arXiv subjects

Cory Hauck

Publications and source records attributed to Cory Hauck.

21 records · Page 2Linked to original sources

arXiv2016

A new class of high order semi-Lagrangian schemes for rarefied gas dynamics

In this paper we genealize the fast semi-Lagrangian scheme developed in [J. Comput. Phys., Vol. 255, 2013, pp 680-698] to the case of high order reconstructions of the distribution function. The original first order accurate semi-Lagrangian scheme is supplemented with polynomial reconstructions of the distribution function and of the collisional operator leading to an effective high order accurate numerical scheme for all regimes, from extremely rarefied gas to highly collisional siuation. The main idea relies on updating at each time step the extreme points of the distribution function for each velocity of the lattice instead of updating the solution in the cell centers, these extremes points being located at different positions for any fixed velocity of the lattice. The result is a class of scheme which permits to preserve the structure of the solution over very long times compared to existing schemes from the literature. We propose a proof of concept of this new approach along with numerical tests and comparisons with classical numerical methods.

math.NA↗

arXiv2012

Sparse Dynamics for Partial Differential Equations

We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the coefficients of the basis approximation. By reducing or compressing the information needed to represent the solution at every step, only the essential dynamics are represented. In many cases, there are natural bases derived from the differential equations which promote sparsity. We find that our method successfully reduces the dynamics of convection equations, diffusion equations, weak shocks, and vorticity equations with high frequency source terms.

math.NA↗

arXiv2012

On Cellular Automata Models of Traffic Flow with Look-Ahead Potential

We study the statistical properties of a cellular automata model of traffic flow with the look-ahead potential. The model defines stochastic rules for the movement of cars on a lattice. We analyze the underlying statistical assumptions needed for the derivation of the coarse-grained model and demonstrate that it is possible to relax some of them to obtain an improved coarse-grained ODE model. We also demonstrate that spatial correlations play a crucial role in the presence of the look-ahead potential and propose a simple empirical correction to account for the spatial dependence between neighboring cells.

math.PR↗