Zhenquan Li

An accurate and comprehensive model of thin fluid flows with inertia on curved substrates

Consider the three-dimensional flow of a viscous Newtonian fluid upon a curved two-dimensional substrate when the fluid film is thin, as occurs in many draining, coating and biological flows. We derive a comprehensive model of the dynamics of the film, the model being expressed in terms of the film thickness n and the average lateral velocity Pu. Centre manifold theory assures us that the model accurately and systematically includes the effects of the curvature of substrate, gravitational body force, fluid inertia and dissipation. The model resolves wavelike phenomena in the dynamics of viscous fluid flows over arbitrarily curved substrates such as cylinders, tubes and spheres. We briefly illustrate its use in simulating drop formation on cylindrical fibres, wave transitions, three-dimensional instabilities, Faraday waves, viscous hydraulic jumps, flow vortices in a compound channel and flow down and up a step. These models are the most complete models for thin-film flow of a Newtonian fluid; many other thin-film models can be obtained by different restrictions and truncations of the model derived here.

Fuzzified neural network based on fuzzy number operations

The fuzzified neural network based on fuzzy number operations is presented as a powerful modelling tool here. We systematically introduce ideas and concepts of a novel neural network based on fuzzy number operations. First we suggest how to compute the results of addition, subtraction, multiplication and division for two fuzzy numbers. Second we propose a learning algorithm, and present some ideas about the choice of fuzzy weights and fuzzy biases and a numerical scheme for the calculation of outputs of the fuzzified neural network. Finally, we show some results of computer simulations.

Modelling the Dynamics of Turbulent Floods

Consider the dynamics of turbulent flow in rivers, estuaries, and floods. Based on the widely used k-

Suitability of fuzzy reasoning methods

\epsilon

Accuracy analysis of an adaptive mesh refinement method using benchmarks of 2-D steady incompressible lid-driven cavity flows and coarser meshes

model for turbulence, we use the techniques of center manifold theory to derive dynamical models for the evolution of the water depth and of vertically averaged flow velocity and turbulent parameters. This new model for the shallow water dynamics of turbulent flow resolves the vertical structure of the flow and the turbulence, includes interaction between turbulence and long waves, and gives a rational alternative to classical models for turbulent environmental flows.

Weak local residuals as smoothness indicators for the shallow water equations

Abstract Similarity, commutativity, continuity and computational times of the currently existing six reasoning methods are discussed. All six have commutativity and continuity. It is found that the reasoning precision of a reasoning method has relations with similarity degree. The computational complexities of the six reasoning methods are given.

Accuracy analysis of a mesh refinement method using benchmarks of 2-D lid-driven cavity flows and finer meshes

Lid-driven cavity flows have been widely investigated and accurate results have been achieved as benchmarks for testing the accuracy of computational methods. This paper verifies the accuracy of an adaptive mesh refinement method numerically using 2-D steady incompressible lid-driven cavity flows and coarser meshes. The accuracy is shown by verifying that the centres of vortices given in the benchmarks are located in the refined grids of refined meshes for Reynolds numbers 100, 1000 and 2500 using coarser meshes. The adaptive mesh refinement method performs mesh refinement based on the numerical solutions of Navier-Stokes equations solved by a finite volume method with a well known SIMPLE algorithm for pressure-velocity coupling. The accuracy of the refined meshes is shown by comparing the profiles of horizontal and vertical components of velocity fields with the corresponding components of the benchmarks together and drawing closed streamlines. The adaptive mesh refinement method verified in this paper can be applied to find the accurate numerical solutions of any mathematical models containing continuity equations for incompressible fluid, steady state fluid flows or mass and heat transfer.

A Mass Conservative Streamline Tracking Method for Three Dimensional CFD Velocity Fields

Abstract The system of shallow water equations admits infinitely many conservation laws. This paper investigates weak local residuals as smoothness indicators of numerical solutions to the shallow water equations. To get a weak formulation, a test function and integration are introduced into the shallow water equations. We use a finite volume method to solve the shallow water equations numerically. Based on our numerical simulations, the weak local residual of a simple conservation law with a simple test function is identified to be the best as a smoothness indicator.

Sensitivity analysis of a mesh refinement method using the numerical solutions of 2D lid-driven cavity flow

Lid-driven cavity flows have been widely investigated and accurate results have been achieved as benchmarks for testing the accuracy of computational methods. This paper verifies the accuracy of a mesh refinement method numerically using two-dimensional steady incompressible lid-driven flows and finer meshes. The accuracy is shown by comparing the coordinates of centres of vortices located by the mesh refinement method with the corresponding benchmark results. The accuracy verification shows that the mesh refinement method provides refined meshes that all centres of vortices are contained in refined grids based on the numerical solutions of Navier-Stokes equations solved by finite volume method except for one case. The well known SIMPLE algorithm is employed for pressure–velocity coupling. The accuracy of the numerical solutions is shown by comparing the profiles of horizontal and vertical components of velocity fields with the corresponding components of the benchmarks and also streamlines. The mesh refinement method verified in this paper can be applied to find the accurate numerical solutions of any mathematical models containing continuity equations for incompressible fluid or steady state fluid flows or heat transfer.

Accuracy verification of a 2D adaptive mesh refinement method for incompressible or steady flow

Mass conservation is a key issue for accurate streamline visualization of flow fields. This paper presents a mass conservative streamline construction method for CFD velocity fields defined at discrete locations in three dimensions for incompressible flows. Linear mass conservative interpolation is used to approximate velocity fields. Demonstration examples are shown.Copyright