Related papers: Direct Flux Gradient Approximation to Close Moment…
Moment-closure approximations are an important tool in the analysis of the dynamics on both static and adaptive networks. Here, we provide a broad survey over different approximation schemes by applying each of them to the adaptive voter…
This work focuses on the numerical solution of hyperbolic conservations laws (possibly endowed with a source term) using the Active Flux method. This method is an extension of the finite volume method. Instead of solving a Riemann Problem,…
We use a macroscopic description of a system of relativistic particles based on adding a nonequilibrium tensor to the usual hydrodynamic variables. The nonequilibrium tensor is linked to relativistic kinetic theory through a nonlinear…
A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent…
Resolvent analysis of the linearized Navier-Stokes equations provides useful insight into the dynamics of transitional and turbulent flows and can provide a model for the dominant coherent structures within the flow, particularly for flows…
A method for finding reduced-order approximations of turbulent flow models is presented. The method preserves bounds on the production of turbulent energy in the sense of the $\curly{L}_2$ norm of perturbations from a notional laminar…
We consider linear, hyperbolic systems of balance laws in several space dimensions. They possess non-trivial steady states, which result from the equilibrium between derivatives of the unknowns in different directions, and the sources.…
We develop a general framework in the renormalization-group (RG) method for extracting a mesoscopic dynamics from an evolution equation by incorporating some excited (fast) modes as additional components to the invariant manifold spanned by…
The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations. In this work, we derive and investigate a neural…
We describe an approximate dynamic programming approach to compute lower bounds on the optimal value function for a discrete time, continuous space, infinite horizon setting. The approach iteratively constructs a family of lower bounding…
A detailed treatment of the classical Chapman-Enskog derivation of hydrodynamics is given in the framework of Grad's moment equations. Grad's systems are considered as the minimal kinetic models where the Chapman-Enskog method can be…
An exact closure for hydrodynamic variables is rigorously derived from the linear Boltzmann kinetic equation. Our approach, based on spectral theory, structural properties of eigenvectors and the theory of slow manifolds, allows us to…
In this paper, we present a regularization to 1D Grad's moment system to achieve global hyperbolicity. The regularization is based on the observation that the characteristic polynomial of the Jacobian of the flux in Grad's moment system is…
We present a new time-dependent Density Functional approach to study the relaxational dynamics of an assembly of interacting particles subject to thermal noise. Starting from the Langevin stochastic equations of motion for the velocities of…
In this work we propose a new approach for the numerical simulation of kinetic equations through Monte Carlo schemes. We introduce a new technique which permits to reduce the variance of particle methods through a matching with a set of…
The inclusion of kinetic effects into fluid models has been a long standing problem in magnetic reconnection and plasma physics. Generally the pressure tensor is reduced to a scalar which is an approximation used to aid in the modeling of…
Using the recently developed ``Maximum Entropy'' (or ``least biased'') distribution function to truncate the moment hierarchy arising from kinetic theory, we formulate a far-from-equilibrium macroscopic theory that provides the possibility…
We propose a novel framework for model-order reduction of hyperbolic differential equations. The approach combines a relaxation formulation of the hyperbolic equations with a discretization using shifted base functions. Model-order…
In this work, we propose a novel phase-field model for the simulation of two-phase flows that is accurate, conservative, bounded, and robust. The proposed model conserves the mass of each of the phases, and results in bounded transport of…
The description of a stellar system as a continuous fluid represents a convenient first approximation to stellar dynamics, and its derivation from the kinetic theory is standard. The challenge lies in providing adequate closure…