We present a class of arbitrarily high order fully explicit kinetic numerical methods in compressible fluid dynamics, both in time and space, which include the relaxation schemes by S. Jin and Z. Xin. These methods can use CFL number larger or equal to unity on regular Cartesian meshes for multi-dimensional case. These kinetic models depend on a small parameter that can be seen as a "Knudsen" number. The method is asymptotic preserving in this Knudsen number. Also, the computational costs of the method are of the same order of a fully explicit scheme. This work is the extension of Abgrall et al. (2022) \cite{Abgrall} to multi-dimensional systems. We have assessed our method on several problems for two dimensional scalar problems and Euler equations and the scheme has proven to be robust and to achieve the theoretically predicted high order of accuracy on smooth solutions.

翻译：我们提出了一类在可压缩流体动力学中时空均任意高阶的全显式动力学数值方法，该方法包含了Jin和Xin的松弛格式。这些方法可在规则笛卡尔网格上使用大于或等于1的CFL数处理多维问题。这些动力学模型依赖于一个可视为"克努森"数的小参数，该方法在该克努森数下具有渐进保持性。此外，其计算成本与全显式格式相当。该研究是Abgrall等人(2022)\cite{Abgrall}工作向多维系统的拓展。我们通过二维标量问题和欧拉方程的多个数值算例对方法进行了验证，结果表明该格式具有稳健性，并在光滑解上达到了理论预测的高阶精度。