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An implicit LU‐SGS spectral volume method for the moment models in device simulations III: accuracy enhancement using the LDG2 flux formulation for non‐uniform grids
Author(s) -
Kannan Ravi
Publication year - 2012
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.1851
Subject(s) - discretization , moment (physics) , grid , stability (learning theory) , mathematics , constraint (computer aided design) , penalty method , mathematical optimization , mathematical analysis , computer science , physics , classical mechanics , geometry , machine learning
The LDG2 viscous flux formulation was recently developed by Kannan and Wang for the spectral volume setting. The LDG2 scheme is a variant of the more popular LDG formulation and retains the attractive features of the latter. In addition, it also displays higher degree of symmetry and accuracy than the LDG approach and has a milder stability constraint than the original formulation. In this paper, the third in a series, the accuracy of the high‐order spectral volume method for the moment models in device simulations is enhanced by using the LDG2 formulation for discretizing the second derivative diffusive fluxes. More specifically, the emphasis is on showing the efficacy of the new formulation, when used in a domain discretized with highly non‐uniform grids. Unlike the penalty formulations such as the interior penalty and the Bassi and Rebay 2 (BR2) schemes, the LDG2 formulation requires no length‐based penalizing terms and is compact. This eliminates problems associated with obtaining a right length scale when the grid sizes are varying rapidly. A n + –n–n + diode was assumed for simulation purposes. The results obtained by solving the steady state hydrodynamic models and the energy transport models are compared with the existing LDG, penalty, and the BR2 results. The new formulation always yields more accurate solutions than the ones that used the LDG formulation. It also displays (i) higher fidelity than the BR2 formulations and (ii) comparable fidelity to the penalty formulation when the grids are highly non‐uniform. The LDG2 formulation is compact and hence can be easily parallelized. In general, the numerical results are very promising and indicate that the new diffusive flux formulation is suited better than the existing formulations when the grids are non‐uniform. Copyright © 2012 John Wiley & Sons, Ltd.