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Volume 29, Issue 5
Arbitrarily High-Order (Weighted) Essentially Non-Oscillatory Finite Difference Schemes for Anelastic Flows on Staggered Meshes

Siddhartha Mishra, Carlos Parés-Pulido & Kyle G. Pressel

DOI: 10.4208/cicp.OA-2020-0046

Commun. Comput. Phys., 29 (2021), pp. 1299-1335.

Published online: 2021-03

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  • 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

Weighted essentially non-oscillatory schemes, finite difference, anelastic flow, staggered mesh, high-order methods.

  • AMS Subject Headings

65M06, 65M22, 76M20

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{CiCP-29-1299, author = {Mishra , SiddharthaParés-Pulido , Carlos and G. Pressel , Kyle}, title = {Arbitrarily High-Order (Weighted) Essentially Non-Oscillatory Finite Difference Schemes for Anelastic Flows on Staggered Meshes}, journal = {Communications in Computational Physics}, year = {2021}, volume = {29}, number = {5}, pages = {1299--1335}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0046}, url = {http://global-sci.org/intro/article_detail/cicp/18715.html} }
TY - JOUR T1 - Arbitrarily High-Order (Weighted) Essentially Non-Oscillatory Finite Difference Schemes for Anelastic Flows on Staggered Meshes AU - Mishra , Siddhartha AU - Parés-Pulido , Carlos AU - G. Pressel , Kyle JO - Communications in Computational Physics VL - 5 SP - 1299 EP - 1335 PY - 2021 DA - 2021/03 SN - 29 DO - http://doi.org/10.4208/cicp.OA-2020-0046 UR - https://global-sci.org/intro/article_detail/cicp/18715.html KW - Weighted essentially non-oscillatory schemes, finite difference, anelastic flow, staggered mesh, high-order methods. AB -

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.

Mishra , SiddharthaParés-Pulido , Carlos and G. Pressel , Kyle. (2021). Arbitrarily High-Order (Weighted) Essentially Non-Oscillatory Finite Difference Schemes for Anelastic Flows on Staggered Meshes. Communications in Computational Physics. 29 (5). 1299-1335. doi:10.4208/cicp.OA-2020-0046
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