dorsal/arxiv
View SchemaOptimizing the Source Distribution in Fluid Mixing
| Authors | Jean-Luc Thiffeault, G. A. Pavliotis |
|---|---|
| Categories | |
| ArXiv ID | physics/0703135 |
| URL | https://arxiv.org/abs/physics/0703135 |
| DOI | 10.1016/j.physd.2007.11.013 |
Abstract
A passive scalar is advected by a velocity field, with a nonuniform spatial source that maintains concentration inhomogeneities. For example, the scalar could be temperature with a source consisting of hot and cold spots, such that the mean temperature is constant. Which source distributions are best mixed by this velocity field? This question has a straightforward yet rich answer that is relevant to real mixing problems. We use a multiscale measure of steady-state enhancement to mixing and optimize it by a variational approach. We then solve the resulting Euler--Lagrange equation for a perturbed uniform flow and for simple cellular flows. The optimal source distributions have many broad features that are as expected: they avoid stagnation points, favor regions of fast flow, and their contours are aligned such that the flow blows hot spots onto cold and vice versa. However, the detailed structure varies widely with diffusivity and other problem parameters. Though these are model problems, the optimization procedure is simple enough to be adapted to more complex situations.
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"abstract": "A passive scalar is advected by a velocity field, with a nonuniform spatial\nsource that maintains concentration inhomogeneities. For example, the scalar\ncould be temperature with a source consisting of hot and cold spots, such that\nthe mean temperature is constant. Which source distributions are best mixed by\nthis velocity field? This question has a straightforward yet rich answer that\nis relevant to real mixing problems. We use a multiscale measure of\nsteady-state enhancement to mixing and optimize it by a variational approach.\nWe then solve the resulting Euler--Lagrange equation for a perturbed uniform\nflow and for simple cellular flows. The optimal source distributions have many\nbroad features that are as expected: they avoid stagnation points, favor\nregions of fast flow, and their contours are aligned such that the flow blows\nhot spots onto cold and vice versa. However, the detailed structure varies\nwidely with diffusivity and other problem parameters. Though these are model\nproblems, the optimization procedure is simple enough to be adapted to more\ncomplex situations.",
"arxiv_id": "physics/0703135",
"authors": [
"Jean-Luc Thiffeault",
"G. A. Pavliotis"
],
"categories": [
"physics.flu-dyn"
],
"doi": "10.1016/j.physd.2007.11.013",
"title": "Optimizing the Source Distribution in Fluid Mixing",
"url": "https://arxiv.org/abs/physics/0703135"
},
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