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Decomposition of the multidimensional Euler equations into advection equations

by M. Fey

(Report number 1995-14)

Abstract
Based on a genuine multi-dimensional numerical scheme, called Method of Transport, we derive a form of the compressible Euler-equations, capable of a linearization for any space dimension. This form allows a rigorous error analysis of the linearization error without the knowledge of the numerical method. The generated error can be eliminated by special correction terms in the linear equations. Hence, existing scalar high order methods can be used to solve the linear equations and obtain high order accuracy in space and time for the non-linear conservation law. In our approach, the scalar version of the method of transport is used to solve the linear equations. This method is multi-dimensional and reduces the solution of the partial differential equation to an integration process. Convergence histories presented at the end of the paper show that the numerical results agree with the theoretical predictions.

Keywords: conservation laws, flux vector splitting, characteristic surfaces

@Techreport{F95_181,
  author = {M. Fey},
  title = {Decomposition of the multidimensional Euler equations into advection equations},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1995-14},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1995/1995-14.pdf },
  year = {1995}
}

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