Sparse data formats and efficient numerical methods for uncertainties quantification in numerical aerodynamics
Sparse data formats and efficient numerical methods for uncertainties quantification in numerical aerodynamics
复制标题
数值空气动力学中不确定性量化的稀疏数据格式和高效数值方法
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
H. Matthies
中科院分区：
文献类型：
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作者：
A. Litvinenko;H. Matthies
所考虑的问题是具有不确定参数和不确定计算区域的定常Navier-Stokes方程组。我们研究了攻角、马赫数和翼型几何形状的不确定性如何在解中传播。该问题的不确定解（压力、密度、速度等）通过随机场近似。由于这类随机场的全部实现信息量太大，我们给出了它们的低秩逼近算法。该算法基于QR分解，具有线性复杂度。这种低秩近似允许我们进行有效的后处理（计算平均值，方差，重复概率），大大降低了内存需求。
The problem to be considered is the stationar system of Navier-Stokes equations with uncertain parameters and uncertain computational domain. We research how uncertainties in the angle of attack, in the Mach number and in the geometry of the airfoil propagate in the solution. The uncertain solution of this problem (pressure, density, velocity etc) is approximated via random fields. Since the whole set of realisations of these random fields are too much information, we demonstrate an algorithm of their low-rank approximation. This algorithm, working on the fly, is based on the QR-decomposition and has a linear complexity. This low-rank approximation allows us an effective postprocessing (computation of the mean value, variance, exceedance probability) with drastically reduced memory requirements.