When astrophysical jets were discovered one hundred years ago, the field of numerical simulations did not yet exit. Since the arrival of programmable computers though, numerical simulations have increasingly become an indispensable tool for dealing with “tough nut” problems which involve complex dynamic and non-linear phenomena. Astrophysical jets are an ideal example of such a tough nut, where multi-scale plasma physics, radiative and non-thermal processes, turbulence and relativity combine to present a formidable challenge to researchers.

Highlighting major achievements obtained through numerical simulations concerning the validity and nature of the Blandford–Znajek mechanism, the launching, collimation, acceleration and stability of jets, their interaction with the surrounding plasma, jet-galaxy feedback mechanisms etc., we trace how the field developed from its first tentative steps into the age of “maturity”. We also give a brief and personal outlook on how the field may evolve in the foreseeable future.

一百年前发现天体物理射流时，数值模拟领域尚未出现。自从可编程计算机问世以来，数值模拟已越来越成为解决涉及复杂的动态和非线性现象的“棘手问题”的必不可少的工具。天体物理射流是这种强硬螺母的理想示例，多尺度等离子体物理学，辐射和非热过程，湍流和相对论相结合，对研究人员提出了严峻的挑战。

重点介绍了通过数值模拟获得的主要成就，这些数值模拟涉及Blandford-Znajek机理的有效性和性质，射流的发射，准直，加速度和稳定性，它们与周围等离子体的相互作用，射流-银河反馈机制等，我们将追踪该领域从最初的尝试性步骤发展到“成熟”时代。我们还简要介绍了该领域在可预见的未来将如何发展。