Characteristic Based Methods for the Time-Domain Maxwell Equations

Shang, J. S.

doi:10.21236/ada272973

Cited by 10 publications

(13 citation statements)

References 20 publications

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“…The time derivative of the polarization vector on the right hand sides of Eqs. (15)- (16) and (20)-(22) can be omitted in case of simulation of steady-state EMHD flows, because these terms vanish at the converged final steady state.…”

Section: Axisymmetric Emhd Flowsmentioning

confidence: 99%

“…Usually the no-slip conditions and jump conditions are imposed at the solid walls, while non-reflective (for incoming waves) or characteristic (for outgoing waves) boundary conditions are used at the open boundaries. Shankar et al (1989) and Shang (1991) have performed numerical simulations of electromagnetic fields with fluid flow, but they did not include the effects of fluid polarization and magnetization.…”

Section: Introductionmentioning

confidence: 99%

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Non-Reflective Boundary Conditions for a Consistent Model of Axisymmetric Electro-Magneto-Hydrodynamic Flows

Ko¹,

Dulikravich²

2000

International Journal of Nonlinear Sciences and Numerical Simulation

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In this paper, the non-reflective boundary conditions for the axisymmetric electro-magneto-hydrodynamic (EMHD) flows have been derived. The electro-magneto-hydrodynamics (EMHD) deals with the motion of electrically conducting incompressible fluids under the combined influence of externally applied and internally generated electric and magnetic fields. A consistent axisymmetric EMHD flow model with linear constitutive relations and artificial compressibility was expressed in cylindrical coordinates. After some simplifications, the resulting EMHD system comprised of modified Maxwell equations for the electro-magnetic fields and modified Navier-Stokes equations for the flow-field, was transformed to a characteristic form, and the non-reflective boundary conditions were derived. The results show the strong mutual interactions between the axisymmetric flow-field and the electro-magnetic fields. The limiting cases, including the conventional axisymmetric flowfield model and the electro-magnetic field model in vacuum, are recoverable from these results. Nomenclature Β = μ 0 (Η + Μ) magnetic flux density, kg A" 1 s" 2 Ε electric field intensity, kg m s" 3 A" 1 S specific heat at constant pressure, E = E + vxB electromotive intensity, kg m s" 3 A" 1 K"' m 2 s" 2 f mechanical body force per unit mass, D = ε 0 Ε + Ρ electric displacement vector, Asm" 2 m S -J D d " .,,... Η magnetic field intensity, A m" 1 -= -+ ν · V

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Section: Axisymmetric Emhd Flowsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Non-Reflective Boundary Conditions for a Consistent Model of Axisymmetric Electro-Magneto-Hydrodynamic Flows

Ko¹,

Dulikravich²

2000

International Journal of Nonlinear Sciences and Numerical Simulation

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“…8 The undesirable reflection from numerical boundaries can be eliminated by the characteristic formulation. 13 " 15 The fundamental idea of this approach for solving a hyperbolic system of equations is derived from eigenvalue and eigenvector analysis. 13 ' 25 From the field-action approach, differential geometry yields a domain of influence partitioned by characteristics.…”

Section: Boundary Conditionsmentioning

confidence: 99%

“…13 " 15 The fundamental idea of this approach for solving a hyperbolic system of equations is derived from eigenvalue and eigenvector analysis. 13 ' 25 From the field-action approach, differential geometry yields a domain of influence partitioned by characteristics. 29 At present the characteristic formulation has an inherent limitation in that the coefficient matrices of the governing equations can be diagonalized only in one dimension at a time.…”

Section: Boundary Conditionsmentioning

confidence: 99%

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Scattered electromagnetic field of a re-entry vehicle

Shang

Gaitonde

1995

Journal of Spacecraft and Rockets

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Scattered electromagnetic fields around the X24C lifting body illuminated by both transverse electric and transverse magnetic incident plane waves are simulated. The refractive and diffractive phenomena are studied in the resonant and the optical regimes. The numerical solutions are generated by solving the three-dimensional Maxwell equations in the time domain using an upwind-biased finite-volume algorithm. The numerical results are third order accurate in space and second order accurate in time. The simulations are validated on simpler shapes, including a cylinder and a sphere, for which the solutions are well known. The scattered field is then described for the re-entry vehicle in the resonant and optical regimes. The numerical results demonstrate that accurate radar cross sections can be obtained by implementation of consistent boundary conditions developed for a perfectly conducting scatterer. Nomenclature B = magnetic flux density, Wb/m 2 D = electric displacement, C/m 2 E = electric field intensity, V/m 2 / = wave frequency, s" 1 H = magnetic flux intensity, A/m i, 7, k = index of discretized volume J = electric current density, A/m 2 n = outer normal of a surface R = numerical residual r, 0, $ = spherical coordinates t -time, s U = dependent variables V = elementary cell volume, m 3 € = electric permittivity, F/m X = wavelength, m 41 = magnetic permeability, H/m §» *?» £ = general curvilinear coordinates a) = angular frequency of wave, s" 1 Subscripts ch = characteristic time required for wave to traverse one body length = incident field property Superscripts +, -= flux vector associated with positive and negative eigenvalue

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A scalable HPF implementation of a finite‐volume computational electromagnetics application on a CRAY T3E parallel system

Pan

Shang

Guo

2003

Concurrency and Computation

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SUMMARYThe time-dependent Maxwell equations are one of the most important approaches to describing dynamic or wide-band frequency electromagnetic phenomena. A sequential finite-volume, characteristic-based procedure for solving the time-dependent, three-dimensional Maxwell equations has been successfully implemented in Fortran before. Due to its need for a large memory space and high demand on CPU time, it is impossible to test the code for a large array. Hence, it is essential to implement the code on a parallel computing system. In this paper, we discuss an efficient and scalable parallelization of the sequential Fortran time-dependent Maxwell equations solver using High Performance Fortran (HPF). The background to the project, the theory behind the efficiency being achieved, the parallelization methodologies employed and the experimental results obtained on the Cray T3E massively parallel computing system will be described in detail. Experimental runs show that the execution time is reduced drastically through parallel computing. The code is scalable up to 98 processors on the Cray T3E and has a performance similar to that of an MPI implementation. Based on the experimentation carried out in this research, we believe that a high-level parallel programming language such as HPF is a fast, viable and economical approach to parallelizing many existing sequential codes which exhibit a lot of parallelism.

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Characteristic Based Methods for the Time-Domain Maxwell Equations

Cited by 10 publications

References 20 publications

Non-Reflective Boundary Conditions for a Consistent Model of Axisymmetric Electro-Magneto-Hydrodynamic Flows

Non-Reflective Boundary Conditions for a Consistent Model of Axisymmetric Electro-Magneto-Hydrodynamic Flows

Scattered electromagnetic field of a re-entry vehicle

A scalable HPF implementation of a finite‐volume computational electromagnetics application on a CRAY T3E parallel system

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