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An implicit LU‐SGS spectral volume method for the moment models in device simulations: Formulation in 1D and application to a p‐multigrid algorithm
Author(s) -
Kannan Ravishekar
Publication year - 2011
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.1359
Subject(s) - discretization , discontinuous galerkin method , solver , finite volume method , multigrid method , mathematics , inviscid flow , moment (physics) , riemann solver , mathematical analysis , mathematical optimization , physics , mechanics , finite element method , classical mechanics , partial differential equation , thermodynamics
A high‐order spectral volume (SV) method was implemented for solving the steady‐state moment models, such as the hydrodynamic (HD) models and the energy transport (ET) models for semiconductor device simulations (in 1D). The first derivative inviscid/convective fluxes are handled using an approximate Riemann flux and the second derivative diffusive fluxes are discretized using the local discontinuous Galerkin formulation (LDG). The LDG method is also used for discretizing the potential equation. An implicit pre‐conditioned LU‐SGS p‐multigrid method developed for the SV Navier–Stokes (NS) solver by Kannan and Wang is adopted here for time marching. The entire formulation is compact and hence can be easily parallelized. A n + ‐ n ‐ n + diode was assumed for simulation purposes and the results are compared with the existing discontinuous Galerkin simulation results. In general, the numerical results are very promising and indicate that the approach has a great potential for higher‐dimensional device problems. Copyright © 2010 John Wiley & Sons, Ltd.