Analysis and Numerical Computation of Conversation Laws by Gerald Warnecke

By Gerald Warnecke

The concern examine application research and Numerics for Conservation legislation was once funded via the German learn origin Deutsche Forschungsgemeinschaft (DFG) for a interval of six years beginning in 1997. the variety of subject matters, represented within the current ebook, used to be one of many energy of the examine software. examine teams of very diverse history, so much of that have been interacting for the 1st time, contributed to this interdisciplinary paintings. the current booklet includes contributions from interlinked partaking initiatives starting from the research of hyperbolic structures of first order partial differential equations, the advance of better numerical tools for those equations to purposes in astrophysics and engineering. It goals at conveying their effects accomplished within the software to readers outdoors in their personal specific box. The e-book encompasses a huge variety of figures and a few colour plates. The reader can locate an updated presentation of many present examine themes within the box.

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To the mean free 52 H. e. n(a), v f (a, v)d3 v = 0 . (30) lR3 In this paper we are interested in the case of small Knudsen number ǫ2 , with the curvature of ∂Ω being large compared to ǫ. As was analyzed in [15], the flow may be decomposed into a thin kinetic boundary layer (with a thickness ∼ ǫ2 ) which is appropriately described by a low order Hilbert expansion (and thus by the linearized Boltzmann equation), a viscous boundary layer (with thickness ∼ ǫ), and an outer domain well described by the Euler equations.

40 J. Heiermann, M. Auweter-Kurtz, C. Sleziona Anode Insulator • m Cathode Fig. 5. 8 g/s. (250 A between 2 isolines) Anode Insulator • m Cathode Fig. 6. 8 g/s. (250 A between 2 isolines) Numerics for Magnetoplasmadynamic Propulsion 41 Fig. 7. 8 g/s. ) Fig. 8. 8 g/s. ) J. Heiermann, M. Auweter-Kurtz, C. Sleziona Insulator 42 Anode Insulator • m Cathode Insulator Fig. 9. 8 g/s. (250 A between 2 isolines) Anode Insulator • m Cathode Fig. 10. 8 g/s. (250 A between 2 isolines) Numerics for Magnetoplasmadynamic Propulsion 43 Fig.

2 shows the thruster HAT being fired in the laboratory. A typical discretization of the computational domain is shown in Fig. 3. In the nozzle area, the mesh is highly refined for a good resolution of the boundary layers and for capturing the oblique shock (Fig. 4) which is also visible in the experiment (Fig. 2). The current distributions at high currents of 4000 A (Fig. 5) and 5000 A (Fig. 6) show that the electric arc starts to constrict downstream of the nozzle throat because of the pinch effect.

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