1,895 research outputs found
Aircraft Trajectory Planning Under Uncertainty by Light Propagation
AbstractIn the SESAR framework (Single European Sky ATM Research), the need to increase the air traffic capacity motivated the 4D (space + time) aircraft trajectory planning. This paper deals with an important Air Traffic Management (ATM) problem that consists in generating sets of 4D conflict-free trajectories (the tactical planning problem). The Light Propagation Algorithm (LPA) was introduced in [1] to deal with this problem. LPA has recently been shown to manage successfully a full day of traffic over the French airspace, removing all conflicts while satisfying ATM constraints.In this paper, we adapt the LPA to take into account uncertainties in trajectory prediction. We introduce and test a new algorithm called u/LPA (LPA under uncertainty) on the same day of traffic. For some situations, uncertainties reduce so much the search space that the standard algorithm cannot guarantee conflict free situation. As a consequence, one must include some time constraints for few trajectories (so-called RTA points: Real Time of Arrival constraints) in order to remove the remaining conflicts. The goal of RTA points is to impose an aircraft to be at a specified position at some given time. This results into a new optimization formulation of the tactical trajectory planning problem involving the decision as to where/when RTA points should be imposed. In order to solve this new problem, here we are content with a simple heuristic that yields encouraging results
Dusty gas with one fluid in smoothed particle hydrodynamics
In a companion paper we have shown how the equations describing gas and dust
as two fluids coupled by a drag term can be reformulated to describe the system
as a single fluid mixture. Here we present a numerical implementation of the
one-fluid dusty gas algorithm using Smoothed Particle Hydrodynamics (SPH). The
algorithm preserves the conservation properties of the SPH formalism. In
particular, the total gas and dust mass, momentum, angular momentum and energy
are all exactly conserved. Shock viscosity and conductivity terms are
generalised to handle the two-phase mixture accordingly. The algorithm is
benchmarked against a comprehensive suit of problems: dustybox, dustywave,
dustyshock and dustyoscill, each of them addressing different properties of the
method. We compare the performance of the one-fluid algorithm to the standard
two-fluid approach. The one-fluid algorithm is found to solve both of the
fundamental limitations of the two- fluid algorithm: it is no longer possible
to concentrate dust below the resolution of the gas (they have the same
resolution by definition), and the spatial resolution criterion h < csts,
required in two-fluid codes to avoid over-damping of kinetic energy, is
unnecessary. Implicit time stepping is straightforward. As a result, the
algorithm is up to ten billion times more efficient for 3D simulations of small
grains. Additional benefits include the use of half as many particles, a single
kernel and fewer SPH interpolations. The only limitation is that it does not
capture multi-streaming of dust in the limit of zero coupling, suggesting that
in this case a hybrid approach may be required.Comment: Accepted for publication in MNRAS. Numerical code and input files for
dustybox, wave and shock tests available from
http://users.monash.edu.au/~dprice/ndspmhd
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