26 citations · 101 across the 13 of their papers we have counts for
14 papers
Non-uniqueness of smooth solutions of the Navier-Stokes equations from almost the same initial conditions
Shijun Liao, Shijie Qin
Using clean numerical simulation (CNS) which can give very accurate spatiotemporal trajectory of Navier-Stokes turbulence in a finite but long enough interval of time, we give some…
Reply to the comments of McMullen et al. (arXiv:2510.04828)
Shijun Liao, Shijie Qin
McMullen et al. [1] comment that the numerical simulations that explicitly include random velocity fluctuations ``should exhibit a thermal-fluctuation-dominated range'' consistent…
Ultra-chaotic property of Navier-Stokes turbulence
Shijie Qin, Kun Xu, Shijun Liao
A chaotic system is called ultra-chaos when its statistics have sensitivity dependence on initial condition and/or other small disturbances. In this paper, using two-dimensional tu…
A paradox of the Navier-Stokes turbulence
Shijie Qin, Kun Xu, Shijun Liao
The Navier-Stokes (NS) equations as a turbulence model have been widely applied in lots of fields. The NS equations contain such a fundamental assumption that all small physical/ar…
Clean numerical simulation (CNS) of three-dimensional turbulent Kolmogorov flow
Shijie Qin, Shijun Liao
Turbulence holds immense importance across various scientific and engineering disciplines. The direct numerical simulation (DNS) of turbulence proposed by Orszag in 1970 is a miles…
Physical significance of artificial numerical noise in direct numerical simulation of turbulence
Shijun Liao, Shijie Qin
Using clean numerical simulation (CNS) in which artificial numerical noise is negligible over a finite, sufficiently long interval of time, we provide evidence, for the first time,…
Noise-expansion cascade: an origin of randomness of turbulence
Shijun Liao, Shijie Qin
Randomness is one of the most important characteristics of turbulence, but its origin remains an open question. By means of a ``thought experiment'' via several clean numerical exp…
Is a direct numerical simulation (DNS) of Navier-Stokes equations with small enough grid spacing and time-step definitely reliable/correct?
Shejie Qin, Yu Yang, Yongxiang Huang +3
Traditionally, results given by the direct numerical simulation (DNS) of Navier-Stokes equations are widely regarded as reliable benchmark solutions of turbulence, as long as grid…
A Self-Adaptive Algorithm of the Clean Numerical Simulation (CNS) for Chaos
Shijie Qin, Shijun Liao
The background numerical noise is determined by the maximum of truncation error and round-off error. For a chaotic system, the numerical error g…
Large-scale influence of numerical noises as artificial stochastic disturbances on a sustained turbulence
Shijie Qin, Shijun Liao
We investigate the large-scale influence of numerical noises as tiny artificial stochastic disturbances on a sustained turbulence. Using the two-dimensional (2D) turbulent Rayleigh…
A kind of Lagrangian chaotic property of the Arnold-Beltrami-Childress flow
Shijie Qin, Shijun Liao
Three-dimensional steady-state Arnold-Beltrami-Childress (ABC) flow has a chaotic Lagrangian structure, and also satisfies the Navier-Stokes (NS) equations with an external force p…
Ultra-chaos: an insurmountable objective obstacle of reproducibility and replicability
Shijun Liao, Shijie Qin
In this paper, a new concept, i.e. ultra-chaos, is proposed for the first time. Unlike a normal-chaos, statistical properties such as the probability density functions (PDF) of an…
Influence of database noises to machine learning for spatiotemporal chaos
Yu Yang, Shijie Qin, Shijun Liao
A new strategy, namely the "clean numerical simulation" (CNS), was proposed (J. Computational Physics, 418:109629, 2020) to gain reliable/convergent simulations (with negligible nu…
Influence of round-off errors on the reliability of numerical simulations of chaotic dynamic systems
Shijie Qin, Shijun Liao
We illustrate that, like the truncation error, the round-off error has a significant influence on the reliability of numerical simulations of chaotic dynamic systems. Due to the bu…