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The Method of Transport for mixed hyperbolic-parabolic systems

by J. Maurer

(Report number 1997-13)

Abstract
Starting from a numerical scheme for solving systems of hyperbolic partial differential equations the transition to parabolic equations of the type of advection-diffusion equations needs a different treatment of the viscous part. Since we are using a genuine multi-dimensional scheme also the fact that the diffusion acts in infinitely many directions shall be captured properly. Therefore, to be able to use this scheme we have developed a decomposition of the scalar advection-diffusion equation into a special system of advection equations. In particular the interaction of the advection and diffusion part will be taken into account. The extension to the Navier-Stokes equations which are a system of mixed hyperbolic-parabolic type is possible and will be pointed out.

Keywords: Finite Volume Schemes, Hyperbolic Conservation Laws, Numerical Viscosity, Euler Equations, Advection-Diffusion Equation, Navier-Stokes Equations

@Techreport{M97_218,
  author = {J. Maurer},
  title = {The Method of Transport for mixed hyperbolic-parabolic systems},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1997-13},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1997/1997-13.pdf },
  year = {1997}
}

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