Controlled time integration for the numerical simulation of meteor radar reflections

Abstract

We model meteoroids entering the Earth's atmosphere as objects surrounded by non-magnetized plasma, and consider ecient numerical simulation of radar reections from meteors in the time domain. Instead of the widely used nite dierence time domain method (FDTD), we use more generalized nite dierences by applying the discrete exterior calculus (DEC) and non-uniform leapfrog-style time discretization. The computational domain is presented by convex polyhedral elements. The convergence of the time integration is accelerated by the exact controllability method. The numerical experiments show that our code is eciently parallelized. The DEC approach is compared to the volume integral equation (VIE) method by numerical experiments. The result is that both methods are competitive in modelling non-magnetized plasma scattering. For demonstrating the simulation capabilities of the DEC approach, we present numerical experiments of radar reections and vary parameters in a wide range.

On shock waves and the role of hyperthermal chemistry in the early diffusion of overdense meteor trains

“…1998;William & Murad 2002;Vondrak et al 2008). The high temperature ablated and ionized meteor atoms and electrons, together with ionized and dissociated atmospheric atoms, explosively form a dynamically stable meteor trail cylindrical volume with an initial radius r 0 , which is approximated as a quasineutral plasma that can subsequently be observed by meteor radars (McKinley 1961;Baggaley & Fisher 1980;Räbinä et al 2016). Here, the term initial radius refers to the half-width of the initial (assumed) Gaussian distribution of the ions (or in the case of radio studies, electrons) that has "instantaneously" and adiabatically formed immediately after the passage of the meteoroid, where the volume density of the free electrons is a function of meteoroid mass, size and ionization coefficient (e.g.…”

Generalized wave propagation problems and discrete exterior calculus

“…We The described algorithms are implemented in C++ programming language, and the parallelization is applied with a message passing interface (MPI). Similarly to other nite dierence approaches, the particular implementation parallelizes almost perfectly, as our previous studies suggest [33].…”

Systematisation of Systems Solving Physics Boundary Value Problems

“…We have further developed the geometric approach and created a generic software system based on it. The system can be employed to solve hyperbolic application problems from classical and quantum physics [24], [29], [31], such as electromagnetic, elastic, and acoustic wave problems, the Schrödinger equation [13], or Gross-Pitayevskii equations [30], and so on. We explain the mathematical foundations of the software system in [22].…”

“…In our earlier papers, we have demonstrated the proposed approach with several numerical experiments. Such experiments include simulations with acoustic, elastodymanic, electromagnetic and quantum mechanic waves [28], [29], [30], [31]. For the extended accuracy, the mesh structures play an essential role [29].…”

“…It is namely possible to simulate the wave propagation in moving (and even deforming) spatial domains. In the papers [28], [29], [30] and [31], the spatial mesh generation together with the associated spatial finite difference approximation and time-stepping were considered as separate entities, without emphasizing the fact that the usual leap-frog time integration scheme for first order systems could also be derived from geometrical principles analogous to the spatial mesh generation which is based on the Delaunay-Voronoi duality. This chapter contains numerical experiments that demonstrate how the general model of the Minkowski space can be discretized.…”