Related papers: On the numerical simulation of propagation of micr…
It is well known that chaotic dynamic systems (such as three-body system, turbulent flow and so on) have the sensitive dependence on initial conditions (SDIC). Unfortunately, numerical noises (such as truncation error and round-off error)…
It is well known that chaotic dynamic systems (such as three-body system, turbulent flow and so on) have the sensitive dependance on initial conditions (SDIC). Unfortunately, numerical noises (such as truncation error and round-off error)…
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…
The background numerical noise $\varepsilon_{0} $ is determined by the maximum of truncation error and round-off error. For a chaotic system, the numerical error $\varepsilon(t)$ grows exponentially, say, $\varepsilon(t) = \varepsilon_{0}…
It is important to know the accurate trajectory of a free fall object in fluid (such as a spacecraft), whose motion might be chaotic in many cases. However, it is impossible to accurately predict its chaotic trajectory in a long enough…
A new strategy, namely the "clean numerical simulation" (CNS), was proposed (J. Computational Physics, 418:109629, 2020) to gain reliable/convergent simulations (with negligible numerical noises) of spatiotemporal chaotic systems in a long…
It is traditionally believed that the macroscopic randomness has nothing to do with the micro-level uncertainty. Besides, the sensitive dependence on initial condition (SDIC) of Lorenz chaos has never been considered together with the…
Yao and Hughes commented (Tellus-A, 60: 803 - 805, 2008) that "all chaotic responses are simply numerical noise and have nothing to do with the solutions of differential equations". However, using 1200 CPUs of the National Supercomputer…
In this paper a new concept, namely the critical predictable time $T_c$, is introduced to give a more precise description of computed chaotic solutions of nonlinear differential equations: it is suggested that computed chaotic solutions are…
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-B\'enard (RB) convection as an example, we numerically…
Turbulence holds immense importance across various scientific and engineering disciplines. The direct numerical simulation (DNS) of turbulence proposed by Orszag in 1970 is a milestone in fluid mechanics, which began an era of numerical…
In this paper, we consider discrete-time non-linear stochastic dynamical systems with additive process noise in which both the initial state and noise distributions are uncertain. Our goal is to quantify how the uncertainty in these…
A new type of instability - electrokinetic instability - and an unusual transition to chaotic motion near a charge-selective surface was studied by numerical integration of the Nernst-Planck-Poisson-Stokes system and a weakly nonlinear…
Using 1200 CPUs of the National Supercomputer TH-A1 and a parallel integral algorithm based on the 3500th-order Taylor expansion and the 4180-digit multiple precision data, we have done a reliable simulation of chaotic solution of Lorenz…
Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical…
Traditionally, chaotic systems are built on the domain of infinite precision in mathematics. However, the quantization is inevitable for any digital devices, which causes dynamical degradation. To cope with this problem, many methods were…
Numerical precision in large-scale scientific computations has become an emerging topic due to recent developments in computer hardware. Lower floating point precision offers the potential for significant performance improvements, but the…
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 spacing is fine enough (i.e. less than the minimum…
The theory of covariance control and covariance steering (CS) deals with controlling the dispersion of trajectories of a dynamical system, under the implicit assumption that accurate prior knowledge of the system being controlled is…
Chaos reveals a fundamental paradox in the scientific understanding of Complex Systems. Although chaotic models may be mathematically deterministic, they are practically non-determinable due to the finite precision, which is inherent in all…