Developments of entropy-stable residual distribution methods for conservation laws I: Scalar problems

作者：Ismail Farzad; Chizari Hossain

来源：Journal of Computational Physics, 2017, 330: 1093-1115.

DOI：10.1016/j.jcp.2016.10.065

• Entropy conservation
• Entropy-stable
• Residual distribution
• Semi-discrete
• Scalar advection

This paper presents preliminary developments of entropy-stable residual distribution Methods for scalar problems. Controlling entropy generation is achieved by formulating an entropy conserved signals distribution coupled with an entropy-stable signals distribution. Numerical results of the entropy-stable residual distribution methods are accurate and comparable with the classic residual distribution methods for steady-state problems. High order accurate extensions for the new method on steady-state problems are also demonstrated. Moreover, the new method preserves second order accuracy on unsteady problems using an explicit time integration scheme. The idea of the multi-dimensional entropy-stable residual distribution method is generic enough to be extended to the system of hyperbolic equations, which will be presented in the sequel of this paper.

• 出版日期2017-2-1