This paper extends our recent results on multi-dimensional discrete-velocity models to the numerical level. By adopting an operator splitting scheme and introducing a suitable discrete Lyapunov function, we derive numerical control laws that ensure the corresponding numerical solutions decay exponentially in time. To handle the stiff source term, we also use an implicit scheme for the collision part and prove the stability of the resulting schemes. The theoretical results are validated through three numerical simulations for the two-dimensional coplanar model.

翻译：本文将我们近期在多维离散速度模型方面的研究成果拓展至数值层面。通过采用算子分裂格式并引入合适的离散Lyapunov函数，我们推导出能保证相应数值解随时间指数衰减的数值控制律。为处理刚性源项，我们在碰撞部分采用隐式格式，并证明了所得格式的稳定性。通过针对二维共面模型的三次数值模拟，验证了理论结果的有效性。