European Numerical Mathematics and
Advanced Applications Conference 2019
30th sep - 4th okt 2019, Egmond aan Zee, The Netherlands
10:40   MS15: Novel flux approximation schemes for advection-diffusion problems (Part 2)
Chair: Martijn Anthonissen
10:40
25 mins
Novel schemes for drift-diffusion semiconductor problems
Patricio Farrell
Abstract: We present accurate finite volume methods for semiconductor problems with nonlinear diffusion. Nonlinear diffusion is important at low temperatures, for organic materials or large doping concentrations. We develop schemes which are physically correct and stable, expanding ideas by Scharfetter and Gummel for linear diffusion.
11:05
25 mins
ENATE for complex domains II. Von Newmann and Robin boundary conditions
Víctor Javier Llorente, Antonio Pascau
Abstract: ENATE (Enhanced Numerical Approximation of a Transport Equation) is a high-order scheme that provides the exact solution of the one-dimensional transport equation for arbitrary coefficients and source. In this paper how to deal with complex domains and Von Newmann and Robin boundary conditions is described under the framework of ENATE.
11:30
25 mins
Novel Flux Approximation Schemes for Systems of Coupled Advection-Diffusion-Reaction Equations
Jan van Dijk, Jan ten Thije Boonkkamp, Chris Schoutrop, Robert van Gestel
Abstract: Novel approximation schemes will be presented for the mass flux densities in multi-component advection-diffusion-reaction systems. These expressions take into account the coupling between the fluxes and ensure that essential system invariants are respected without any discretization error when used in a finite-volume based numerical simulation of the system.
11:55
25 mins
Modified exponential fitting schemes for degenerate semiconductors and electrolytes
Jürgen Fuhrmann, Patricio Farrell
Abstract: A common characteristic trait of degenerate semiconductors and electrolytes are constraints on the density of charge carriers - electrons, holes or ions, either due to their energetic distribution (Fermi statistics for electrons and holes in semicondutors) or ther finite size (ions in electrolytes). As a result, the classical drift-diffusion model (van Roosbroeck resp. Nernst-Planck-Poisson system) which assumes that charge carrier transport is induced by linear Fickian diffusion and drift (convection) in the self-consistent electric field is rendered untrue. The classical exponential fitting upwind discretization scheme which was derived independently, among others, by Il'in and by Scharfetter and Gummel, in combination with the Voronoi finite volume method has a very successful application history in semiconductor device simulation. One reason for this success is are the thermodynamical consistency properties of the scheme. However, it was initially derived for the classical drift-diffusion system. The talk discusses classical and recent approaches to generalize the Scharfetter-Gummel scheme in the context of generalized Nernst-Planck-Poisson systems and provides examples of their application in semiconductor device and electrolyte simulation.