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首页> 外文期刊>Journal of Computational Physics >Insights from von Neumann analysis of high-order flux reconstruction schemes
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Insights from von Neumann analysis of high-order flux reconstruction schemes

机译：冯·诺依曼分析高阶通量重建方案的见解

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摘要

The flux reconstruction (FR) approach unifies various high-order schemes, including collocation based nodal discontinuous Galerkin methods, and all spectral difference methods (at least for a linear flux function), within a single framework. Recently, an infinite number of linearly stable FR schemes were identified, henceforth referred to as Vincent-Castonguay-Jameson-Huynh (VCJH) schemes. Identification of VCJH schemes offers significant insight into why certain FR schemes are stable (whereas others are not), and provides a simple prescription for implementing an infinite range of linearly stable high-order methods. However, various properties of VCJH schemes have yet to be analyzed in detail. In the present study one-dimensional (1D) von Neumann analysis is employed to elucidate how various important properties vary across the full range of VCJH schemes. In particular, dispersion and dissipation properties are studied, as are the magnitudes of explicit time-step limits (based on stability considerations). 1D linear numerical experiments are undertaken in order to verify results of the 1D von Neumann analysis. Additionally, two-dimensional non-linear numerical experiments are undertaken in order to assess whether results of the 1D von Neumann analysis (which is inherently linear) extend to real world problems of practical interest.
机译：通量重建（FR）方法在单个框架内统一了各种高阶方案，包括基于搭配的节点不连续Galerkin方法以及所有谱差法（至少对于线性通量函数而言）。最近，确定了无数个线性稳定的FR方案，此后称为Vincent-Castonguay-Jameson-Huynh（VCJH）方案。 VCJH方案的识别可为某些FR方案为何稳定（而其他FR方案不稳定）的原因提供重要的见解，并为实现无限范围的线性稳定高阶方法提供了简单的方法。但是，VCJH方案的各种属性尚未详细分析。在本研究中，采用一维（1D）冯·诺依曼分析来阐明各种重要特性在整个VCJH方案中如何变化。特别是，研究了色散和耗散特性，以及明确的时间步长极限的大小（基于稳定性考虑）。为了验证一维冯·诺伊曼分析的结果，进行了一维线性数值实验。另外，为了评估一维冯·诺依曼分析（固有的线性）的结果是否扩展到具有实际意义的现实世界问题，还进行了二维非线性数值实验。

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