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.

翻译：在这份简短的文件中,我们打算描述一种在常规贝壳上建立任意高顺序运动计划的方法。 这种方法在空间和时间上可以任意高顺序,至少运行一个CFL1,在空间和时间上可以任意高顺序。 这种方法在保存和计算上是模糊的,也就是说,计算成本与完全明确的计划相同。 我们还引入了一种非线性稳定方法,可以模拟不连续问题,而且不会破坏正常解决方案的准确性。