The multi-moments method of S. Tzivion, G. Feingold, and Z. Levin was applied to the original kinetic collection equation in order to obtain a set of equations with respect to moments in spectral bins.
The resulting large time step, multi-moment, low communication scheme is of great interest for exascale architectures.
Three methods are implemented: (1) single-moment WENO (WENO), (2) two-moment Hermite WENO (HWENO), and (3) entirely local multi-moment (MM-Loc).
These combinatorial formulas allow for the efficient implementation and development of a new multi-moment vortex method (MMVM) using a Hermite expansion to simulate 2D vorticity.
We then present two more examples of the full multi-moment vortex method and discuss the results in the context of classic vortex methods.
New Hermite Weighted Essentially Non-Oscillatory (HWENO) interpolants are developed and investigated within the Multi-Moment Finite-Volume (MMFV) formulation using the ADER-DT time discretization.
The Boundary Averaged Multi-moment Constrained finite-Volume (BA-MCV) method is de- rived, explained, and evaluated for 1-D transport to assess accuracy, maximum stable time step (MSTS), oscillations for discontinuous data, and parallel communication burden.
This paper presents an extension of the robust and accurate finite volume method (FVM), so-called VPM (Volume integrated average and Point value based Multi-moment) method, to structured and unstructured grids with arbitrary quadrilateral and hexahedral mesh elements.
A novel accurate numerical model for shallow water equations on sphere have been developed by implementing the high order multi-moment constrained finite volume (MCV) method on the icosahedral geodesic grid.
Minoshima, Y. Matsumoto, T. Amano, Multi-moment advection scheme for Vlasov simulations, Journal of Computational Physics 230 (2011) 6800 6823] to the three-dimensional case, for full electromagnetic Vlasov simulations of magnetized plasma.
Following the underlying idea of the volume-average/point-value multi-moment (VPM) method (Xie et al. (2014) [71]), this formulation is developed on arbitrary unstructured hybrid grids by employing the point values (PV) at both cell vertex and barycenter as the prognostic variables.
