论文标题
校正后的Navier-Stokes方程可压缩流
Corrected Navier-Stokes equations for compressible flows
论文作者
论文摘要
对于气体流，Navier-Stokes（NS）方程是通过数学表达质量，动量和能量保护的。 NS方程比Euler方程的优点是，NS方程已考虑到由分子的热运动引起的粘性应力。粘性应力是由将Isaac Newton的第二定律应用于流体运动的，并假设应力与速度梯度成正比。因此，假设是NS方程中唯一的经验元素，这实际上就是为什么NS方程在特殊情况下表现较差的原因。例如，NS方程无法描述稀疏的气流和冲击结构。这项工作提出了对NS方程的校正，即粘应力与流量处于压缩后的动量梯度成正比，并具有零额外的经验参数。 NS方程首次能够准确求解冲击结构和稀有气流。此外，即使为了获得完美的气体，预测热通量速率的准确性也得到了极大的提高。校正后的NS方程可轻松地用于提高与密度变化的流量计算的准确性，而密度变化本质上是常见的。
For gas flows, the Navier-Stokes (NS) equations are established by mathematically expressing conservations of mass, momentum and energy. The advantage of the NS equations over the Euler equations is that the NS equations have taken into account the viscous stress caused by the thermal motion of molecules. The viscous stress arises from applying Isaac Newton's second law to fluid motion, together with the assumption that the stress is proportional to the gradient of velocity1. Thus, the assumption is the only empirical element in the NS equations, and this is actually the reason why the NS equations perform poorly under special circumstances. For example, the NS equations cannot describe rarefied gas flows and shock structure. This work proposed a correction to the NS equations with an argument that the viscous stress is proportional to the gradient of momentum when the flow is under compression, with zero additional empirical parameters. For the first time, the NS equations have been capable of accurately solving shock structure and rarefied gas flows. In addition, even for perfect gas, the accuracy of the prediction of heat flux rate is greatly improved. The corrected NS equations can readily be used to improve the accuracy in the computation of flows with density variations which is common in nature.
