dorsal/arxiv
View SchemaCoarse-grained analysis of a lattice Boltzmann model for planar streamer fronts
| Authors | Wim Vanroose, Giovanni Samaey, Pieter Van Leemput |
|---|---|
| Categories | |
| ArXiv ID | physics/0701031 |
| URL | https://arxiv.org/abs/physics/0701031 |
Abstract
We study the traveling wave solutions of a lattice Boltzmann model for the planar streamer fronts that appear in the transport of electrons through a gas in a strong electrical field. To mimic the physical properties of the impact ionization reaction, we introduce a reaction matrix containing reaction rates that depend on the electron velocities. Via a Chapman--Enskog expansion, one is able to find only a rough approximation for a macroscopic evolution law that describes the traveling wave solution. We propose to compute these solutions with the help of a coarse-grained time-stepper, which is an effective evolution law for the macroscopic fields that only uses appropriately initialized simulations of the lattice Boltzmann model over short time intervals. The traveling wave solution is found as a fixed point of the sequential application of the coarse-grained time-stepper and a shift-back operator. The fixed point is then computed with a Newton-Krylov Solver. We compare the resulting solutions with those of the approximate PDE model, and propose a method to find the minimal physical wave speed.
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"date_created": "2026-03-02T18:01:14.823000Z",
"date_modified": "2026-03-02T18:01:14.823000Z",
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"abstract": "We study the traveling wave solutions of a lattice Boltzmann model for the\nplanar streamer fronts that appear in the transport of electrons through a gas\nin a strong electrical field. To mimic the physical properties of the impact\nionization reaction, we introduce a reaction matrix containing reaction rates\nthat depend on the electron velocities. Via a Chapman--Enskog expansion, one is\nable to find only a rough approximation for a macroscopic evolution law that\ndescribes the traveling wave solution. We propose to compute these solutions\nwith the help of a coarse-grained time-stepper, which is an effective evolution\nlaw for the macroscopic fields that only uses appropriately initialized\nsimulations of the lattice Boltzmann model over short time intervals. The\ntraveling wave solution is found as a fixed point of the sequential application\nof the coarse-grained time-stepper and a shift-back operator. The fixed point\nis then computed with a Newton-Krylov Solver. We compare the resulting\nsolutions with those of the approximate PDE model, and propose a method to find\nthe minimal physical wave speed.",
"arxiv_id": "physics/0701031",
"authors": [
"Wim Vanroose",
"Giovanni Samaey",
"Pieter Van Leemput"
],
"categories": [
"physics.comp-ph"
],
"title": "Coarse-grained analysis of a lattice Boltzmann model for planar streamer fronts",
"url": "https://arxiv.org/abs/physics/0701031"
},
"schema_id": "dorsal/arxiv",
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"type": "Model",
"variant": "snapshot-2026-03-01",
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