可压缩流动的二阶精度大时间步长、高分辨率差分格式研究及其验证

项目名称： 可压缩流动的二阶精度大时间步长、高分辨率差分格式研究及其验证

项目编号： No.11202199

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 钱战森

作者单位： 中国航空工业集团公司沈阳空气动力研究所

项目金额： 25万元

中文摘要： 计算速度仍是当前制约计算流体力学（CFD）应用的一大瓶颈，在计算机性能和资源相对有限的情况下，建立高效的数值算法以提高计算速度对开展大规模科学与工程计算具有重大的现实意义。本项研究的目的是发展能够实现显式大时间步长推进的单步高效、高分辨率数值计算格式。该类显式格式的特点在于能够稳定进行CFL数（Courant, Friedrichs and Levy number）大于1.0的时间推进，可克服目前单步显式格式由于受制于CFL条件而导致求解效率较低的问题，同时可继承显式格式易于并行化的优点，在大规模数值模拟上具有独特的优势。本项研究将在申请人已建立的一阶精度大时间步长Godunov格式的研究基础上，将其进一步推广至更高精度，拟建立能实现大时间步长（CFL >1）计算的二阶精度高分辨率显式差分格式，提高其工程实用价值，并将所发展的格式应用于典型可压缩空气动力学问题的计算，验证其可靠性和高效性。

中文关键词： 大时间步长格式；高分辨率；高效率；Godunov格式；TVD格式

英文摘要： Computational speed remains one of the bottlenecks in the utilization of the computational fluid dynamics (CFD) at the present stage for massive computations in engineering practice. It is meaningfull for both foundamental investigations and engineering applications to establish a highly efficient numerical algorithm to improve the computational speed, when the capacities and the resources of the computers are relatively limited. The present study aims at developing a class of single time step, highly efficient, and high resolution finite difference scheme which can maintain computational stability at large time step. The proposed explicit scheme can perform Large time step time integration with CFL (Courant, Friedrichs and Levy number) number larger than 1.0, overcome the low computational efficiency problem due to the restriction of CFL condition when a single step explicit time scheme is utilized, consequently it can inherit the merit of easily parallelization property of an conventional explicit scheme with huge potential in large scale engineering computation. The present study will develop a class of second-order explicit large time step finite difference scheme based on the candidate's previous investigation on the first-order large time step Godunov scheme. And the proposed schemes will be applied to som

英文关键词： Large time step scheme；High resolution scheme；High efficiency scheme；Godunov scheme；TVD scheme