The Discontinuous Galerkin method for partially ionized gas compressible flows under the influence of electromagnetic fields

Panourgias, Konstantinos; Ekaterinaris, John A.

doi:10.2514/6.2014-1428

Cited by 1 publication

(3 citation statements)

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“…The numerical errors in the divergence of the electric field were found much larger when divergence‐free vector bases are used only for the magnetic field instead of the PHM equations. These errors were of the order of 10 −3 even for simpler case with constant in time charge distribution, the P 3 approximation and the 64×64 mesh and are expected to interfere with the physics of plasma flows …”

Section: Numerical Resultsmentioning

confidence: 99%

“…These errors were of the order of 10 −3 even for simpler case with constant in time charge distribution, the P 3 approximation and the 64 × 64 mesh and are expected to interfere with the physics of plasma flows. 39 For the most difficult case, with moving time varying charge distribution, the errors (∇ · E) error obtained with the PHM equations (see Table 6 still diminishes with rate k (e.g. linearly for P 1 expansion) and for higher order of expansions are still at very low level.…”

Section: Plane Wave Propagationmentioning

confidence: 90%

“…In the presence of charge, the divergence‐free bases cannot guarantee preservation of the Gauss constraint for the electric field ∇· E = ρ / ϵ at the numerical level. As a result, for simulation of plasma, these numerical errors can contaminate the numerical solution beyond acceptable limits. Therefore, a technique that extends the system of the Maxwell equations to obtain the so‐called perfectly hyperbolic Maxwell (PHM) equations is used to ensure the preservation at the numerical level of both Gauss constraints.…”

Section: Introductionmentioning

confidence: 99%

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A p‐adaptive method for electromagnetic wave propagation

Panourgias

Ekaterinaris²

2017

Numerical Meth Engineering

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Summary The discontinuous Galerkin FEM is used for the numerical solution of the three‐dimensional Maxwell equations. Control of errors in the numerical level for the divergence‐free constraint of the magnetic field can be obtained through the use of divergence‐free vector bases. In this work, the so‐called perfectly hyperbolic formulation of the Maxwell equations is used to retain both divergence‐free magnetic field and in the presence of charges to satisfy the Gauss constraint for the electric field at the numerical level. For both approaches, it is found that higher‐order approximations have favorable effect on the preservation of the divergence constraints and that the perfectly hyperbolic formulations retains these errors to a lower level. It is shown that high‐order accuracy in space and time is achieved in unstructured meshes using implicit time marching. For nonuniform meshes, local resolution refinement is used using p‐type adaptivity to ensure accurate electromagnetic wave propagation. Thus, the potential of the method to reach the required higher resolution in anisotropic meshes and obtain accurate electromagnetic wave propagation with reduced computational effort is demonstrated.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Plane Wave Propagationmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

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