arXiv subjects

Guangzhao Zhou

Publications and source records attributed to Guangzhao Zhou.

7 recordsLinked to original sources

arXiv2026

K41 Scaling in Bubble-Induced Turbulence Arises from Single-Bubble Wakes

We use high-resolution, interface-resolved direct numerical simulations (DNS) to investigate the origin of Kolmogorov (K41) scaling in bubble-induced turbulence (BIT). Region-wise velocity structure functions show that the 2/3 scaling appears only within bubble wake regions. Comparison with matched single-bubble DNS further indicates that the K41 scaling observed in the full BIT field arises from the superposition of individual bubble wakes. On this basis, we derive a scaling for the dissipation rate in dilute BIT that is consistent with experimental results from the literature.

physics.flu-dyn↗

arXiv2026

Modeling and dynamics of axisymmetric thin liquid film flow along a conical surface

This study focuses on the modeling and dynamics of gravity-driven, axisymmetric thin liquid film flow along a conical surface. Spatial linear stability analysis is performed on the basis of a Benney-type equation derived for the present configuration. In particular, streamwise curvature of the free surface is found to exert a crucial influence on the stability threshold. For simulations of surface waves, a second-order low-dimensional model is developed under the long-wave assumption, achieving accuracy comparable to direct numerical simulations at far lower cost. With this model, the characteristics of both linear and nonlinear waves are examined. A key difference from the flow over a flat plate is the dependence of wave dynamics on radial distance from the cone apex. At relatively high flow rates, a transition from solitary to sinusoidal waves is observed, with the transition position correlating closely with the linear stability threshold. Within the parameter range investigated, quantitative results of the conical film flow are almost identical to those in the flat-plate case when local parameters are substituted, indicating that inertial effects of the conical geometry are negligible. The models and findings presented in this paper may aid the design and optimization of industrial processes such as film coating and liquid-film-based heat and mass transfer on conical surfaces.

physics.flu-dyn↗

arXiv2026

Rising bubbles draw surface patterns: a numerical study

Small bubbles rising in a chain can self-organize into regular patterns upon reaching a liquid's free surface. This phenomenon is investigated through direct numerical simulations. By varying the bubble release period, distinct branching patterns characterized by different numbers of arms are observed. These macroscopic regular configurations arise from localized non-contact repulsion and pair collisions between bubbles as they arrive at the free-surface emergence site. A theoretical model is proposed to quantitatively relate the number of branches to the bubble release period. The model also predicts probabilities of observing specific arm counts in reality. This study provides insights into broader nonlinear pattern formation and self-organization phenomena.

physics.flu-dyn↗

arXiv2025

Linearly Stable KAM Tori for One Dimensional Forced Kirchhoff Equations under Periodic Boundary Conditions

We prove an abstract infinite dimensional KAM theorem, which could be applied to prove the existence and linear stability of small-amplitude quasi-periodic solutions for one dimensional forced Kirchhoff equations with periodic boundary conditions \[ u_{tt}-(1+\int_{0}^{2π} |u_x|^2 dx)u_{xx}+ M_ξu+εg(\barωt,x) =0,\quad u(t,x+2π)=u(t,x),\] where $M_ξ$ is a real Fourier multiplier, $g(\barωt,x)$ is real analytic with forced Diophantine frequencies $\barω$, $ε$ is a small parameter. The paper generalizes the previous results from the simple eigenvalue to the double eigenvalues under the quasi-linear perturbation.

math.DS↗

arXiv2018

Cell Size Effect on Computational Fluid Dynamics: The Limitation Principle for Flow Simulation

For theoretical gas dynamics, the flow regimes are classified according to the Knudsen number. For computational fluid dynamics (CFD), the numerical flow field is the projection of the physical flow field onto the discrete space and time, which is related to the cell Knudsen number. The real representable flow regimes are controlled by these two parameters. According to the values of Knudsen number and cell Knudsen number, we study the classification of the numerical flow regimes. In the process of mesh refinement, the numerical experiments show the change of numerical flow regime from continuum, to near-continuum, and to non-equilibrium one. The change of flow regime with different cell resolution is the limitation principle for the numerical simulation, which is the best a multiscale method can do. In other words, we should have changeable numerical governing equations in different mesh size scale, and they are coupled with the traditional physical equations in different scales, such as the Navier-Stokes and Boltzmann. Under the multiscale modeling, a mesh refinement is a process in resolving the flow physics in different scale. The verification and validation (V$\&$V) need include the physical modeling mechanism in the mesh refinement process. The traditional idea of mesh refinement for targeting a fixed partial differential equation cannot achieve the final goal of computation, which is to recover the flow physics as truthfully as possible under the limitation of the cell resolution.

physics.comp-ph↗

arXiv2017

Grid-converged Solution and Analysis of the Unsteady Viscous Flow in a Two-dimensional Shock Tube

The flow in a shock tube is extremely complex with dynamic multi-scale structures of sharp fronts, flow separation, and vortices due to the interaction of the shock wave, the contact surface, and the boundary layer over the side wall of the tube. Prediction and understanding of the complex fluid dynamics is of theoretical and practical importance. It is also an extremely challenging problem for numerical simulation, especially at relatively high Reynolds numbers. Daru & Tenaud (Daru, V. & Tenaud, C. 2001 Evaluation of TVD high resolution schemes for unsteady viscous shocked flows. Computers & Fluids 30, 89-113) proposed a two-dimensional model problem as a numerical test case for high-resolution schemes to simulate the flow field in a square closed shock tube. Though many researchers have tried this problem using a variety of computational methods, there is not yet an agreed-upon grid-converged solution of the problem at the Reynolds number of 1000. This paper presents a rigorous grid-convergence study and the resulting grid-converged solutions for this problem by using a newly-developed, efficient, and high-order gas-kinetic scheme. Critical data extracted from the converged solutions are documented as benchmark data. The complex fluid dynamics of the flow at Re = 1000 are discussed and analysed in detail. Major phenomena revealed by the numerical computations include the downward concentration of the fluid through the curved shock, the formation of the vortices, the mechanism of the shock wave bifurcation, the structure of the jet along the bottom wall, and the Kelvin-Helmholtz instability near the contact surface.

physics.flu-dyn↗

arXiv2016

Simplification of the Flux Function for a Higher-order Gas-kinetic Evolution Model

The higher-order gas-kinetic scheme for solving the Navier-Stokes equations has been studied in recent years. In addition to the use of higher-order reconstruction techniques, many terms are used in the Taylor expansion of the gas distribution functions. Therefore, a large number of coefficients need to be determined in the calculation of the time evolution of the gas distribution function at cell interfaces. As a consequence, the higher-order flux function takes much more computational time than that of a second-order gas-kinetic scheme. This paper aims to simplify the evolution model by two steps. Firstly, the coefficients related to the higher-order spatial and temporal derivatives of a distribution function are redefined to reduce the computational cost. Secondly, based on the physical analysis, some terms can be removed without loss of accuracy. Through the simplifications, the computational efficiency of the higher-order scheme is increased significantly. In addition, a self-adaptive numerical viscosity is designed to minimize the necessary numerical dissipation. Several numerical examples are tested to demonstrate the accuracy and robustness of the current scheme.

physics.comp-ph↗