In this paper, a domain decomposition technique in the finite volume framework is presented to propagate small amplitude acoustic and entropy waves in a linearized Euler region and simulate the interaction of these waves with an initially steady normal shock in a nonlinear region. An overset method is used to two-way couple the linear and nonlinear regions that overlap each other. Linearized solvers alone cannot capture this interaction due to the discontinuity encountered at shocks. On the other hand, nonlinear solvers based on second order shock-capturing schemes will result in excessive dissipation and dispersion for the small disturbances. The domain decomposition technique provides a good balance between minimizing dissipation and dispersion errors while enabling nonlinear shock-acoustic interactions. To preserve low dispersion and dissipation, a DRP scheme is used to simulate the incoming and outgoing waves in the linear region. To capture the shock wave interaction and motion, a hybrid central-upwind flux scheme is used in the nonlinear region that contains the shock. Grid sensitivity studies for an acoustic wave propagating in stationary flow were performed to compare the linear, nonlinear, and domain decomposition solvers. The nonlinear solver required ten times the mesh resolution to achieve similar accuracy as the linear solver, resulting in a forty-fold increase in computational time. For modest cell size ratios, the domain decomposition solver reduced the computational time by a factor of three compared to the nonlinear solver while achieving similar accuracy. Interaction of standing shocks with acoustic and entropy waves of amplitudes $ϵ=\pm {10}^{-2}$ and $\pm {10}^{-5}$ was investigated using the domain decomposition technique. The numerical results for $ϵ=\pm {10}^{-2}$ compared well with the linearized interaction analysis (LIA) with less than 3% discrepancy in terms of the amplification factors. The domain decomposition technique acts as a low pass filter that averages the post-shock oscillations generated by the slow-moving shocks in the nonlinear region, resulting in the correct amplification factors in the linear region. For the smaller amplitudes of $ϵ=\pm {10}^{-5}$, the amplification factors deviated from LIA predictions by up to 70%. Numerical results suggest that the large discrepancy for the small amplitude cases is due to insufficient mesh resolution for capturing extremely slow-moving shocks.

在本文中，提出了一种在有限体积框架中的区域分解技术，以在线性Euler区域中传播小振幅声波和熵波，并模拟这些波与非线性区域中最初稳定的法向激波的相互作用。过度方法用于双向耦合彼此重叠的线性和非线性区域。由于在激波中遇到的不连续性，仅线性化求解器无法捕获这种相互作用。另一方面，基于二阶冲击捕获方案的非线性求解器将导致较小的干扰产生过多的耗散和弥散。域分解技术在最小化耗散和色散误差之间实现了良好的平衡，同时实现了非线性冲击声相互作用。为了保持较低的色散和耗散，DRP方案用于模拟线性区域中的传入和传出波。为了捕获冲击波的相互作用和运动，在包含冲击的非线性区域中使用了混合的中心-上风通量方案。进行了在固定流中传播的声波的网格灵敏度研究，以比较线性，非线性和域分解求解器。非线性求解器需要10倍的网格分辨率才能达到与线性求解器相似的精度，从而导致计算时间增加了40倍。对于适度的像元大小比率，与非线性求解器相比，域分解求解器将计算时间减少了三倍，同时实现了相似的精度。$ϵ=\pm {10}^{-\mathrm{2个}}$ 和 $\pm {10}^{-5}$使用域分解技术进行了研究。的数值结果$ϵ=\pm {10}^{-\mathrm{2个}}$与线性化交互作用分析（LIA）相比，在放大因子方面的差异小于3％。域分解技术用作低通滤波器，可对非线性区域中缓慢移动的冲击所产生的震后振荡进行平均，从而在线性区域中获得正确的放大因子。对于较小的振幅$ϵ=\pm {10}^{-5}$，放大因子与LIA预测的偏差高达70％。数值结果表明，小振幅情况的较大差异是由于网格分辨率不足，无法捕获极慢运动的冲击。