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On fully-implicit solutions of the time-linearized Euler equations in a DG-Chimera solver

机译：DG-Chimera求解器中时间线性化Euler方程的全隐式解

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摘要

This work demonstrates fully-implicit solutions of the time-linearized Euler equations using a discontinuous Galerkin discretization on Chimera overset grids. Solutions are obtained via a single linear system solve. The linear system matrix is generated with an intrinsic automatic differentiation capability that computes the linear system in the context of Newton's method while evaluating the system residual. A flexible implementation of the Generalized Minimum Residual algorithm coupled with a block-ILU0 preconditioner is used to solve the linear system. Results include a simulation of acoustic scattering off multiple rigid geometries and also acoustic radiation from a cylindrical duct using Kirchoff's method to compute the observed noise at far-field locations. For the acoustic scattering case, excellent comparison was observed between the numerical and analytical solutions for surface pressure on the rigid geometries. For the cylindrical duct case, the directivity of unsteady pressure for the numerical solution was compared to the analytical solution in the far-field. The directivity patterns were well-matched for several duct modes, however the numerical solution was attenuated due to low grid resolution. A lack of parallelism in the current code prohibited more refined numerical calculations due to memory constraints.
机译：这项工作演示了在Chimera重叠网格上使用不连续的Galerkin离散化方法对时间线性化Euler方程进行完全隐式解。通过单个线性系统求解获得求解。线性系统矩阵具有固有的自动微分功能，可以在牛顿方法的上下文中计算线性系统，同时评估系统残差。通用最小残差算法的灵活实现与块ILU0预调节器结合使用来求解线性系统。结果包括模拟使用多种刚性几何形状的声散射，以及使用基尔霍夫（Kirchoff）方法计算圆柱管道的声辐射，以计算在远场位置观察到的噪声。对于声散射情况，在刚性几何体上的表面压力的数值解和解析解之间观察到了极好的对比。对于圆柱管的情况，将数值解中非定常压力的方向性与远场中的解析解进行了比较。方向性模式在几种风道模式下都很好地匹配，但是由于网格分辨率低，数值解被削弱了。由于内存限制，当前代码缺乏并行性，无法进行更精确的数值计算。

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