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

Abstract

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.

A high order spectral volume solution to the Burgers' equation using the Hopf–Cole transformation

“…In this approach, the numerical fluxes are defined by alternating the direction in the following manner [7,15] u D u L , (2.14) In this approach, the numerical fluxes are defined by alternating the direction in the following manner [7,15] u D u L , (2.14)…”

“…The commonly used approach for obtaining the numerical fluxes is the LDG approach. In this approach, the numerical fluxes are defined by alternating the direction in the following manner [7,15] u D u L , (2.14)…”

“…Kannan implemented the SV method for the Navier-Stokes equations using the LDG2 (which is an improvised variant of the LDG approach) [11] and direct discontinuous Galerkin approaches [12]. Even more recently, Kannan extended the SV method to solve the moment models in semiconductor device simulations [13][14][15]. The latest SV developments include incorporating the moving body method [16], discretizing the higher spatial derivative terms [17] and solving the elastohydrodynamic problem [18].…”