Numerical Solution to the Time-Dependent Maxwell Equations in Two-Dimensional Singular Domains: The Singular Complement Method

2000 ◽  
Vol 161 (1) ◽  
pp. 218-249 ◽  
Author(s):  
F. Assous ◽  
P. Ciarlet ◽  
J. Segré
Keyword(s):  
Numerical Solution ◽  
Maxwell Equations ◽  
Time Dependent ◽  
Two Dimensional ◽  
Singular Domains

scholarly journals Numerical Solution to the 3D Static Maxwell Equations in Axisymmetric Singular Domains with Arbitrary Data

2020 ◽  
Vol 20 (3) ◽  
pp. 419-435
Author(s):  
Franck Assous ◽  
Irina Raichik
Keyword(s):  
Numerical Solution ◽  
Variational Formulation ◽  
Numerical Experiments ◽  
Maxwell Equations ◽  
Three Dimensional ◽  
Singular Part ◽  
Time Dependent ◽  
Singular Domains ◽  
Depth Study ◽  
Axisymmetric Problems

AbstractWe propose a numerical method to solve the three-dimensional static Maxwell equations in a singular axisymmetric domain, generated by the rotation of a singular polygon around one of its sides. The mathematical tools and an in-depth study of the problem set in the meridian half-plane are exposed in [F. Assous, P. Ciarlet, Jr., S. Labrunie and J. Segré, Numerical solution to the time-dependent Maxwell equations in axisymmetric singular domains: the singular complement method, J. Comput. Phys. 191 2003, 1, 147–176] and [P. Ciarlet, Jr. and S. Labrunie, Numerical solution of Maxwell’s equations in axisymmetric domains with the Fourier singular complement method, Differ. Equ. Appl. 3 2011, 1, 113–155]. Here, we derive a variational formulation and the corresponding approximation method. Numerical experiments are proposed, and show that the approach is able to capture the singular part of the solution. This article can also be viewed as a generalization of the Singular Complement Method to three-dimensional axisymmetric problems.

scholarly journals Numerical modeling of an avalanche impact against an obstacle with account of snow compressibility

2008 ◽  
Vol 49 ◽  
pp. 27-32 ◽  
Author(s):  
V.S. Kulibaba ◽  
M.E. Eglit
Keyword(s):  
Numerical Modeling ◽  
Equation Of State ◽  
Numerical Solution ◽  
Pressure Distribution ◽  
Time Dependent ◽  
Low Density ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Flow Depth ◽  
Rarefaction Waves

AbstractThe numerical solution to a time-dependent two-dimensional problem of an avalanche impact against a wall is presented. The height of the wall is much larger than the flow depth. Compressibility of the moving snow as well as the effect of gravity is taken into account. Calculations are made for an impact of low-density avalanches with densities <100 kgm–3 obeying the equation of state for a mixture of two gases (air and gas of ice/snow particles). The pressure, density and velocity distributions in the flow as functions of time and space coordinates are calculated, as well as the variation of the flow depth. In particular, the flow height at the wall, the pressure at the wall and the pressure distribution on the slope near the wall are given, demonstrating peaks and falls due to compression shocks and rarefaction waves.

The inviscid transonic flow about a cylinder

1995 ◽  
Vol 301 ◽  
pp. 225-250 ◽  
Author(s):  
Nicola Botta
Keyword(s):  
Mach Number ◽  
Numerical Solution ◽  
Transonic Flow ◽  
Oscillating Solution ◽  
Time Dependent ◽  
Turbulent Regime ◽  
Two Dimensional ◽  
Chaotic Flow ◽  
Regular Flow ◽  
Upwind Method

The two-dimensional inviscid transonic flow about a circular cylinder is investigated. To do this, the Euler equations are integrated numerically with a time-dependent technique. The integration is based on an high-resolution finite volume upwind method.Time scales are introduced and the flow at very short, short and large times is studied. Attention is focused on the behaviour of the numerical solution at large times, after the breakdown of symmetry and the onset of an oscillating solution have occurred. This solution is known to be periodic at Mach number between 0.5 and 0.6.At higher speed, however, a richer behaviour is observed. As the Mach number is increased from 0.6 to 0.98 the numerical solution undergoes two transitions. Through a first one the periodical, regular flow enters a chaotic, turbulent regime. Through the second transition the chaotic flow comes back to an almost stationary state. The flow in the chaotic and in the almost stationary regimes is investigated. A numerical conjecture for the behaviour of the solution at large times is advanced.

Two-Dimensional Simulation of EM Scattering from a Rotating Circular Dielectric Cylinder

2013 ◽  
Vol 284-287 ◽  
pp. 1007-1011 ◽  
Author(s):  
Ming Tsu Ho
Keyword(s):  
Maxwell Equations ◽  
Method Of Characteristics ◽  
Rotating Cylinder ◽  
Time Dependent ◽  
Dielectric Cylinder ◽  
Computational Results ◽  
Two Dimensional ◽  
Grid System ◽  
Em Scattering ◽  
Dimensional Simulation

The computational results of the scattered electromagnetic (EM) fields from a rotating circular dielectric cylinder were presented in this paper. The method of characteristics (MOC) was applied in a two dimensional modified O-type grid system to the solutions of the time-dependent Maxwell equations. To accurately model the rotating cylinder under the illumination of EM pulse, the passing center swing back grids (PCSBG) technique is employed in cooperation with MOC to overcome the difficulty of grid distortion due to the rotational movement of the cylinder. A number of electric and magnetic field distributions over the whole computational space were demonstrated in a side-by-side fashion for the comparison of the scattered EM fields from rotating circular dielectric cylinder with those from the stationary one. The numerical results exhibit feasible trends.

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