Asymptotic-Preserving Scheme for the M1-Maxwell System in the Quasi-Neutral Regime

2016 ◽  
Vol 19 (2) ◽  
pp. 301-328 ◽  
Author(s):  
S. Guisset ◽  
S. Brull ◽  
B. Dubroca ◽  
E. d'Humières ◽  
S. Karpov ◽  
...  
Keyword(s):  
Numerical Scheme ◽  
Numerical Test ◽  
Test Cases ◽  
Maxwell System ◽  
Asymptotic Preserving ◽  
Numerical Resolution ◽  
Moment Models ◽  
Asymptotic Preserving Scheme ◽  
The Stability ◽  
Limit Models

AbstractThis work deals with the numerical resolution of the M1-Maxwell system in the quasi-neutral regime. In this regime the stiffness of the stability constraints of classical schemes causes huge calculation times. That is why we introduce a new stable numerical scheme consistent with the transitional and limit models. Such schemes are called Asymptotic-Preserving (AP) schemes in literature. This new scheme is able to handle the quasi-neutrality limit regime without any restrictions on time and space steps. This approach can be easily applied to angular moment models by using a moments extraction. Finally, two physically relevant numerical test cases are presented for the Asymptotic-Preserving scheme in different regimes. The first one corresponds to a regime where electromagnetic effects are predominant. The second one on the contrary shows the efficiency of the Asymptotic-Preserving scheme in the quasi-neutral regime. In the latter case the illustrative simulations are compared with kinetic and hydrodynamic numerical results.

scholarly journals EVALUATION OF THE PERFORMANCE OF THE HYBRID LATTICE BOLTZMANN BASED NUMERICAL FLUX

2016 ◽  
Vol 42 ◽  
pp. 1660152
Author(s):  
H. W. ZHENG ◽  
C. SHU
Keyword(s):  
Lattice Boltzmann ◽  
Numerical Scheme ◽  
Navier Stokes ◽  
Bench Mark ◽  
Test Cases ◽  
Numerical Flux ◽  
Mark Test ◽  
Key Factor ◽  
The Stability ◽  
Stability And Accuracy

It is well known that the numerical scheme is a key factor to the stability and accuracy of a Navier-Stokes solver. Recently, a new hybrid lattice Boltzmann numerical flux (HLBFS) is developed by Shu's group. It combines two different LBFS schemes by a switch function. It solves the Boltzmann equation instead of the Euler equation. In this article, the main object is to evaluate the ability of this HLBFS scheme by our in-house cell centered hybrid mesh based Navier-Stokes code. Its performance is examined by several widely-used bench-mark test cases. The comparisons on results between calculation and experiment are conducted. They show that the scheme can capture the shock wave as well as the resolving of boundary layer.

scholarly journals Fitted numerical scheme for singularly perturbed convection-diffusion reaction problems involving delays

2021 ◽  
pp. 6-6
Author(s):  
Mesfin Woldaregay ◽  
Worku Aniley ◽  
Gemechis Duressa
Keyword(s):  
Numerical Scheme ◽  
Numerical Test ◽  
Singularly Perturbed ◽  
Diffusion Reaction ◽  
Convection Diffusion ◽  
Solution Methods ◽  
Solution Bound ◽  
The Stability ◽  
Delay Differential ◽  
Exponential Boundary Layer

This paper deals with solution methods for singularly perturbed delay differential equations having delay on the convection and reaction terms. The considered problem exhibits an exponential boundary layer on the left or right side of the domain. The terms with the delay are treated using Taylor?s series approximation and the resulting singularly perturbed boundary value problem is solved using a specially designed exponentially finite difference method. The stability of the scheme is analysed and investigated using a comparison principle and solution bound. The formulated scheme converges uniformly with linear order of convergence. The theoretical findings are validated using three numerical test examples.

scholarly journals An Asymptotic Preserving Scheme for Kinetic Models for Chemotaxis Phenomena

2018 ◽  
Vol 9 (2) ◽  
pp. 61-75
Author(s):  
Abdelghani Bellouquid ◽  
Jacques Tagoudjeu
Keyword(s):  
Kinetic Equation ◽  
Kinetic Model ◽  
Small Parameter ◽  
Kinetic Models ◽  
Numerical Approach ◽  
Test Cases ◽  
Equivalent Formulation ◽  
Asymptotic Preserving ◽  
Standard Methods ◽  
Asymptotic Preserving Scheme

Abstract In this paper, we propose a numerical approach to solve a kinetic model of chemotaxis phenomena. This scheme is shown to be uniformly stable with respect to the small parameter, consistent with the uid-di usion limit (Keller-Segel model). Our approach is based on the micro-macro decomposition which leads to an equivalent formulation of the kinetic model that couples a kinetic equation with macroscopic ones. This method is validated by various test cases and compared to other standard methods.

Numerical studies for the variable-order nonlinear fractional wave equation

2012 ◽  
Vol 15 (4) ◽  
Author(s):  
N. Sweilam ◽  
M. Khader ◽  
H. Almarwm
Keyword(s):  
Wave Equation ◽  
Stability Analysis ◽  
Numerical Scheme ◽  
Numerical Test ◽  
Variable Order ◽  
Fractional Wave Equation ◽  
Numerical Studies ◽  
Explicit Finite Difference ◽  
The Stability ◽  
Explicit Finite Difference Method

AbstractIn this paper, the explicit finite difference method (FDM) is used to study the variable order nonlinear fractional wave equation. The fractional derivative is described in the Riesz sense. Special attention is given to study the stability analysis and the convergence of the proposed method. Numerical test examples are presented to show the efficiency of the proposed numerical scheme.

The Numerical Analysis and Simulation of a Linearized Crank-Nicolson H1-GMFEM for Nonlinear Coupled BBM Equations

2014 ◽  
Vol 513-517 ◽  
pp. 1919-1926 ◽  
Author(s):  
Min Zhang ◽  
Zu Deng Yu ◽  
Yang Liu ◽  
Hong Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Scheme ◽  
Mixed Finite Element ◽  
A Priori ◽  
Numerical Test ◽  
Mixed Finite Element Method ◽  
Spatial Direction ◽  
Time Direction ◽  
Crank Nicolson

In this article, the numerical scheme of a linearized Crank-Nicolson (C-N) method based on H1-Galerkin mixed finite element method (H1-GMFEM) is studied and analyzed for nonlinear coupled BBM equations. In this method, the spatial direction is approximated by an H1-GMFEM and the time direction is discretized by a linearized Crank-Nicolson method. Some optimal a priori error results are derived for four important variables. For conforming the theoretical analysis, a numerical test is presented.

A TWELFTH-ORDER FOUR-STEP FORMULA FOR THE NUMERICAL INTEGRATION OF THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION

2003 ◽  
Vol 14 (08) ◽  
pp. 1087-1105 ◽  
Author(s):  
ZHONGCHENG WANG ◽  
YONGMING DAI
Keyword(s):  
Schrödinger Equation ◽  
Numerical Integration ◽  
Schrodinger Equation ◽  
Numerical Test ◽  
New Method ◽  
Step Method ◽  
One Dimensional ◽  
The Stability ◽  
The One ◽  
Order Four

A new twelfth-order four-step formula containing fourth derivatives for the numerical integration of the one-dimensional Schrödinger equation has been developed. It was found that by adding multi-derivative terms, the stability of a linear multi-step method can be improved and the interval of periodicity of this new method is larger than that of the Numerov's method. The numerical test shows that the new method is superior to the previous lower orders in both accuracy and efficiency and it is specially applied to the problem when an increasing accuracy is requested.

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