A Modified Homotopy Analysis Method for Solving Boundary Layer Equations

A new modification of the Homotopy Analysis Method (HAM) is presented for highly nonlinear ODEs on a semi-infinite domain. The main advantage of the modified HAM is that the number of terms in the series solution can be greatly reduced;meanwhile the accuracy of the solution can be well retained. In this way, much less CPU is needed. Two typical examples are used to illustrate the efficiency of the proposed approach.

Sea surface reconstruction from marine radar images using deep convolutional neural networks

The sea surface reconstructed from radar images provides valuable information for marine operations and maritime transport.The standard reconstruction method relies on the three-dimensional fast Fourier transform(3D-FFT),which introduces empirical parameters and modulation transfer function(MTF)to correct the modulation effects that may cause errors.In light of the convolutional neural networks’(CNN)success in computer vision tasks,this paper proposes a novel sea surface reconstruction method from marine radar images based on an end-to-end CNN model with the U-Net architecture.Synthetic radar images and sea surface elevation maps were used for training and testing.Compared to the standard reconstruction method,the CNN-based model achieved higher accuracy on the same data set,with an improved correlation coefficient between reconstructed and actual wave fields of up to 0.96-0.97,and a decreased non-dimensional root mean square error(NDRMSE)of around 0.06.The influence of training data on the deep learning model was also studied.Additionally,the impact of the significant wave height and peak period on the CNN model’s accuracy was investigated.It has been demonstrated that the accuracy will fluctuate as the wave steepness increases,but the correlation coefficient remains above 0.90,and the NDRMSE remains less than 0.11.

On the origin of intrinsic randomness of Rayleigh-Benard turbulence

It is of broad interest to understand how the evolution of non-equilibrium systems can be triggered and the role played by external perturbations. A famous example is the origin of randomness in the laminar-turbulence transition, which is raised in the pipe flow experiment by Reynolds as a century old unresolved problem. Although there exist different hypotheses, it is widely believed that the randomness is "intrinsic", which, however, remains as an open question to be verified. Simulating the modeled RayleighB′enard convection system by means of the so-called clean numerical simulation(CNS) with negligible numerical noises that are smaller even than thermal fluctuation, we verify that turbulence can be self-excited from the inherent thermal fluctuation without any external disturbances, i.e. out of nothing. This reveals a relationship between microscopic physical uncertainty and macroscopic randomness. It is found that in physics the system nonlinearity functions as a channel for randomness information,and energy as well, to transport microscopic uncertainty toward large scales. Such scenario can generally be helpful to understand the various relevant phenomena. In methodology, compared with direct numerical simulation(DNS), CNS opens a new direction to investigate turbulent flows with largely improved accuracy and reliability.

Flow and magnetic structures in a kinematic ABC-dynamo

Dynamo theory describes the magnetic field induced by the rotating,convecting and electrically conducting fluid in a celestial body.The classical ABC-flow model represents fast dynamo action,required to sustain such a magnetic field.In this letter,Lagrangian coherent structures(LCSs)in the ABC-flow are detected through Finite-time Lyapunov exponents(FTLE).The flow skeleton is identified by extracting intersections between repelling and attracting LCSs.For the case A=B=C=1,the skeleton structures are made up from lines connecting two different types of stagnation points in the ABC-flow.The corresponding kinematic ABC-dynamo problem is solved using a spectral method,and the distribution of cigar-like magnetic structures visualized.Inherent links are found to exist between LCSs in the ABC-flow and induced magnetic structures,which provides insight into the mechanism behind the ABC-dynamo.

Entropy Generation Analysis around Airfoil using Multi-Block Lattice Boltzmann Method

This present paper proposes aerodynamic forces and entropy generation characteristics on theflow past two-dimensional airfoil at low Reynolds number by multiple-relaxation-time lattice Boltzmann method to clarify theflow loss mechanism.The block mesh refinement was adopted in which a higher accuracy was needed in parts of the domain characterized by complexflow.The interpolated bounce-back method was used to treat the irregular curve.This numerical method can effectively solve the complexflowfield simulation problems with reasonable accuracy and reli-ability by simulatingflow around plate and airfoil.Based on second law of thermo-dynamics,an expression of entropy generation rate for arbitrary control volume was derived theoretically which could accurately quantify the local irreversible loss of theflowfield at any position.After that,a comprehensive numerical study was conducted to analyze relationship of entropy generation and drag force by taking NACA0012 air-foil as the research object.For unsteady condition,entropy generation rate and the drag force are not linearly related any more.Losses due to steady effects mainly con-sider the irreversibility in the boundary layer and wake while the unsteady effects come from the interaction between the main separation vortex and the trailing shed-ding vortex.