论文标题
节能方程的保守半拉格朗日方案第一部分：重建
Conservative semi-Lagrangian schemes for kinetic equations Part I: Reconstruction
论文作者
论文摘要
在本文中，我们提出和分析一种重建技术，该技术使人们能够为动力学方程设计高阶保守的半拉格朗日式方案。可以通过取用给定多项式重建的数值解的平均平均值来获得所提出的重建。提供了一个和两个空间维度的高阶保守重建的紧凑表示，并分析了其数学特性。为了展示提出的技术的性能，我们考虑了类似动力学方程（例如Xin-Jin模型和Broadwell模型）的隐式半拉格朗日方案，然后解决在松弛极限中出现的相关冲击问题。本文的第二部分将介绍对BGK和Vlasov-Poisson方程的应用。
In this paper, we propose and analyse a reconstruction technique which enables one to design high-order conservative semi-Lagrangian schemes for kinetic equations. The proposed reconstruction can be obtained by taking the sliding average of a given polynomial reconstruction of the numerical solution. A compact representation of the high order conservative reconstruction in one and two space dimension is provided, and its mathematical properties are analyzed. To demonstrate the performance of proposed technique, we consider implicit semi-Lagrangian schemes for kinetic-like equations such as the Xin-Jin model and the Broadwell model, and then solve related shock problems which arise in the relaxation limit. Applications to BGK and Vlasov-Poisson equations will be presented in the second part of the paper.
