相关论文: Clean Numerical Simulation: A New Strategy to Obta…

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)…

In this paper, an extremely accurate numerical algorithm, namely the "clean numerical simulation" (CNS), is proposed to accurately simulate the propagation of micro-level inherent physical uncertainty of chaotic dynamic systems. The chaotic…

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}…

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…

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…

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…

Direct numerical simulations (DNS) are an indispensable tool for understanding the fundamental physics of turbulent flows. Because of their steep increase in computational cost with Reynolds number ($R_{\lambda}$), well-resolved DNS are…

Deducing the states of spatiotemporally chaotic systems (SCSs) as they evolve in time is crucial for various applications. However, it is a dramatic challenge for generally achieving so due to the complexity of non-periodic dynamics and the…

The famous three-body problem is investigated by means of a numerical approach with negligible numerical noises in a long enough time interval, namely the Clean Numerical Simulation (CNS). From physical viewpoints, position of any bodies…

In this study, we address the problem of chaotic synchronization over a noisy channel by introducing a novel Deep Chaos Synchronization (DCS) system using a Convolutional Neural Network (CNN). Conventional Deep Learning (DL) based…

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…

The real-time prediction of chaotic systems requires a nonlinear-reduced order model (ROM) to forecast the dynamics, and a stream of data from sensors to update the ROM. Data-driven ROMs are typically built with a two-step strategy: data…

Turbulent flow has been extensively studied using computational fluid dynamics (CFD) simulations since turbulent flow regime is so frequently encountered in both academic and engineering applications. The high-fidelity simulation of the…

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 turbulent Kolmogorov flow as an example, we illustrate that…

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…

Chaotic dynamical systems such as turbulent flows are characterized by an exponential divergence of infinitesimal perturbations to initial conditions. Therefore, conventional adjoint/tangent sensitivity analysis methods that are successful…

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…

The direct numerical simulation (DNS) of the Taylor--Couette flow in the fully turbulent regime is described. The numerical method extends the work by Quadrio & Luchini (Eur. J. Mech. B / Fluids, v.21, pp.413--427, 2002), and is based on a…