NUMERICAL SOLUTION FOR HYDRODYNAMICAL MODELS OF SEMICONDUCTORS

2000 ◽  
Vol 10 (07) ◽  
pp. 1099-1120 ◽  
Author(s):  
VITTORIO ROMANO ◽  
GIOVANNI RUSSO
Keyword(s):  
Numerical Scheme ◽  
Space Dimension ◽  
Numerical Solutions ◽  
Type System ◽  
Splitting Scheme ◽  
Diffusion Type ◽  
Hydrodynamical Models ◽  
Convection Diffusion ◽  
Relaxation Effects ◽  
Self Consistent

Numerical solutions of recent hydrodynamical models of semiconductors are computed in one-space dimension. Such models describe charge transport in semiconductor devices. Two models are taken into consideration. The first one has been developed by Blotekjaer, Baccarani et al., and the second one by Anile et al. In both cases the system of equations can be written as a convection-diffusion type system, with a right-hand side describing relaxation effects and interaction with a self-consistent electric field. The numerical scheme is a splitting scheme based on the Nessyahu–Tadmor scheme for the hyperbolic step, and a semi-implicit scheme for the relaxation step. The numerical results are compared to detailed Monte-Carlo simulation.

scholarly journals Enhanced positive vertex-centered finite volume scheme for anisotropic convection-diffusion equations

2020 ◽  
Vol 54 (2) ◽  
pp. 591-618 ◽  
Author(s):  
El Houssaine Quenjel
Keyword(s):  
Numerical Scheme ◽  
Control Volume ◽  
Positive Control ◽  
Finite Volume Scheme ◽  
Discrete Solution ◽  
Finite Element Scheme ◽  
Diffusion Type ◽  
Convection Diffusion ◽  
Anisotropic Fields ◽  
Control Volume Finite Element

This article is about the development and the analysis of an enhanced positive control volume finite element scheme for degenerate convection-diffusion type problems. The proposed scheme involves only vertex unknowns and features anisotropic fields. The novelty of the approach is to devise a reliable upwind approximation with respect to flux-like functions for the elliptic term. Then, it is shown that the discrete solution remains nonnegative. Under general assumptions on the data and the mesh, the convergence of the numerical scheme is established owing to a recent compactness argument. The efficiency and stability of the methodology are numerically illustrated for different anisotropic ratios and nonlinearities.

scholarly journals A NUMERICAL SCHEME FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS OF CONVECTION-DIFFUSION TYPE ON AN ADAPTIVE GRID

2018 ◽  
Vol 23 (4) ◽  
pp. 686-698 ◽  
Author(s):  
ramod Chakravarthy Podila ◽  
Trun Gupta ◽  
Nageshwar Rao
Keyword(s):  
Delay Differential Equations ◽  
Numerical Scheme ◽  
Adaptive Mesh ◽  
Singularly Perturbed ◽  
Adaptive Meshes ◽  
Diffusion Type ◽  
Convection Diffusion ◽  
Computational Work ◽  
Delay Differential ◽  
Central Finite Difference

In this paper, an adaptive mesh strategy is presented for solving singularly perturbed delay differential equation of convection-diffusion type using second order central finite difference scheme. Layer adaptive meshes are generated via an entropy production operator. The details of the location and width of the layer is not required in the proposed method unlike the popular layer adaptive meshes mainly by Bakhvalov and Shishkin. An extensive amount of computational work has been carried out to demonstrate the applicability of the proposed method.

scholarly journals Numerical Boundary Conditions for Solar Magnetic Hydrodynamic Flows Using the Method of Characteristics

1996 ◽  
Vol 154 ◽  
pp. 149-153
Author(s):  
S. T. Wu ◽  
A. H. Wang ◽  
W. P. Guo
Keyword(s):  
Boundary Conditions ◽  
Method Of Characteristics ◽  
Numerical Solutions ◽  
The Self ◽  
Time Dependent ◽  
Solar Plasma ◽  
The Method Of Characteristics ◽  
Mhd Simulations ◽  
Self Consistent ◽  
Dynamic Structures

AbstractWe discuss the self-consistent time-dependent numerical boundary conditions on the basis of theory of characteristics for magnetohydrodynamics (MHD) simulations of solar plasma flows. The importance of using self-consistent boundary conditions is demonstrated by using an example of modeling coronal dynamic structures. This example demonstrates that the self-consistent boundary conditions assure the correctness of the numerical solutions. Otherwise, erroneous numerical solutions will appear.

scholarly journals A self-consistent hybrid model of kinetic striations in low-current Argon discharges

2022 ◽  
Author(s):  
Vladimir Kolobov ◽  
Juan Alonso Guzmán ◽  
R R Arslanbekov
Keyword(s):  
Kinetic Equation ◽  
Hybrid Model ◽  
Noble Gases ◽  
Numerical Solutions ◽  
Penning Ionization ◽  
Poisson Solver ◽  
Glow Discharges ◽  
Self Consistent ◽  
Ionization Model ◽  
Positive Column Plasma

Abstract A self-consistent hybrid model of standing and moving striations was developed for low-current DC discharges in noble gases. We introduced the concept of surface diffusion in phase space (r,u) (where u denotes the electron kinetic energy) described by a tensor diffusion in the nonlocal Fokker-Planck kinetic equation for electrons in the collisional plasma. Electrons diffuse along surfaces of constant total energy ε=u-eφ(r) between energy jumps in inelastic collisions with atoms. Numerical solutions of the 1d1u kinetic equation for electrons were obtained by two methods and coupled to ion transport and Poisson solver. We studied the dynamics of striation formation in Townsend and glow discharges in Argon gas at low discharge currents using a two-level excitation-ionization model and a “full-chemistry” model, which includes stepwise and Penning ionization. Standing striations appeared in Townsend and glow discharges at low currents, and moving striations were obtained for the discharge currents exceeding a critical value. These waves originate at the anode and propagate towards the cathode. We have seen two types of moving striations with the 2-level and full-chemistry models, which resemble the s and p striations previously observed in the experiments. Simulations indicate that processes in the anode region could control moving striations in the positive column plasma. The developed model helps clarify the nature of standing and moving striations in DC discharges of noble gases at low discharge currents and low gas pressures.

scholarly journals Strong convergence rates of semidiscrete splitting approximations for the stochastic Allen–Cahn equation

2018 ◽  
Vol 39 (4) ◽  
pp. 2096-2134 ◽  
Author(s):  
Charles-Edouard Bréhier ◽  
Jianbo Cui ◽  
Jialin Hong
Keyword(s):  
Convergence Rate ◽  
Strong Convergence ◽  
Convergence Rates ◽  
Numerical Solutions ◽  
A Priori Estimates ◽  
A Priori ◽  
Auxiliary Problem ◽  
Splitting Scheme ◽  
Cahn Equation ◽  
Strong Convergence Rate

Abstract This article analyses an explicit temporal splitting numerical scheme for the stochastic Allen–Cahn equation driven by additive noise in a bounded spatial domain with smooth boundary in dimension $d\leqslant 3$. The splitting strategy is combined with an exponential Euler scheme of an auxiliary problem. When $d=1$ and the driving noise is a space–time white noise we first show some a priori estimates of this splitting scheme. Using the monotonicity of the drift nonlinearity we then prove that under very mild assumptions on the initial data this scheme achieves the optimal strong convergence rate $\mathcal{O}(\delta t^{\frac 14})$. When $d\leqslant 3$ and the driving noise possesses some regularity in space we study exponential integrability properties of the exact and numerical solutions. Finally, in dimension $d=1$, these properties are used to prove that the splitting scheme has a strong convergence rate $\mathcal{O}(\delta t)$.

Hybrid Nodal Integral / Finite Element Method for Time-Dependent Convection Diffusion Equation

2021 ◽  
Author(s):  
Sundar Namala ◽  
Rizwan Uddin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Numerical Solutions ◽  
Second Order ◽  
Time Dependent ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Integral Methods ◽  
Element Method

Abstract Nodal integral methods (NIM) are a class of efficient coarse mesh methods that use transverse averaging to reduce the governing partial differential equation(s) (PDE) into a set of ordinary differential equations (ODE). The standard application of NIM is restricted to domains that have boundaries parallel to one of the coordinate axes/palnes (in 2D/3D). The hybrid nodal-integral/finite-element method (NI-FEM) reported here has been developed to extend the application of NIM to arbitrary domains. NI-FEM is based on the idea that the interior region and the regions with boundaries parallel to the coordinate axes (2D) or coordinate planes (3D) can be solved using NIM, and the rest of the domain can be discretized and solved using FEM. The crux of the hybrid NI-FEM is in developing interfacial conditions at the common interfaces between the NIM regions and FEM regions. We here report the development of hybrid NI-FEM for the time-dependent convection-diffusion equation (CDE) in arbitrary domains. Resulting hybrid numerical scheme is implemented in a parallel framework in Fortran and solved using PETSc. The preliminary approach to domain decomposition is also discussed. Numerical solutions are compared with exact solutions, and the scheme is shown to be second order accurate in both space and time. The order of approximations used for the development of the scheme are also shown to be second order. The hybrid method is more efficient compared to standalone conventional numerical schemes like FEM.

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