Related papers: Moment Methods for the 3D Radiative Transfer Equat…
In this paper, we propose a moment method to numerically solve the Vlasov equations using the framework of the NRxx method developed in [6, 8, 7] for the Boltzmann equation. Due to the same convection term of the Boltzmann equation and the…
A solution is proposed to a longstanding open problem in kinetic theory, namely, given any set of realizable velocity moments up to order 2n, a closure for the moment of order 2n+1 is constructed for which the moment system found from the…
In this paper we introduce simplified, combinatorially exact formulas that arise in the vortex interaction model found in (Nagem, et al., SIAM J. Appl. Dyn. Syst. 2009). These combinatorial formulas allow for the efficient implementation…
In this introductory work I will present the Finite Difference method for hyperbolic equations, focusing on a method which has second order precision both in time and space (the so-called staggered leapfrog method) and applying it to the…
Many physical systems are described by probability distributions that evolve in both time and space. Modeling these systems is often challenging to due large state space and analytically intractable or computationally expensive dynamics. To…
The unique properties of anisotropic and composite particles are increasingly being leveraged in modern particulate products. However, tailored synthesis of particles characterized by multi-dimensional dispersed properties remains in its…
Molecular structure elucidation is a fundamental step in understanding chemical phenomena, with applications in identifying molecules in natural products, lab syntheses, forensic samples, and the interstellar medium. We consider the task of…
The ability to directly measure the momentum distribution of quantum gases is both unique to these systems and pivotal in extracting many other important observables. Here we use Raman transitions to measure the momentum distribution of a…
We combine the recent relaxation approach with multiderivative Runge-Kutta methods to preserve conservation or dissipation of entropy functionals for ordinary and partial differential equations. Relaxation methods are minor modifications of…
We investigate the application of the method of moments approach for the one-dimensional population balance equation. We consider different types of moment closures, namely polynomial (P_N) closures, maximum entropy (M_N) closures and the…
We present the new Guided Moments ($\texttt{GM}$) formalism for neutrino modeling in astrophysical scenarios like core-collapse supernovae and neutron star mergers. The truncated moments approximation ($\texttt{M1}$) and Monte-Carlo…
In the present work, an approach to the moment closure problem on the basis of orthogonal polynomials derived from Gram matrices is proposed. Its properties are studied in the context of the moment closure problem arising in gas kinetic…
Shallow flow models are used for a large number of applications including weather forecasting, open channel hydraulics and simulation-based natural hazard assessment. In these applications the shallowness of the process motivates…
An interesting and satisfactory fluid model has been proposed in literature for the the description of relativistic electron beams. It was obtained with 14 independent variables by imposing the entropy principle and the relativity…
We derive the equations of motion of relativistic, non-resistive, second-order dissipative magnetohydrodynamics from the Boltzmann equation using the method of moments. We assume the fluid to be composed of a single type of point-like…
The Boltzmann equation for $d$-dimensional inelastic Maxwell models is considered to determine the collisional moments of second, third and fourth degree in a granular binary mixture. These collisional moments are exactly evaluated in terms…
We study the transition from hydrodynamic to collisionless behavior in collective modes of ultracold trapped Fermi gases. To that end, we solve the Boltzmann equation for the trapped Fermi gas via the moments method. We showed previously…
A new kinetic model is proposed where the equilibrium distribution with bounded support has a range of velocities about two average velocities in 1D. In 2D, the equilibrium distribution function has a range of velocities about four average…
Melting and solidification processes are often affected by natural convection of the liquid, posing a multi-physics problem involving fluid flow, convective and diffusive heat transfer, and phase-change reactions. Enthalpy methods formulate…
A new method for the formal solution of the 2D radiative transfer equation in axial symmetry in the presence of arbitrary velocity fields is presented. The combination of long and short characteristics methods is used to solve the radiative…