Volume 51, Number 5, September-October 2017
|Page(s)||1583 - 1615|
|Published online||27 September 2017|
1 Computing and Mathematical Sciences, California Institute of Technology, 1200 E California Blvd. MC 305-16, Pasadena, CA 91125 USA.
Present address: Department of Mathematics, University of Wisconsin-Madison, Madison, WI, 53705 USA. firstname.lastname@example.org
2 Department of Mathematics, Department of Physics, and Department of Chemistry, Duke University, Box 90320, Durham, NC 27708 USA.
3 Department of Mathematics, Simon Fraser University, 8888 University Dr., Burnaby, BC V5A 1S6, Canada.
Received: 13 May 2015
Revised: 12 July 2016
Accepted: 29 November 2016
We give a unified proof for the well-posedness of a class of linear half-space equations with general incoming data and construct a Galerkin method to numerically resolve this type of equations in a systematic way. Our main strategy in both analysis and numerics includes three steps: adding damping terms to the original half-space equation, using an inf-sup argument and even-odd decomposition to establish the well-posedness of the damped equation, and then recovering solutions to the original half-space equation. The proposed numerical methods for the damped equation is shown to be quasi-optimal and the numerical error of approximations to the original equation is controlled by that of the damped equation. This efficient solution to the half-space problem is useful for kinetic-fluid coupling simulations.
Mathematics Subject Classification: 35F15 / 35Q79
Key words: Half-space equations / boundary layer / kinetic-fluid coupling / Galerkin method
We would like to express our gratitude to the NSF grant RNMS11-07444 (KI-Net), whose activities initiated our collaboration. The research of Q.L. was supported in part by the AFOSR MURI grant FA9550-09-1-0613 and the National Science Foundation under award DMS-1318377. The research of J.L. was supported in part by the Alfred P. Sloan Foundation and the National Science Foundation under award DMS-1312659. The research of W.S. was supported in part by the Simon Fraser University President’s Research Start-up Grant PRSG-877723 and NSERC Discovery Individual Grant #611626.
© EDP Sciences, SMAI 2017
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