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Journal Article
New Low-Dissipation Central-Upwind Schemes
2023
Overview
In this paper, we develop new second-order low-dissipation central-upwind (LDCU) schemes for hyperbolic systems of conservation laws. Like all of the Godunov-type schemes, the proposed LDCU schemes are developed in three steps: reconstruction, evolution, and projection. A major novelty of our approach is in the projection step, which is based on a subcell resolution and designed to sharper approximate contact waves while ensuring a non-oscillatory property of the projected solution. In order to achieve this goal, we take into account properties of the contact waves. We design the LDCU schemes for both the one- and two-dimensional Euler equations of gas dynamics. The new schemes are tested on a variety of numerical examples. The obtained results clearly demonstrate that the proposed LDCU schemes contain substantially smaller amount of numerical dissipation and achieve higher resolution compared with their existing counterparts.
Publisher
Springer US,Springer Nature B.V
