# Some preliminary results on a high order asymptotic preserving computationally explicit kinetic scheme

## TL;DR

This paper presents a method to construct high-order, explicit kinetic schemes that are asymptotic preserving and stable for discontinuities, maintaining accuracy for smooth solutions with computational costs similar to explicit schemes.

## Contribution

It introduces a novel high-order kinetic scheme on regular meshes that is asymptotic preserving, explicit, and includes a nonlinear stability method for discontinuities.

## Key findings

- Scheme can be arbitrarily high order in space and time
- Runs at least CFL one, with explicit computational costs
- Stable for problems with discontinuities without losing accuracy

## Abstract

In this short paper, we intend to describe one way to construct arbitrarily high order kinetic schemes on regular meshes. The method can be arbitrarily high order in space and time, run at least CFL one, is asymptotic preserving and computationally explicit, i.e., the computational costs are of the same order of a fully explicit scheme. We also introduce a non linear stability method that enables to simulate problems with discontinuities, and it does not kill the accuracy for smooth regular solutions.