基于熵的局部特征分解

中文摘要 AI 辅助

局部特征分解（LCD）广泛应用于守恒律双曲系统的高阶数值方法中，以减少计算解中出现的伪振荡。LCD的实现需要一个代表性的平均界面状态，通常通过取相邻网格值的算术平均或Roe型平均获得。我们提出了一种基于熵的局部特征分解（ELCD），其中将界面相邻两个单元中的状态与相空间中附近的若干状态一起考虑。在这些候选中，我们选择局部最小化熵的状态，并将其用作平均界面状态以线性化通量雅可比矩阵。我们将ELCD纳入多个二阶有限体积和五阶有限差分格式中。针对气体动力学二维欧拉方程的数值实验表明，使用ELCD过程的格式通常比使用算术平均的对应格式更清晰地分辨复杂波结构。

英文摘要

Local characteristic decomposition (LCD) is widely used in high-order numerical methods for hyperbolic systems of conservation laws to reduce spurious oscillations appearing in the computed solutions. The LCD implementation requires a representative average interface state, typically obtained using arithmetic or Roe-type averages of the nearly grid values. We propose an entropy-based LCD (ELCD), in which the states in the two cells adjacent to an interface are considered together with several nearby states in phase space. Among these candidates, we select the state that locally minimizes the entropy and use it as an average interface state for linearizing the flux Jacobian. We incorporate the ELCD into several second-order finite-volume and fifth-order finite-difference schemes. Numerical experiments for the two-dimensional Euler equations of gas dynamics show that the schemes, which utilize the ELCD procedure generally resolve complex wave structures more sharply than their counterparts, which use the arithmetic averages.

发表机构

• RWTH Aachen University（亚琛工业大学）
• University of Pretoria（比勒陀利亚大学）
• Southern University of Science and Technology（南方科技大学）

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