论文标题
振荡缓解保存超波利度的诱人不确定性量化方法，用于保护法。
Oscillation Mitigation of Hyperbolicity-Preserving Intrusive Uncertainty Quantification Methods for Systems of Conservation Laws
论文作者
论文摘要
在本文中，我们研究了具有不确定性的保护定律系统的侵入性不确定性量化方案。标准侵入性方法导致振荡溶液，有时甚至会导致双曲线丧失。我们考虑了随机的Galerkin方案，在该方案中，我们过滤了多项式扩展的系数，以减少振荡。我们进一步采用多元素方法，并通过双曲线限制器确保保留双曲线溶液。除此之外，我们还研究了侵入性多项式力矩方法，该方法以解决每个空间细胞和每个时间步骤的优化问题而保证双曲线。为了降低数值成本，我们将多元素ANSATZ应用于IPM。这个ansatz解除了所有多元素的优化问题。因此，我们能够显着降低计算成本，同时提高并行性。我们最终在各种数值示例（例如NACA机翼和二维Euler方程的喷嘴测试用例）上评估了这些缓解方法。在我们的数值实验中，我们观察到减轻虚假伪影的缓解。此外，使用多元素ANSATZ进行IPM大大降低了计算成本。
In this article we study intrusive uncertainty quantification schemes for systems of conservation laws with uncertainty. Standard intrusive methods lead to oscillatory solutions which sometimes even cause the loss of hyperbolicity. We consider the stochastic Galerkin scheme, in which we filter the coefficients of the polynomial expansion in order to reduce oscillations. We further apply the multi-element approach and ensure the preservation of hyperbolic solutions through the hyperbolicity limiter. In addition to that, we study the intrusive polynomial moment method, which guarantees hyperbolicity at the cost of solving an optimization problem in every spatial cell and every time step. To reduce numerical costs, we apply the multi-element ansatz to IPM. This ansatz decouples the optimization problems of all multi elements. Thus, we are able to significantly decrease computational costs while improving parallelizability. We finally evaluate these oscillation mitigating approaches on various numerical examples such as a NACA airfoil and a nozzle test case for the two-dimensional Euler equations. In our numerical experiments, we observe the mitigation of spurious artifacts. Furthermore, using the multi-element ansatz for IPM significantly reduces computational costs.
