基于微可压液体的统一对流扩散型流体力学方程组

UNIFIED CONVECTION DIFFUSION EQUATIONS BASED ON WEAKLY COMPRESSIBLE LIQUID

为了表达上的方便及求解格式的统一,通常采用统一的方程形式来表达连续方程,动量方程、能量方程、湍动能方程和耗散方程等。除了连续方程外,其他方程都可以写成对流扩散方程的形式,由于没有扩散项,连续方程比较特别,也相对不便处理。在微可压液体区,通过合理的数学推导,不作任何近似、假定与简化,本文得到一套全新的连续方程形式。该新方程以压力为未知变量,是对流扩散型的,使得所有的流体动力学方程组都具有完全统一的方程形式。

For the sake of convenience of expression and unification of numerical scheme for the solution,a unified form is usually adopt to express the continuity equation,momentum equation, energy equation,turbulent kinetic equation and diffusion equation etc.All the equations can be written in convection diffusion form except the continuity one,which has a vanishing diffusion coefficient.So the continuity equation is some kind special and relatively hard to deal with.By rational deduction, without any approximation,assumption and simplification,a new form of continuity equation for weakly compressible liquid has been deduced in this paper.The new equation using pressure as its unknown valuable,and also in convection diffusion form,makes the fluid equation system have a monolithic form.