An implicit LU-SGS spectral volume method for moment models in device simulations II: Accuracy studies and performance enhancements using the penalty and BR2 formulations

Abstract

SUMMARYIn this paper, the second in a series, the accuracy and performance of the high-order spectral volume (SV) method for moment models in device simulations is enhanced by employing the penalty and BR2 formulations for discretizing the second derivative diffusive fluxes. The potential equation is also discretized using the above formulations. The actual accuracy and the numerical orders are obtained by performing accuracy studies. An n + -n-n + diode was assumed for simulation purposes. The results obtained by solving steady-state hydrodynamic (HD) and energy transport (ET) models are compared with the existing local discontinuous Galerkin formulation (LDG) results. The newer formulations yield more accurate solutions than the ones which used the LDG formulation. In addition, the newer formulations converge to steady state much faster than the LDG formulation. The BR2 formulation is compact and hence can be easily parallelized. The penalty formulation is however not compact. In general, the numerical results are very promising and indicate that the newer diffusive flux formulations are more accurate, converge faster, have greater potential and hence are suited better than the LDG for higher dimensional device problems.

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

“…In the earlier papers of this series, Kannan et al . used the LDG, penalty, and the BR2 formulations to discretize the diffusive flux. Unlike the penalizing schemes, the LDG2 method requires no length scales and is more symmetrical than the traditional LDG method.…”

“…The SV method is a high-order method originally developed by Wang et al [3][4][5][6][7][8] and further improved by Kannan et al [1,2,[9][10][11][12][13][14][15][16][17][18][19] for hyperbolic and elliptical equations on unstructured grids The SV method can be viewed as an extension of the Godunov method to higher order by adding more DOFs in the form of subcells in each cell (simplex). The simplex is referred to as an SV, and the subcells are referred to as control volumes (CVs).…”

“…In this paper, we further extend the SV method for the moment models in device simulations by implementing the LDG2 flux discretization procedure. In the earlier papers of this series, Kannan et al [1,2] used the LDG, penalty, and the BR2 formulations to discretize the diffusive flux. Unlike the penalizing schemes, the LDG2 method requires no length scales and is more symmetrical than the traditional LDG method.…”

“…We continue with the development of the spectral volume (SV) method for the moment models n device simulations, following the first two papers in the series , wherein (i) a basic formulation and application to a p‐multigrid algorithm was presented in 1D and (ii) accuracy studies and performance enhancements were carried out using a variety of viscous flux discretization procedures. The ultimate goal of this research study is to have an SV for the moment models with the following attributes: (i) high‐order accurate; (ii) easily applicable to multidimensional problems; (iii) geometrically flexible; (iv) easily hook up with an implicit solver and algebraic, geometric, and polynomial multigrid preconditioners; and (v) easily applicable for various moment models.…”

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

“…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].…”