lagrange reconstructing polynomial by combination of substencils

Cited by in corpus (22)

• High order direct Arbitrary-Lagrangian-Eulerian schemes on moving Voronoi meshes with topology changes
• High order ADER schemes for continuum mechanics
• High order pressure-based semi-implicit IMEX schemes for the 3D Navier-Stokes equations at all Mach numbers
• Arbitrary order finite volume well-balanced schemes for the Euler equations with gravity
• Cool WENO schemes
• An Adaptive Characteristic-wise Reconstruction WENOZ scheme for Gas Dynamic Euler Equations
• High order ADER schemes and GLM curl cleaning for a first order hyperbolic formulation of compressible flow with surface tension
• Optimal definition of the nonlinear weights in multidimensional Central WENOZ reconstructions
• Third and fourth order well-balanced schemes for the shallow water equations based on the CWENO reconstruction
• An efficient targeted ENO scheme with local adaptive dissipation for compressible flow simulation
• Well-balanced finite volume schemes for nearly steady adiabatic flows
• Conservative semi-Lagrangian schemes for kinetic equations Part I: Reconstruction
• Efficient implementation of adaptive order reconstructions
• Maximum principle satisfying CWENO schemes for non-local conservation laws
• Conservative semi-Lagrangian schemes for kinetic equations Part II: Applications
• A class of high-order weighted compact central schemes for solving hyperbolic conservation laws
• Fifth order finite volume WENO in general orthogonally-curvilinear coordinates
• Invariant-region-preserving WENO schemes for one-dimensional multispecies kinematic flow models
• Kinetic models of BGK type and their numerical integration
• An efficient implicit scheme for the multimaterial Euler equations in Lagrangian coordinates
• One- and multi-dimensional CWENOZ reconstructions for implementing boundary conditions without ghost cells
• High-order well-balanced finite volume schemes for the Euler equations with gravitation