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A projection method for the computation of admissible measure valued solutions of the incompressible Euler equations

by F. Leonardi

(Report number 2017-06)

Abstract
We formulate a fully discrete finite difference numerical method to approximate the incompressible Euler equations and prove that the sequence generated by the scheme converges to an admissible measure valued solution. The scheme combines an energy conservative flux with a velocity-projection temporal splitting in order to efficiently decouple the advection from the pressure gradient. With the use of robust Monte Carlo approximations, statistical quantities of the approximate solution can be computed. We present numerical results that agree with the theoretical findings obtained for the scheme.

Keywords: Monte Carlo methods, Measure valued solutions, Incompressible inviscid fluids, Projection methods

@Techreport{L17_702,
  author = {F. Leonardi},
  title = {A projection method for the computation of admissible measure valued solutions of the incompressible Euler equations},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2017-06},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2017/2017-06.pdf },
  year = {2017}
}

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