Shape derivatives for the compressible Navier-Stokes equations in variational form
Shape derivatives for the compressible Navier-Stokes equations in variational form
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DOI：
10.1016/j.cam.2015.09.010
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发表时间：
2013-12
期刊：
影响因子：
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通讯作者：
Matthias Sonntag;S. Schmidt;N. Gauger
中科院分区：
文献类型：
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作者：
Matthias Sonntag;S. Schmidt;N. Gauger
考虑了基于表面梯度和Hadamard-form的可压缩粘性流体形状优化。特别注意涉及局部形状导数的“函数组合”方法与基于状态方程弱形式的替代方法之间的区别。所得的梯度表达式只有在强形式解存在的前提下才相等。基于这两种公式的曲面形状导数在变阶的间断伽辽金流求解器中实现。与有限差分相比，由变分方法产生的梯度表达式具有更高的精度。
Shape optimization based on surface gradients and the Hadamard-form is considered for a compressible viscous fluid. Special attention is given to the difference between the “function composition” approach involving local shape derivatives and an alternate methodology based on the weak form of the state equation. The resulting gradient expressions are found to be equal only if the existence of a strong form solution is assumed. Surface shape derivatives based on both formulations are implemented within a Discontinuous Galerkin flow solver of variable order. The gradient expression stemming from the variational approach is found to give superior accuracy when compared to finite differences.