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Arbitrarily high-order (weighted) essentially non-oscillatory finite difference schemes for anelastic flows on staggered meshes

by S. Mishra and C. Parés-Pulido and K. Pressel

(Report number 2019-27)

Abstract
We propose a WENO finite difference scheme to approximate anelastic flows, and scalars advected by them, on staggered grids. In contrast to existing WENO schemes on staggered grids, the proposed scheme is designed to be arbitrarily high-order accurate as it judiciously combines ENO interpolations of velocities with WENO reconstructions of spatial derivatives. A set of numerical experiments are presented to demonstrate the increase in accuracy and robustness with the proposed scheme, when compared to existing WENO schemes and state-of-the-art central finite difference schemes.

Keywords: WENO, anelastic Euler equations, high-order schemes, atmospheric science

@Techreport{MPP19_831,
  author = {S. Mishra and C. Parés-Pulido and K. Pressel},
  title = {Arbitrarily high-order (weighted) essentially non-oscillatory finite difference schemes for anelastic flows on staggered meshes},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2019-27},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2019/2019-27.pdf },
  year = {2019}
}

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