C. Frueh¹

CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.2, pp. 171-201, 2016, DOI:10.3970/cmes.2016.111.171

Abstract In recent years, probabilistic tracking methods have been becoming increasingly popular for solving the multi-target tracking problem in Space Situational Awareness (SSA). Bayesian frameworks have been used to describe the objects' of interest states and cardinality as point processes. The inputs of the Bayesian framework filters are a probabilistic description of the scene at hand, the probability of clutter during the observation, the probability of detection of the objects, the probability of object survival and birth rates, and in the state update, the measurement uncertainty and process noise for the propagation. However, in the filter… More >

Xiaoli Bai¹, John L. Junkins²

CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.2, pp. 129-146, 2016, DOI:10.3970/cmes.2016.111.129

Abstract This paper presents Modified Chebyshev-Picard Iteration (MCPI) methods for long-term integration of the coupled orbit and attitude dynamics. Although most orbit predictions for operational satellites have assumed that the attitude dynamics is decoupled from the orbit dynamics, the fully coupled dynamics is required for the solutions of uncontrolled space debris and space objects with high area-to-mass ratio, for which cross sectional area is constantly changing leading to significant change on the solar radiation pressure and atmospheric drag. MCPI is a set of methods for solution of initial value problems and boundary value problems. The methods… More >

Maruthi R. Akella¹, Sofokli Cakalli²

CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.2, pp. 119-127, 2016, DOI:10.3970/cmes.2016.111.119

Abstract The planar motion of a particle within an arbitrary potential field is considered. The particle is additionally subject to an external force wherein the applied thrust-acceleration is constrained to remain normal to the velocity vector. The system is thus non-conservative but since the thrust force is non-working, the total energy is a conserved quantity. Under this setting, a major result of fundamental importance is established in this paper: that the flight direction angle (more precisely, the sine of the angle between the position and velocity vectors) is shown to always satisfy a linear first-order differential… More >

V. Vittaldev¹, R. P. Russell²

CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.1, pp. 83-117, 2016, DOI:10.3970/cmes.2016.111.083

Abstract Monte Carlo simulations are an accurate but computationally expensive procedure for approximating the resultant non-Gaussian probability density function (PDF) after propagation of an initial Gaussian PDF through a nonlinear function. Univariate splitting libraries for Gaussian Mixture Models (GMMs) exist with up to five elements in the literature. The number of splits are extended in the present work by generating three homoscedastic univariate splitting libraries with up to 39 elements. Mulitvariate GMMs are typically handled with splits along a single direction. Instead, we generate a regular multidirectional grid over the initial multivariate Gaussian distribution by recursively… More >

J.L. Read¹, A. Bani Younes², J.L. Junkins³

CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.1, pp. 65-81, 2016, DOI:10.3970/cmes.2016.111.065

Abstract This paper focuses on propagating perturbed two-body motion using orbital elements combined with a novel integration technique. While previous studies show that Modified Chebyshev Picard Iteration (MCPI) is a powerful tool used to propagate position and velocity, the present results show that using orbital elements to propagate the state vector reduces the number of MCPI iterations and nodes required, which is especially useful for reducing the computation time when including computationally-intensive calculations such as Spherical Harmonic gravity, and it also converges for > 5.5x as many revolutions using a single segment when compared with cartesian… More >

B. Macomber¹, A. B. Probe¹, R. Woollands¹, J. Read¹, J. L. Junkins¹

CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.1, pp. 29-64, 2016, DOI:10.3970/cmes.2016.111.029

Abstract Modified Chebyshev Picard Iteration is an iterative numerical method for solving linear or non-linear ordinary differential equations. In a serial computational environment the method has been shown to compete with, or outperform, current state of practice numerical integrators. This paper presents several improvements to the basic method, designed to further increase the computational efficiency of solving the equations of perturbed orbit propagation. More >

Darin Koblick^1,2,3, Shujing Xu⁴, Joshua Fogel⁵, Praveen Shankar¹

CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.1, pp. 1-27, 2016, DOI:10.3970/cmes.2016.111.001

Abstract The Modified Picard-Chebyshev Method (MPCM) is implemented as an orbit propagation solver for a numerical optimization method that determines minimum time orbit transfer trajectory of a satellite using a series of multiple impulses at intermediate waypoints. The waypoints correspond to instantaneous impulses that are determined using a nonlinear constrained optimization routine, SNOPT with numerical force models for both Two-Body and J2 perturbations. It is found that using the MPCM increases run-time performance of the discretized lowthrust optimization method when compared to other sequential numerical solvers, such as Adams-Bashforth-Moulton and Gauss-Jackson 8th order methods. More >

S. Fashu^{1 *}, M.Tozvireva¹, L.Mudzingwa¹, R.Khan², A. Mukuya¹

FDMP-Fluid Dynamics & Materials Processing, Vol.12, No.4, pp. 173-192, 2016, DOI:10.3970/fdmp.2016.012.173

Abstract This paper outlines the findings in the comparison of the influence of mechanical and electromagnetic stirring on ingot long term purity and uniformity during Ohno Continuous Casting. The magnitude of the average optimum velocity flow field and stirring parameters required to effectively purify aluminum ingots using mechanical stirring of the melt was determined and analyzed. Basing on the determined optimum mechanical flow field, electromagnetic parameters producing almost the same flow field near the interface were obtained through careful adjustments of parameters. Optimum parameters of the mechanical and electromagnetic stirring were obtained by numerically solving the… More >

Anupam Bhandari¹

FDMP-Fluid Dynamics & Materials Processing, Vol.12, No.4, pp. 155-171, 2016, DOI:10.3970/fdmp.2016.012.155

Abstract The present problem addresses a thermally driven two-dimensional, buoyant flow in a vessel with the application of magnetic field directed in the radial and tangential direction. In the present study, a trough filled with ferrofluid is heated along the center strip by an applied heat flux. Thereby the convection pattern along with the heat distribution is observed. The half of the trough dynamics is calculated with the symmetric plane in the center. On the surface of the bowl, penalty function is applied to enforce the no-slip boundary condition. This problem is then modelled and the More >

Saber Hamimid¹, Messaoud Guellal²

FDMP-Fluid Dynamics & Materials Processing, Vol.12, No.4, pp. 137-153, 2016, DOI:10.32604/fdmp.2016.012.137

Abstract The numerical study of combined thermo-magnetic convection and surface radiation is presented in this paper and computations are performed for a paramagnetic fluid filled square cavity whose four walls have the same emissivity, placed in a micro-gravity environment (g ≈0), and subjected to various strong non-uniform magnetic field gradients. The vertical walls were isothermal, and the horizontal walls were adiabatic. Finite volume method based on the concepts of staggered grid and SIMPLER algorithm has been applied, and the view factors were determined by analytical formula. Representative results, illustrating the effect of magnetic field strength on More >