5 citations · 13 across the 10 of their papers we have counts for
11 papers
Spatial symmetry invariance of solution of Kolmogorov flow
Shijun Liao
We prove a mathematical theorem that solution for all of the two-dimensional (2D) Kolmogorov flow governed by Navier-Stokes (NS) equations with periodic boundary condition…
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,…
Effects of appendages on the turbulence and flow noise of a submarine model using high-order scheme
Peng Jiang, Shijun Liao, Ling Liu +1
This study employs high-fidelity numerical simulations to investigate the influence of appendages on the turbulent flow dynamics and far-field acoustic radiation of the SUBOFF subm…
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…
Utility of High-Order Scheme for Unsteady Flow Simulations: Comparison with Second-Order Tool
Peng Jiang, Yichen Huang, Yong Cao +2
The objective of this work is to investigate the utility and effectiveness of the high-order scheme for simulating unsteady turbulent flows. To achieve it, the studies were conduct…
Large-eddy simulation of hydrodynamic noise from turbulent flows past an axisymmetric hull using high-order schemes
Peng Jiang, Shijun Liao, Bin Xie
In this paper, wall-modeled large-eddy simulation (WMLES) is carried out with Ffowcs-Williams and Hawkings (FW-H) acoustic analogy to investigate the turbulent flow and hydrodynami…