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An efficient semi-implicit solver for direct numerical simulation of compressible flows at all speeds

机译:一种有效的半隐式求解器,用于直接数值模拟   所有速度下的可压缩流动

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摘要

We develop a semi-implicit algorithm for time-accurate simulation of thecompressible Navier-Stokes equations, with special reference to wall-boundedflows. The method is based on linearization of the partial convective fluxesassociated with acoustic waves, in such a way to suppress, or at least mitigatethe acoustic time step limitation. Together with replacement of the totalenergy equation with the entropy transport equation, this approach avoids theinversion of block-banded matrices involved in classical methods, which isreplaced by less demanding inversion of standard banded matrices. The method isextended to deal with implicit integration of viscous terms and to multiplespace dimensions through approximate factorization, and used as a buildingblock of third-order Runge-Kutta time stepping scheme. Numerical experimentsare carried out for isotropic turbulence, plane channel flow, and flow in asquare duct. All available data support higher computational efficiency thanexisting methods, and saving of resources ranging from $85\%$ underlow-subsonic flow conditions, to about $50\%$ in supersonic flow.
机译:我们开发了一种半隐式算法,用于可压缩的Navier-Stokes方程的时间精确仿真,并特别参考了壁边界流。该方法基于与声波相关联的部分对流通量的线性化,以抑制或至少减轻声波时间步长限制的方式。与用熵传输方程替换总能量方程一起,此方法避免了经典方法中涉及的块带矩阵的求逆,而经典带方法对标准带矩阵的求逆则要求较低。该方法被扩展为通过近似因式分解处理粘性项的隐式积分和多维空间维度,并用作三阶Runge-Kutta时间步进方案的构造块。对各向同性湍流,平面通道流和方管中的流进行了数值实验。与现有方法相比,所有可用数据均支持更高的计算效率,并节省资源,从低亚音速流条件下的$ 85 \%$到超音速流中的约$ 50 \%$。

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