CAJ | 학술논문

根据伪时均流假设，推导了波动量的非守恒非线性欧拉方程；采用频率变化的方法，给出了一个时间与空间坐标变换关系，并将波动量的非守恒非线性欧拉方程变换至新坐标系；通过复数变换方法引入阻尼，构建了斜流非守恒非线性x层、y层及角层完全耦合层(PML)吸收边界条件；最后用算例测试了该吸收边界条件的精度和收敛性。研究结果表明：当吸收层数等于10时，最大反射量不超过0·5%，并且随着PML层数的增加而迅速减小；当吸收层数为40层时，最大反射量小于0·1%，达到收敛；在背景斜流下，该PML吸收边界条件能较好地吸收熵波与声波，可用于气动声学计算。
근거위시균류가설，추도료파동량적비수항비선성구랍방정；채용빈솔변화적방법，급출료일개시간여공간좌표변환관계，병장파동량적비수항비선성구랍방정변환지신좌표계；통과복수변환방법인입조니，구건료사류비수항비선성x층、y층급각층완전우합층(PML)흡수변계조건；최후용산례측시료해흡수변계조건적정도화수렴성。연구결과표명：당흡수층수등우10시，최대반사량불초과0·5%，병차수착PML층수적증가이신속감소；당흡수층수위40층시，최대반사량소우0·1%，체도수렴；재배경사류하，해PML흡수변계조건능교호지흡수적파여성파，가용우기동성학계산。
For nonlinear Euler equations in primitive variables,a pseudo mean flow was introduced in the derivation of the time-dependent fluctuation equations.Then a hypothesis for changed frequen-cy was employed,a proper space-time transformation was presented for deriving the time-dependent fluctuation equations in transformed coordinates.A complex change was applied to the new equations and a damping parameter was introduced.Several nonlinear PML absorbing boundary condition in primitive variables for x layer,y layer and corner layer were derived.Finally,the stability and effec-tiveness of nonlinear PML absorbing boundary conditions were validated by computing the CAA benchmark problems.The results prove that:the maximum reflection error is less than 0·5% and 0·1% with PML width of 10 and 40 layers grid points,respectively,and the reflection error reduces with the increase of PML width;for actual CAA problems in the case of oblique mean flow,the pro-posed PML absorbing boundary conditions can absorb the vortex and acoustic wave with little or no reflection.