Zhenquan Li

• PhD
• Senior Lecturer at Charles Sturt University

The study applies a two-dimensional adaptive mesh refinement (AMR) method to estimate the coordinates of the locations of the centre of vortices in steady, incompressible flow around a square cylinder placed within a channel. The AMR method is robust and low cost, and can be applied to any incompressible fluid flow. The considered channel has a blo...

The lid-driven cavity flow problem stands as a widely recognized benchmark in fluid dynamics, serving to validate CFD algorithms. Despite its geometric simplicity, the lid-driven cavity flow problem exhibits a complex flow regime primarily characterized by the formation of vortices at the centre and corners of the square domain. This study evaluate...

The lid-driven cavity flow problem is a well-known test case in fluid dynamics for validating computational fluid dynamics (CFD) algorithms. Despite its geometrical simplicity, the lid driven cavity flow problem exhibits a complex flow regime, mainly due to the vortices formed in the centre and at the corners of the square domain. Consequently, thi...

The traditional Shan-Chen pseudo-potential model has limitations, such as pseudo-velocity, density ratio limitation, and thermodynamic consistency defect. A method based on the improved Shan-Chen pseudo-potential model to study fluid flow in rock microfractures using the multiple-relaxation-time lattice Boltzmann method is proposed and validated us...

Appropriate mesh refinement plays a vital role in the accuracy and convergence of computational fluid dynamics solvers. This work is an extension of the previous work that further demonstrates the accuracy of the 3D adaptive mesh refinement method by comparing the accuracy measures between the ones derived from the analytical fields and those ident...

This study involves the estimation of a key epidemiological parameter for evaluating and monitoring the transmissibility of a disease. The time-varying reproduction number is the index for quantifying the transmissibility of infectious diseases. Accurate and timely estimation of the time-varying reproduction number is essential for optimizing non-p...

Meshing plays an important role on the accuracy and convergence of CFD solvers. The accuracy includes quantitative measures such as discretization and truncation errors and qualitative measures such as drawing closed streamline, identifying singular points, asymptotic lines/planes, and (symmetry) axis. The current study builds on previous work by f...

This paper describes the application of an adaptive mesh refinement (AMR) method to estimate centers of vortices of two-dimensional (2D) incompressible fluid flow over a wall-mounted plate. Following the accuracy verification of the AMR method using the benchmarks of 2D lid-driven cavity flows and backward-facing step flows, this study considers th...

Since the novel coronavirus (COVID-19) outbreak in China, and due to the open accessibility of COVID-19 data, several researchers and modellers revisited the classical epidemiological models to evaluate their practical applicability. While mathematical compartmental models can predict various contagious viruses’ dynamics, their efficiency depends o...

Identifying centers of vortices of fluid flow accurately is one of the accuracy measures for computational methods. After verifying the accuracy of the 2D adaptive mesh refinement (AMR) method in the benchmarks of 2D lid-driven cavity flow, this paper shows the accuracy verification by the benchmarks of 2D backward-facing step flow. The AMR method...

Identifying accurate centers of vortices of fluid flow is one of the accuracy measures for computational methods. After verifying the accuracy of the 2D adaptive mesh refinement (AMR) method by the benchmarks of 2D lid-driven cavity flows, this paper shows the accuracy verification by the benchmarks of 2D backward facing step flows. The AMR method...

A study of the behaviour of flow past a square cylinder for Reynolds numbers 10 and 20 is presented. Open source software Navier2d in Matlab is used in this study. The investigation starts from a uniform initial mesh and then refine the initial mesh using a mesh refinement method which was proposed based on both qualitative theory of differential e...

After successful accuracy and reliability verifications of the algorithm for a 2D adaptive mesh refinement method using exact and numerical benchmark results, we consider the computational complexity of this algorithm using 2D steady incompressible lid-driven cavity flows. The algorithm for the 2D adaptive mesh refinement method is proposed based o...

Locating accurate centres of vortices is one of the accuracy measures for computational methods in fluid flow and the lid-driven cavity flows are widely used as benchmarks. This paper analyses the accuracy of an adaptive mesh refinement method using 2D steady incompressible lid-driven cavity flows. The adaptive mesh refinement method performs mesh...

Locating accurate centres of vortices is one of the accurate measures for computational methods in fluid flow and the lid-driven cavity flows are widely used as benchmarks. This paper analyses the accuracy of an adaptive mesh refinement method using 2D steady incompressible lid-driven cavity flows for two refinements. The adaptive mesh refinement m...

This paper investigates the technique of localised mesh refinement to solve the Shallow Water Equations (SWE), by adding nodes only where needed. The discretization process linearizes the nonlinear equations for solving as a linear system. The nonlinear error values at specific nodes are used to indicate which node will have additional nodes added...

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 investigates sensitivity of a mesh refinement method against the accuracy of numerical solutions of the 2-D steady incompressible lid-driven flow from a collocated finite volume me...

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 verifyi...

Lid-driven cavity flows have been widely investigated and accurate results have been achieved as benchmarks for testing the accuracy of computational methods. This pa-per verifies the accuracy of an adaptive mesh refinement method numerically using 2-D steady incompressible lid-driven flows and coarser meshes. The accuracy is shown by verifying tha...

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 investigates sensitivity of a mesh refinement method against the accuracy of numerical solutions of the 2-D steady incompressible lid-driven flow from a colocated finite volume met...

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 solv...

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...

This paper investigates the application of finite difference methods to solve the Shallow Water Equations (SWE's), in the context of mesh refinement through the introduction of an error tolerance. The problem is tackled by linearisation of the nonlinear differential equations through the discretization process. Once the set of equations have been l...

Mass conservation is a key issue for accurate streamline construction. We introduce a mass conservative streamline tracking method using dual stream functions over tetrahedral domains. A set of exact dual stream function solutions for mass conservative linear momentum vectors have been evaluated and are presented here together with their computer g...

This paper introduces the University Course Timetabling Problem (UCTP) using the University of the South Pacific (USP) as a case study. It provides a theoretical presentation on our lecture scheduling problem tailor-made for an automation algorithm structure built around a multi-phase deterministic sequential greedy solver. The solver is inspired b...

The singular points and asymptote lines of velocity fields are important in analyzing the properties of the fields but normally difficult to identify. We have created mesh refinement methods which can find the points and lines, and verified by analytical velocity fields. This paper briefly shows characteristics of the method for two dimensions usin...

This paper introduces the University Course Timetabling Problem (UCTP) using the University of the South Pacific (USP) as a case study. It provides a theoretical presentation on our lecture scheduling problem tailor-made for an automation algorithm structure built around a multi-phase deterministic sequential greedy solver. The solver is inspired b...

Streamribbon is used to visualize the rotation of the fluid flow. The rotation of flow is useful in fluid mechanics, engineering and geophysics. This paper introduces the construction technique of streamribbon using the streamline which is generated based on the law of mass conservation. The accuracy of constructed streamribbons is shown through tw...

Mesh generation is one of key issues in Computational Fluid Dynamics. This paper presents an adaptive three-dimensional mesh refinement method based on the law of mass conservation. The method can be applied to a governing system that includes the law of mass conservation (continuity equation) for incompressible or compressible steady flows. Users...

Streamtube is used to visualize expansion, contraction and various properties of the fluid flow. These are useful in fluid mechanics, engineering and geophysics. The streamtube constructed in this paper only reveals the flow expansion rate along streamline. Based on the mass conservative streamline, we will show how to construct the streamtube.

Mass conservation is a key issue for constructing accurate streamlines of flow fields. We consider the CFD velocity fields without further data available such as the measured velocity fields. This paper presents a mass conservative streamline tracking method for such CFD velocity fields. Linear interpolation is used to approximate velocity fields a...

Summary An adaptive three-dimensional mesh refinement method based on the law of mass conservation has been introduced and tested using some analytical velocity fields as accurate in identifying singular point, asymptotic plane and drawing closed streamlines. This paper further investigates the adaptive mesh refinement method using a velocity field...

Mesh generation is one of key issues in Computational Fluid Dynamics. This paper presents an adaptive two-dimensional mesh refinement method based on the law of mass conservation. The method can be applied to a governing system that includes the law of mass conservation (continuity equation) for incompressible or compressible steady flows. Users ca...

The construction of streamlines is one of the most common methods for visualising fluid motion. Streamlines can be computed from the intersection of two nonparallel stream surfaces, which are iso-surfaces of dual stream functions. Stream surfaces are also useful to isolate part of the flow domain for detailed study. This paper introduces a techniqu...

This paper proposes an adaptive streamline tracking method for two-dimensional CFD velocity fields. We assume that the multiplication of an unknown scalar function and the linear interpolation of a CFD velocity field satisfies the law of mass conservation and then derive the expressions of the scalar function. The adaptive streamline tracking metho...

Mesh generation is one of the key issues in Computational Fluid Dynamics. This paper presents an adaptive two-dimensional mesh refinement method based on the law of mass conservation. The method can be used to a governing system that includes the law of mass conservation (continuity equation) for incompressible or compressible steady flows. We show...

One of the most important ways of visualizing fluid flows is the construction of streamlines, which are lines that are everywhere tangential to the local velocity field. We have created mass conservative streamline tracking methods for two-dimensional (2-D) and 3-D CFD velocity fields. It has been shown that mass conservation is a key issue for acc...

Burgers equation is one of the simplest nonlinear partial differential equations-it combines the basic processes of diffusion and nonlinear steepening. In some applications it is appropriate for the diffusion coefficient to be a time-dependent function. Using a Wayne's transformation and centre manifold theory, we derive l-mode and 2-mode centre ma...

Fuzzified neural network based on fuzzy number operations may be one of powerful fuzzified neural networks. We introduced a fuzzified neural network basd on fuzzy number operations which approximates targets by choosing the shapes of the weights and the biases and calculating the left, mean and right values of each weight or bias. However, as we ha...

We describe a calculation of stream functions for flow visualization using space curve theory. Stream surfaces are represented by holding stream functions constant. The derived equations are given in terms of the gradients of stream functions and velocity field. Examples demonstrate how to calculate the stream functions for analytically defined vel...

Country-Specific Mortality and Growth Failure in Infancy and Yound Children and Association With Material Stature Use interactive graphics and maps to view and sort country-specific infant and early dhildhood mortality and growth failure data and their association with maternal

Consider the dynamics of turbulent flow in rivers, estuaries and floods. Based on the widely used k-epsilon model for turbulence, we use the techniques of centre 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 dyna...

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 pr...

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 on plane. Linear interpolation is used to approximate velocity fields. Demonstration examples show that the method is very accurate.

The paper presents novel modeling of fuzzy inference system by using the ‘fuzzified’ radial basis function (RBF) neural network (NN). RBF NN performs the mapping of the antecedent fuzzy numbers (a.k.a. membership functions, attributes, possibilities degrees) into the consequent ones. In this way, an RBF NN is capable of performing the rigorous calc...

Mass conservation is a key issue for accurate streamline and stream surface visualization of flow fields. This paper complements an existing method (Feng et al., 1997) for CFD velocity fields defined at discrete locations in space that uses dual stream functions to generate streamlines and stream surfaces. Conditions for using the method have been...

In applications of centre manifold theory we need more flexible error estimates than that provided by, for example, the Approximation Theorem~3 by Carr (1981,1983). Here we extend the theory to cover the case where the order of approximation in parameters and that in dynamical variables may be completely different. This allows, for example, the eff...

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.

Consider the 3D flow of a viscous Newtonian fluid upon a curved 2D 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 and the average lateral velocity. Based upon centre manifold theory,...

Consider the dynamics of turbulent flow in rivers, estuaries and floods. Based on the widely used k-epsilon model for turbulence, we use the techniques of centre 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 dyna...

The turbulent flow of shallow layer of fluid as occurs in rivers, estuaries and floods is modelled using the centre manifold reduction of the k-ε model for turbulence. The modelling technique is based on rational and mathematically sound arguments and does not require any ad-hoc assumptions on ordering in the problem. The resulting new dynamical mo...

Models and simulations of the flow of thin films of fluids have many important applications in industrial and natural processes. We consider the motion of a thin layer of an incompressible, Newtonian fluid over an arbitrary solid, stationary curved substrate. Earlier work by Roy, et al has modeled slow fluid flows in which inertia is negligible. Ho...