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Title: Arbitrarily High-Order-Accurate, Hermite WENO Limited, Boundary-Averaged Multi-Moment Constrained Finite-Volume (BA-MCV) Schemes for 1-D Transport

Abstract

This study introduces the Boundary Averaged Multi-moment Constrained finite-Volume (BA- MCV) scheme for 1-D transport with Hermite Weighted Essentially Non-Oscillatory (HWENO) limiting using the ADER Differential Transform (ADER-DT) time discretization. The BA- MCV scheme evolves a cell average using a Finite-Volume (FV) scheme, and it adds further constraints as point wise derivatives of the state at cell boundaries, which are evolved in strong form using PDE derivatives. The resulting scheme maintains a Maximum Stable CFL (MSCFL) value of one no matter how high-order the scheme is. Also, parallel communication requirements are very low and will be described. h-refinement experiments demonstrate proper convergence order, and p-refinement experiments demonstrate expected exponential convergence. The over- all ADER-DT + BA-MCV + HWENO scheme is a scalable and larger time step alternative to Galerkin methods for multi-moment fluid simulation in climate and weather applications.

Authors:
ORCiD logo [1]
  1. ORNL
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1524899
DOE Contract Number:  
AC05-00OR22725
Resource Type:
Conference
Resource Relation:
Journal Volume: 51; Conference: International Conference on Computational Science 2015 - Reykjavik, , Iceland - 6/1/2015 8:00:00 AM-6/3/2015 8:00:00 AM
Country of Publication:
United States
Language:
English

Citation Formats

Norman, Matthew. Arbitrarily High-Order-Accurate, Hermite WENO Limited, Boundary-Averaged Multi-Moment Constrained Finite-Volume (BA-MCV) Schemes for 1-D Transport. United States: N. p., 2015. Web. doi:10.1016/j.procs.2015.05.385.
Norman, Matthew. Arbitrarily High-Order-Accurate, Hermite WENO Limited, Boundary-Averaged Multi-Moment Constrained Finite-Volume (BA-MCV) Schemes for 1-D Transport. United States. doi:10.1016/j.procs.2015.05.385.
Norman, Matthew. Mon . "Arbitrarily High-Order-Accurate, Hermite WENO Limited, Boundary-Averaged Multi-Moment Constrained Finite-Volume (BA-MCV) Schemes for 1-D Transport". United States. doi:10.1016/j.procs.2015.05.385. https://www.osti.gov/servlets/purl/1524899.
@article{osti_1524899,
title = {Arbitrarily High-Order-Accurate, Hermite WENO Limited, Boundary-Averaged Multi-Moment Constrained Finite-Volume (BA-MCV) Schemes for 1-D Transport},
author = {Norman, Matthew},
abstractNote = {This study introduces the Boundary Averaged Multi-moment Constrained finite-Volume (BA- MCV) scheme for 1-D transport with Hermite Weighted Essentially Non-Oscillatory (HWENO) limiting using the ADER Differential Transform (ADER-DT) time discretization. The BA- MCV scheme evolves a cell average using a Finite-Volume (FV) scheme, and it adds further constraints as point wise derivatives of the state at cell boundaries, which are evolved in strong form using PDE derivatives. The resulting scheme maintains a Maximum Stable CFL (MSCFL) value of one no matter how high-order the scheme is. Also, parallel communication requirements are very low and will be described. h-refinement experiments demonstrate proper convergence order, and p-refinement experiments demonstrate expected exponential convergence. The over- all ADER-DT + BA-MCV + HWENO scheme is a scalable and larger time step alternative to Galerkin methods for multi-moment fluid simulation in climate and weather applications.},
doi = {10.1016/j.procs.2015.05.385},
journal = {},
issn = {1877-0509},
number = ,
volume = 51,
place = {United States},
year = {2015},
month = {6}
}

Conference:
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