Quantifying mixing in arbitrary fluid domains: a Padé approximation approach
Quantifying mixing in arbitrary fluid domains: a Padé approximation approach
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量化任意流体域中的混合：Padé 近似方法
DOI：
10.1007/s11075-022-01423-7
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发表时间：
2023
影响因子：
2.1
通讯作者：
Veerapaneni, Shravan
中科院分区：
文献类型：
--
作者：
Anderson, Thomas G.;Bonnet, Marc;Veerapaneni, Shravan
考虑无源示踪剂与不可压缩粘性流体混合的模型问题。在实际几何环境中解决最优控制问题，或者设计能够成功地影响混合的流体限制几何形状，需要一个有意义的规范来量化混合，该规范也适合于简单和有效的计算（例如，用于基于梯度的优化方法）。我们在复杂流体混合域上使用负指数Sobolev范数的物理激发的合理代理，这一任务可以被视为计算昂贵的任务，因为它需要计算特征基来定义。相反，我们在适当的Sobolev空间中计算标量浓度场的表示，以获得Sobolev替代范数的等效定义。代表，反过来，可以通过某些分数伪微分算子的pad<s:1>近似计算到高阶精度，这自然导致一系列具有与时变浓度场快照相关的非均匀性的椭圆问题。快速准确的势理论方法被用来有效地解决这些问题，随着体积势数值方法的最新进展，每快照混合范数的快速计算成为可能。我们将该方法与现有的Stokes方程和平流方程的求解方法相结合，以获得一个统一的框架来模拟和量化任意流体域中的混合。数值结果表明，随着逼近阶数的增加，新方法具有收敛性。
We consider the model problem of mixing of passive tracers by an incompressible viscous fluid. Addressing questions of optimal control in realistic geometric settings or alternatively the design of fluid-confining geometries that successfully effect mixing requires a meaningful norm in which to quantify mixing that is also suitable for easy and efficient computation (as is needed, e.g., for use in gradient-based optimization methods). We use the physically inspired reasonable surrogate of a negative index Sobolev norm over the complex fluid mixing domain, a task which could be seen as computationally expensive since it requires the computation of an eigenbasis forby definition. Instead, we compute a representant of the scalar concentration field in an appropriate Sobolev space in order to obtain an equivalent definition of the Sobolev surrogate norm. The representant, in turn, can be computed to high-order accuracy by a Padé approximation to certain fractional pseudo-differential operators, which naturally leads to a sequence of elliptic problems with an inhomogeneity related to snapshots of the time-varying concentration field. Fast and accurate potential theoretic methods are used to efficiently solve these problems, with rapid per-snapshot mix-norm computation made possible by recent advances in numerical methods for volume potentials. We couple the methodology to existing solvers for Stokes and advection equations to obtain a unified framework for simulating and quantifying mixing in arbitrary fluid domains. We provide numerical results demonstrating the convergence of the new approach as the approximation order is increased.
使用优化的搅拌策略增强二元流体的混合
影响因子：
3.7
作者：
Maximilian F. Eggl;P. Schmid
通讯作者：
P. Schmid
通过内部诺依曼到狄利克雷图的谱流快速计算高频狄利克雷本征模
影响因子：
3
作者：
A. Barnett;Andrew Hassell
通讯作者：
Andrew Hassell