Partial-moment minimum-entropy models for kinetic chemotaxis equations in one and two dimensions

TL;DR

This paper develops partial-moment minimum-entropy models for kinetic chemotaxis equations in 1D and 2D, introducing new closure relations and numerical schemes, and compares their accuracy to reference solutions.

Contribution

It introduces partial-moment minimum-entropy models with novel closure relations for kinetic chemotaxis equations in multiple dimensions.

Findings

Models accurately approximate kinetic solutions

Partial-moment methods outperform full moment methods in certain test cases

Numerical schemes are effective for complex chemotaxis scenarios

Abstract

The aim of this work is to investigate the application of partial moment approximations to kinetic chemotaxis equations in one and two spatial dimensions. Starting with a kinetic equation for the cell densities we apply a half-/quarter-moments method with different closure relations to derive macroscopic equations. Appropriate numerical schemes are presented as well as numerical results for several test cases. The resulting solutions are compared to kinetic reference solutions and solutions computed using a full moment method with a linear superposition strategy.