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.

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