Due to the butterfly-effect, computer-generated chaotic simulations often deviate exponentially from the true solution, so that it is very hard to obtain a reliable simulation of chaos in a long-duration time. In this paper, a new strategy of the so-called Clean Numerical Simulation (CNS) in physical space is proposed for spatio-temporal chaos, which is computationally much more efficient than its predecessor (in spectral space). The strategy of the CNS is to reduce both of the truncation and round-off errors to a specified level by implementing high-order algorithms in multiple-precision arithmetic (with sufficient significant digits for all variables and parameters) so as to guarantee that numerical noise is below such a critical level in a temporal interval $t\in [0,T_c]$ that corresponding numerical simulation remains reliable over the whole interval. Without loss of generality, the complex Ginzburg-Landau equation (CGLE) is used to illustrate its validity. As a result, a reliable long-duration numerical simulation of the CGLE is achieved in the whole spatial domain over a long interval of time $t\in [0,3000]$, which is used as a reliable benchmark solution to investigate the influence of numerical noise by comparing it with the corresponding ones given by the 4th-order Runge-Kutta method in double precision (RKwD). Our results demonstrate that the use of double precision in simulations of chaos might lead to huge errors in the prediction of spatio-temporal trajectories and in statistics, not only quantitatively but also qualitatively, particularly in a long interval of time.

由于蝶形效应，计算机生成的混沌仿真通常会偏离真实解，因此很难在长时间内获得可靠的混沌仿真。在本文中，提出了一种针对时空混沌的物理空间清洁数值模拟（CNS）的新策略，该策略在计算上比其前身（在频谱空间中）效率更高。CNS的策略是通过在多精度算术中实现高阶算法（所有变量和参数都有足够的有效数字），将截断和舍入误差降低到指定水平。在时间间隔内低于此临界水平$Ť\in [0，{Ť}_C]$相应的数值模拟在整个时间间隔内仍然可靠。在不失一般性的情况下，使用复杂的Ginzburg-Landau方程（CGLE）来说明其有效性。结果，在较长的时间间隔内在整个空间域中实现了CGLE的可靠的长期数值模拟$Ť\in [0，3000]$，它是一种可靠的基准解决方案，通过将其与双精度（RKwD）的四阶Runge-Kutta方法给出的值进行比较来研究数字噪声的影响。我们的结果表明，在混沌模拟中使用双精度可能会导致时空轨迹预测和统计方面的巨大误差，不仅在定量上而且在定性上，尤其是在较长的时间间隔内。