Statistics – Computation
Scientific paper
Jan 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006aipc..813.1264m&link_type=abstract
SPACE TECH.& APPLIC.INT.FORUM-STAIF 2006: 10th Conf Thermophys Applic Microgravity; 23rd Symp Space Nucl Pwr & Propulsion; 4th C
Statistics
Computation
1
Magnetohydrodynamics And Electrohydrodynamics, Magnetohydrodynamic Waves, Navier-Stokes Equations, Spaceborne And Space Research Instruments, Apparatus, And Components
Scientific paper
The Navier-Stokes conservation equations may describe behavior for a viscous fluid flow or continuum processes that includes internal flows within a propulsion system, or a reactor, to external flows around spacecrafts, plasmas, and even galactical gas dynamics. Murad in earlier efforts defined a `Method of Potential Surfaces' that converts each steady-state conservation equation into either a set of Poisson equations for subsonic flow or inhomogeneous wave equations for supersonic flow. New developments extend this methodology by defining an integration factor as a function of the potentials themselves whose derivatives are fluid fluxes. Results imply that classical incompressible steady-state subsonic flow solutions can be transformed into viscous solutions by changing the definition of the potential. These equations are further broken-down to define nonlinear relationships for each of the steady-state velocity components as a function of the potential's derivatives. Moreover, the methodology can treat chemical reactions, turbulence and coupling with Maxwell's equations to resolve magnetohydrodynamic (MHD) propulsion challenges. Although closed-form solutions are desirable, any realistic solution requires iterative boundary conditions and the numerical burden may become very intensive making use of closed-form solutions somewhat impractical; however, analytical trends can provide significant insights to develop more efficient and faster computational algorithms to treat larger-scale problems and phenomenon.
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