ENO schemes with subcell resolution

Authors:
Ami Harten
Affiliations:
School of Mathematical Sciences, Tel-Aviv University, Israel and Department of Mathematics, University of California, Los Angeles, California, USA
Venue:
Journal of Computational Physics
Year:
1989

Citing 0
Cited 19

Anti-diffusive flux corrections for high order finite difference WENO schemes

Journal of Computational Physics
High order residual distribution conservative finite difference WENO schemes for steady state problems on non-smooth meshes

Journal of Computational Physics
Edge detection insensitive to changes of illumination in the image

Image and Vision Computing
Short Note: On reinitializing level set functions

Journal of Computational Physics
Photo-realistic visualization for the blast wave of TNT explosion by grid-based rendering

ISHPC'05/ALPS'06 Proceedings of the 6th international symposium on high-performance computing and 1st international conference on Advanced low power systems
High order finite difference methods with subcell resolution for advection equations with stiff source terms

Journal of Computational Physics
Tailored Finite Point Method for First Order Wave Equation

Journal of Scientific Computing
An oscillation-free high order TVD/CBC-based upwind scheme for convection discretization

Numerical Algorithms
A class of hybrid DG/FV methods for conservation laws I: Basic formulation and one-dimensional systems

Journal of Computational Physics
A New Mapped Weighted Essentially Non-oscillatory Scheme

Journal of Scientific Computing
Adaptive interpolation of images using a new nonlinear cell-average scheme

Mathematics and Computers in Simulation
Nonlinear cell-average multiscale signal representations: Application to signal denoising

Signal Processing
WENO Scheme with Subcell Resolution for Computing Nonconservative Euler Equations with Applications to One-Dimensional Compressible Two-Medium Flows

Journal of Scientific Computing
Spurious behavior of shock-capturing methods by the fractional step approach: Problems containing stiff source terms and discontinuities

Journal of Computational Physics
Direct numerical simulation of interfacial instabilities: A consistent, conservative, all-speed, sharp-interface method

Journal of Computational Physics
High order nonlinear interpolatory reconstruction operators and associated multiresolution schemes

Journal of Computational and Applied Mathematics
Learning-based multiresolution transforms with application to image compression

Signal Processing
Subcell resolution in simplex stochastic collocation for spatial discontinuities

Journal of Computational Physics
EASY-FIT: a software system for data fitting in dynamical systems

Structural and Multidisciplinary Optimization

Quantified Score

Hi-index	31.49

Visualization

Abstract

In this paper, we introduce the notion of subcell resolution, which is based on the observation that unlike point values, cell-averages of a discontinuous piecewise-smooth function contain information about the exact location of the discontinuity within the cell. Using this observation we design an essentially non-oscillatory (ENO) reconstruction technique which is exact for cell averages of discontinuous piecewise-polynomial functions of the appropriate degree. Later on we incorporate this new reconstruction technique into Godunov-type schemes in order to produce a modification of the ENO schemes which prevents the smearing of contact discontinuities.