Lagrangian fluid approach for the modeling of peculiarities of the interstellar dust distribution in the astrospheres/heliosphere

Abstract

Interstellar dust penetrates into the heliosphere/astrosphere due to relative motion of the Sun and the local interstellar medium (LISM). Inside the heliosphere/astrosphere and at the heliospheric boundaries, where the solar/stellar wind interacts with LISM, distribution of the interstellar dust is modified due to an action of electromagnetic forces, the solar gravitation and radiation pressure. In this paper we show that the distribution of the interstellar dust particles in the heliosphere has peculiarities of high density layers. In order to understand the nature of the peculiarities Osiptsov’s Lagrangian method has been employed and developed for the case when the force acting on the particles has discontinuity as it is for the electromagnetic force at the helioshperic current sheet. In the result of the modeling we demonstrate existence of multiple layers of high density of the interstellar dust located at 0.03 - 10 AU north and south with respect to the heliospheric current sheet.

Effects of dispersion of the dust velocity in the LISM on the interstellar dust distribution inside the heliosphere

“…In this paper we demonstrated that the singularities of the ISD density in the heliosphere, discovered using the Lagrangian approach in Mishchenko et al (2020), can also be found by the Monte-Carlo simulations. This requires super-small computational cells.…”

“…It was shown by Mishchenko et al (2020) that in the case of zero dispersion the ISD trajectories form caustics at which the number density of ISD is infinite. A caustic is an envelope of the ISD trajectories.…”

“…and for studying local effects near density peculiarities -of 10 −6 a.u. Mishchenko et al (2020) used the assumption that the ISD particles have identical velocities in the LISM. Due to the fact that the ISD particles have nonzero electric charge, they interact with the interstellar magnetic field.…”

Robust interpolation for dispersed gas-droplet flows using statistical learning with the Fully Lagrangian Approach

“…(4), the FLA is still approximately 20 times more efficient than box-counting methods for twodimensional simulations [4,10]. Another analysis found that a box-counting approach for number density requires ∼ 10 6 trajectories to be computed, whereas the FLA only needs ∼ 10 3 trajectories to obtain the same level of detail, however this is offset by the additional expense of calculating the Jacobian along trajectories which entails a fortyfold increase in computational cost for three-dimensional simulations, and also by linear interpolation of the trajectory number density data onto the Eulerian grid which takes almost as long as the numerical integration along trajectories [14]. Therefore, despite providing a 10 3 saving on the number of trajectories computed when compared against the box-counting approach, the overall efficiency improvement of the FLA for calculation of the Eulerian number density field is reduced to around tenfold.…”

“…Previous works have addressed this by using the fact that the sign of the Jacobian determinant J changes every time a droplet crosses the trajectory of another droplet, effectively providing a means of keeping track of which layer of the droplet field a given trajectory is in. Since each layer of the droplet field is single-valued with non-intersecting trajectories, interpolation can be used to calculate the Eulerian number density within each individual layer, and then due to the number density field being additive the contributions from each layer at a given point are summed together to obtain the total number density [11,14,17]. This requires that droplets are indexed in such a way that a distinction is made every time a fold is crossed, with the most straightforward means of doing this being to keep count of the number of times this occurs for each droplet, then all droplets with the same count index form one layer of the droplet field [17].…”