结合泰勒级数时间展开的空间离散算法在CFD中的应用
A combined space discrete algorithm with a Taylor series by time for CFD
AI总结：
提出一种结合空间离散数值格式与泰勒级数时间展开的新数值方法，用于求解一类偏微分方程的初边值问题，旨在优化计算时间与数值解的精度。
摘要：
一阶时间偏微分方程被用作流体流动、传热、固体变形、电磁波等应用中的模型。本文提出了一种新的数值方法，用于求解偏微分方程的一类初边值问题，该方法采用已知的空间离散数值格式和泰勒级数时间展开。通常，空间上采用二阶离散，而时间上一阶离散即可满足要求。然而，在许多不同问题中，时间和空间变量的离散都需要高阶格式，这有时会极大地复杂化数值求解。因此，当某些偏微分方程组的参数在很大范围内变化时，很难应用相同的数值方法，因为其中一些方程在时间上最适合采用不同的数值格式以获得精确的数值解。本文提出了基于泰勒级数的非定常偏微分方程求解策略，用于CFD模拟，旨在优化计算时间和数值解的保真度。
英文摘要：
The first order by time partial differential equations are used as models in applications such as fluid flow, heat transfer, solid deformation, electromagnetic waves, and others. In this paper we propose the new numerical method to solve a class of initial-boundary value problems for the PDEs using one of the known space discrete numerical schemes and a Taylor series expansion by time. Normally a second order discretization by space is applied while a first order by time is satisfactory. Nevertheless, in a number of different problems, discretization both by temporal and by spatial variables is needed of highest orders, which complicates numerical solution, in some cases dramatically. Therefore it is difficult to apply the same numerical methods for the solution of some PDE arrays if their parameters are varying in a wide range so that in some of them different numerical schemes by time fit the best for precise numerical solution. The Taylor series based solution strategy for the non-stationary PDEs in CFD simulations has been proposed here that attempts to optimise the computation time and fidelity of the numerical solution.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
