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

Conference · Mon Jun 01 00:00:00 EDT 2015

DOI:https://doi.org/10.1016/j.procs.2015.05.385· OSTI ID:1524899

Norman, Matthew  ^[1]

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1. ORNL

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.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC05-00OR22725
• OSTI ID: 1524899
• 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