High Resolution Schemes for Hyperbolic Conservation Laws

By A. Harten. 2017

1,493 citations recorded by the source corpus.

A class of new explicit second order accurate finite difference schemes for the computation of weak solutions of hyperbolic conservation laws is presented. These highly nonlinear schemes are obtained by applying a nonoscillatory first order accurate scheme to an appropriately modified flux function. The so-derived second order accurate schemes achieve high resolution while preserving the robustness of the original nonoscillatory first order accurate scheme. Numerical experiments are presented to demonstrate the performance of these new schemes.

Subfields: Atmospheric Science, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/283d33e2f682d251cbe54c5032802eb6a037c77c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atmospheric Science

1. Jan S. Hesthaven

In Computational Mechanics

1. Jan S. Hesthaven
2. Andrea Manzoni
3. Stefania Fresca
4. David I. Gottlieb
5. Gianluigi Rozza
6. Bernie D. Shizgal
7. Bernhard Wieland
8. S. Kristoffersen

Citations in the corpus

• Numerical Methods for Conservation Laws: From Analysis to Algorithms (2017, background): “39) Harten [1983] proved that a sufficient condition for the TVD property of the above formulation is: 0 ≤ Gj+1/2, 0 ≤ Hj+1/2, Gj+1/2 +Hj+1/2 ≤ 1.”