Please cite this article in press as: R. Ahlfeld et al., SAMBA: Sparse approximation of moment-based arbitrary polynomial chaos, J. Comput. Phys. (2016), http://dx.doi.org/10.1016/j. jcp.2016.05.014 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
SAMBA
AbstractA new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability.The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrix is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of
Challenging space missions include those at very low altitudes, where the atmosphere is source of aerodynamic drag on the spacecraft. To extend such missions lifetime, an efficient propulsion system is required. One solution is Atmosphere-Breathing Electric Propulsion (ABEP). It collects atmospheric particles to be used as propellant for an electric thruster. The system would minimize the requirement of limited propellant availability and can also be applied to any planet with atmosphere, enabling new mission at low altitude ranges for longer times. Challenging is also the presence of reactive chemical species, such as atomic oxygen in Earth orbit. Such species cause erosion of (not only) propulsion system components, i.e. acceleration grids, electrodes, and discharge channels of conventional EP systems. IRS is developing within the DISCOVERER project, an intake and a thruster for an ABEP system. The paper describes the design and implementation of the RF helicon-based inductive plasma thruster (IPT). This
Renewed interest in Very Low Earth Orbits (VLEO)-i.e. altitudes below 450 km-has led to an increased demand for accurate environment characterisation and aerodynamic force prediction. While the former requires knowledge of the mechanisms that drive density variations in the thermosphere, the latter also depends on the interactions between the gas-particles in the residual atmosphere and the surfaces exposed to the flow. The determination of the aerodynamic coefficients is hindered by the numerous uncertainties that characterise the physical processes occurring at the exposed surfaces. Several models have been produced over the last 60 years with the intent of combining accuracy with relatively simple implementations. In this paper the most popular models have been selected and reviewed using as discriminating factors relevance with regards to orbital aerodynamics applications and theoretical agreement with gas-beam experimental data. More sophisticated models were neglected, since their increased accuracy is generally accompanied by a substantial increase in computation times which is likely to be unsuitable for most space engineering applications. For the sake of clarity, a distinction was introduced between physical and scattering kernel theory based gas-surface interaction models. The physical model category comprises the Hard Cube model, the Soft Cube model and the Washboard model, while the scattering kernel family consists of the Maxwell model, the Nocilla-Hurlbut-Sherman model and the Cercignani-Lampis-Lord model. Limits and assets of each model have been discussed with regards to the context of this paper. Wherever possible, comments have been provided to help the reader to identify possible future challenges for gas-surface interaction science with regards to orbital aerodynamic applications.
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