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Goal-Oriented Mesh Adaptation using a Dissipation-Based Error Indicator

机译:使用基于耗散的错误指示符的目标导向的网格适应

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A method is proposed to estimate a posteriori that part of the total discretization error which is attributable to the smoothing effect of added dissipation, for finite volume discretizations of the Euler equations. This is achieved by observing variation in a functional of the solution as the level of dissipation is varied, and it is deduced for certain test-cases that the dissipation alone accounts for the majority of the functional error. Based on this result an error estimator and mesh adaptation indicator is proposed for functionals, relying on the solution of an adjoint problem. The scheme is considerably implementationally simpler and computationally cheaper than other recently proposed a posteriori error estimators for finite volume schemes, but does not account for all sources of error. In mind of this, emphasis is placed on numerical evaluation of the performance of the indicator, and it is shown to be extremely effective in both estimating and reducing error for a range of 2d and 3d flows.
机译:提出了一种方法来估计归因于额外耗散的平滑效果的总离散化误差的一部分的后验序,用于欧拉方程的有限体积离散化。这是通过观察解决方案功能的变化,因为随着耗散水平变化,并且它被推导出用于某些测试情况,即单独耗散占多数功能误差的情况。基于该结果,提出了一个错误估计器和网格自适应指示器,依赖于伴随问题的解决方案。该方案大大实施方式比其他最近提出了用于有限卷方案的后验误差估计值,但不考虑所有错误源。值得注意的是,重点放置在对指示符的性能的数值评估上,并且在估计和减少误差范围内显示出一系列2D和3D流动的数值评估。

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