Large-time behavior of discrete velocity boltzmann equations

From Discrete Velocity Boltzmann Equations to Gas Dynamics before Shocks

This article is devoted to the proof of the hydrodynamic limit for a discrete velocity Boltzmann equation before appearance of shocks in the limit system.

Large-time Behavior of Discrete Kinetic Equations with Non-symmetric Interactions

We consider the initial-boundary value problem for general linear discrete velocity models appearing in kinetic theory. With time-independent inflow boundary data we prove the existence of a unique steady state and the exponential convergence in time towards the steady state. The proof is based on the construction of suitable multiplyers used in a weighted L 2-norm.

Investigation of a Discrete Velocity Monte Carlo Boltzmann Equation Solver

A New Consistent Discrete-velocity Model for the Boltzmann Equation

This paper discusses the convergence of a new discrete-velocity model to the Boltz-mann equation. First the consistency of the collision integral approximation is proved. Based on this we prove the convergence of solutions for a modiied model to DiPerna-Lions solutions of the Boltz-mann equation. As a test numerical example, the solutions to the discrete problems are compared to the exact solut...

Solving Large-Scale Discrete-Time Algebraic Riccati Equations by Doubling

We consider the solution of large-scale discrete-time algebraic Riccati equations with numerically low-ranked solutions. The structure-preserving doubling algorithm will be adapted, with the iterates for A not explicitly computed but in the recursive form Ak = A 2 k−1 − D (1) k S −1 k [D (2) k ] >, where D (1) k and D (2) k are low-ranked with S −1 k being small in dimension. With n being the d...