Analysis and Numerical Computation of Conversation Laws by Gerald Warnecke

By Gerald Warnecke

The concern study application research and Numerics for Conservation legislation used to be funded by way of the German learn beginning Deutsche Forschungsgemeinschaft (DFG) for a interval of six years beginning in 1997. the variety of themes, represented within the current booklet, was once one of many energy of the learn application. examine teams of very diversified historical past, so much of that have been interacting for the 1st time, contributed to this interdisciplinary paintings. the current booklet includes contributions from interlinked engaging initiatives starting from the research of hyperbolic platforms of first order partial differential equations, the advance of more desirable numerical equipment for those equations to functions in astrophysics and engineering. It goals at conveying their effects accomplished within the application to readers outdoor in their personal specific box. The ebook features a huge variety of figures and a couple of colour plates. The reader can locate an up to date presentation of many present study issues within the box.

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By appropriate adaption, the computational time for approximating a solution can be reduced considerably. For the calculation of the inviscid fluxes the robust flux vector splitting scheme of Eberle is modified and extended [HAE99, HAK99, Ebe00]. With the heavy particle pressure ph , the electron pressure pe and the magnetic field B the magnetoacoustic speed is defined as c = γ(ph + pe ) B2 + . ρ µ0 ρ (8) One now defines a new reference speed s = αc2 + q 2 1 − 2α + α q2 c2 , (9) with q 2 = min(c2 , qn 2 ) .

Experimental [ABH98, Weg94]). I [A] m ˙ [g/s] 2000 2500 3000 3500 4000 4500 5000 0,8 0,8 0,8 0,8 0,8 0,8 0,8 F [N] num. 4,3 4,8 5,8 6,5 7,1 7,7 8,2 F [N] exp. 4,6 5,2 6,2 7,1 8,3 9,1 - Numerics for Magnetoplasmadynamic Propulsion 37 5 Summary For the numerical solution of the conservation equations for argon plasma flows in magnetoplasmadynamic self–field thrusters a new finite volume method for unstructured, adaptive meshes has been developed. It has been shown for the first time by numerical simulations of the MPD thruster DT2 that a strong depletion of density in front of the anode is caused by the pinch effect at high current settings.

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. 11. 8 g/s. ) Fig. 12. 8 g/s. ) 44 J. Heiermann, M. Auweter-Kurtz, C. : Numerische Simulation von MPD–Triebwerken und Vergleich mit durchzuf¨ uhrenden experimentellen Untersuchungen.

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