Abgrall Rémi, Nassajian Mojarrad Fatemeh
Institute of Mathematics, University of Zürich, Winterthurerstrasse 190, CH 8057 Zürich, Switzerland.
Commun Appl Math Comput. 2024;6(2):963-991. doi: 10.1007/s42967-023-00274-w. Epub 2023 Aug 1.
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 Jin and Xin. These methods can use the CFL number larger or equal to unity on regular Cartesian meshes for the 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) [3] 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.
我们提出了一类在可压缩流体动力学中时空均为任意高阶的完全显式动力学数值方法，其中包括金和辛的松弛格式。对于多维情况，这些方法在规则笛卡尔网格上可以使用大于或等于1的CFL数。这些动力学模型依赖于一个小参数，该参数可被视为一个“克努森”数。该方法在这个克努森数下是渐近保持的。此外，该方法的计算成本与完全显式格式处于同一量级。这项工作是阿布格罗尔等人（2022年）[3]对多维系统的扩展。我们在二维标量问题和欧拉方程的几个问题上评估了我们的方法，该格式已被证明是稳健的，并且在光滑解上达到了理论预测的高阶精度。
