Chinedu NwaigweRivers State University · Mathematics (Computational and Applied Maths Group)
Chinedu Nwaigwe
PhD (Warwick), MSc (RSUST), BSc (RSUST), DNIIT (NIIT)
My research is centered around Numerical Analysis, Scientific Computing and Computational Fluid Dynamics.
About
62
Publications
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Introduction
Chinedu is interested in Numerical Algorithms and Analysis, Scientific Computing, and Computational Fluid Dynamics. He specializes in developing C++ and Python algorithms for (i) solving ordinary and partial differential equations, nonlinear functional integral equations and integro-differential equations, and (ii) for simulating transport process.
Additional affiliations
October 2018 - September 2020
Position
- Lecturer I in Mathematics
Description
- Conduct Research and Teaching in Mathematics. Supervise Graduate and Undergraduate projects including PhDs. Successfully supervised one PhD in Applied Mathematics.
Publications
Publications (62)
In some applications, nano-sized particles are used to enhance heat transfer in thermal energy systems. Two important practical concerns are the shape of the nanoparticles and the volume fraction that would lead to optimal performance. This study investigates the effects which the shape and volume fraction of copper nanoparticles may have on the ve...
A sixth order accurate numerical method is proposed for nonlinear integral equations of the Fredholm type. First the problem is dis-cretized and the integral approximated by the classical second order trapezoid rule. Then, the leading truncation error terms of the quadra-ture rule are approximated. The first derivatives in the error term are approx...
This paper proposes a simple idea to speed-up the convergence of a fixed-point iteration for Fredholm equation defined on a mesh. First, the analytical problem is discretized by using quadrature rule and col-locating at mesh points. Banach Fixed-Point Theorem is used to construct a discrete Picard scheme (PS). To accelerate the computations, the Pi...
Many fixed point iterative methods have been proposed. Their authors provide, theoretically, the rate ofconvergence which indicates how much the error changes after one iteration step. Of practical importanceare the CPU time required by each method and their accuracy. This has never been investigated. In thiswork we investigate nine iterative proce...
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In medical applications some nano-sized particles can be used to guide the delivery of drugs to desired sites in the human body. Understanding the effects of pertinent parameters of the nanoparticle on blood flow is crucial for optimal drug delivery. In this article, we present a model for the flow of nanofluid made of blood and aluminum oxide part...
The current study theoretically and computationally analyses the viscoelastic Sisko fluids during the non-isothermal rollover web phenomenon. The mathematical modeling produces a system of partial differential equations, which we further simplify into ordinary differential equations through appropriate transformations. We have formulated the proble...
Reservoir simulation is an important but tough task in the petroleum sector. Reservoir properties (rocks and uids) exhibit uncertainties in their values thus, quantification of uncertainty of reservoir prediction models becomes a necessity. In this paper, an application of uncertainty quantification has been carried out using the Buckley Leverett m...
A fourth-order numerical method is proposed for solving first-order nonlinear
integro-differential equations. The method is based on finite difference
approximation of derivatives and an unconventional quadrature approximation
of integrals. The unconventional quadrature scheme emanates from
approximating the leading error term of the conventional t...
An unconditionally stable finite difference scheme is developed and fully analyzed for two-dimensional convection-diffusion-reaction equations with nonlinear coefficients and external sources. The well-known difficulty in obtaining a stable second-order discretization of the convection term is resolved by first adopting a central discretiza-tion in...
Abstract—It is well known that the classical trapezoidal rule (TR2) is only second order of convergence. However, Leonhard Euler and Colin Maclaurin had independently discovered that the error terms of TR2 can be represented as an infinite sum of terms in even powers of the mesh size. In this article, we exploit this error representation to constru...
This paper investigates the nonlinear dispersion of a pollutant in a non-isothermal incompressible flow of a temperature-dependent viscosity fluid in a rectangular channel filled with porous materials. The Brinkman-Forch-heimer effects are incorporated and the fluid is assumed to be variably permeable through the porous channel. External pollutant...
An efficient numerical algorithm is developed for solving nonlinear functional Volterra integral equations. The core idea is to define an appropriate operator, then combine the Krasnoselskij iterative scheme with collocation at discrete points and the Newton–Cotes quadrature rule. This results in an explicit scheme that does not require solving a n...
It is well known that the classical trapezoidal rule (TR2) is only second order of convergence. However, Leonhard Euler and Colin Maclau-rin had independently discovered that the error terms of TR2 can be represented as an infinite sum of terms in even powers of the mesh size. In this article, we exploit this error representation to construct a non...
This paper examined the problem of thermosolutal effects in a horizontal cylindrical channel with suction velocity. The fluid flow is assumed to be of constant viscosity, thermal conductivity, diffusivity and it is axi-symmetrical. The problem modelled followed the work of Ize et al.[24] by incorporating suction velocity to their work. Following th...
A fixed point method is developed on a mesh for the solution of nonlinear Fredholm equation. First, the problem is collocated at mesh points and a second order quadrature rule is used to approximate the nonlinear integral. Under the assumption of nonexpansivity of self-map, we construct an Ishikawa iteration to linearize the resulting system and ap...
We construct two numerical methods for solving nonlinear functional Fredholm integral equations and compare their accuracy and computational costs. First, the nonlinear integral is approximated with composite trapezoid rule on the mesh. Then Picard and Newton iterations are designed to linearize the nonlinear system and approximate the solution. Th...
An efficient numerical algorithm is developed for solving nonlinear functional Volterra integral equations. The core idea is to define an appropriate operator, then combine the Krasnoselskij iterative scheme with collocation at discrete points and Newton-Cote quadrature rule. This results to an explicit scheme that does not require to solve a non-l...
It is usually desirable to approximate the solution of mathematical problems with high-order of accuracy and preferably using compact stencils. This work presents an approach for deriving high-order compact discretization of heat equation with source term. The key contribution of this work is the use of Hermite polynomials to reduce second order sp...
This study examines the effect of viscosity and magnetic field on a non-isothermal cylindrical channel flow. This work considered a model of convective-thermal-diffusion with constant viscosity and magnetic field. The governing model equations are nondimensionalized using the dimensionless quantities and then solved analytically using power series...
This paper investigates the nonlinear dispersion of a pollutant in a non-isothermal incompressible flow of a temperature-dependent viscosity fluid in a rectangular channel filled with porous materials. Brinkman-Forchheimmer effects are incorporated and the fluid is assumed to be variably permeable through the porous channel. External pollutant inje...
This is my Curriculum Vitae. It gives you some idea about who I am, what I do, my research interests, the things I have done and the ones I am currently doing.
This study investigates chemical reaction and thermal radiation effects on hydromagnetic nanofluid flow over an exponentially stretching sheet. The governing partial differential equations were transformed to ordinary differential equations by using similarity transformation and the resulting equations were solved using asymptotic series method. Gr...
In this work, the combined effect of slip velocity, pulsatility of the blood flow and body acceleration effect on Newtonian unsteady blood flow past an artery with stenosis and permeable wall is theoretically studied with results discussed. The magnetic field is applied to the stenosed artery with permeable walls which is inclined at a varying angl...
This study analyses the effects of chemical reaction, slip effect and heat source on the MHD flow of blood through an inclined permeable artery with stenosis under body acceleration present. The blood is treated as a non-Newtonian electrically conduction fluid with accumulated substances of fatty substance in the blood cells creating porosity at th...
An investigation of a nonlinear mixed Volterra-Fredholm integral equation of the second kind is undertaken. The equation is constructed as a fixed-point problem, under the condition of Lipschitz continuity, the Generalized Banach fixed-point theorem is used to prove the existence of a unique solution. A double trapezoidal algorithm is constructed f...
An unconditionally stable difference scheme is developed and fully analyzed for two-dimensional convection-diffusion-reaction equations with nonlinear coefficients and external sources. The well-known difficulty in obtaining a stable second-order discretization of the convection term is resolved by first adopting a central discretization in space....
In this paper, we propose the subcell method to couple channel and flood flows. We adopt a 1D Saint Venant channel model with coupling terms and the 2D shallow water flood model. The channel flow is coupled to the flood through the discrete 1D coupling term which we derived in a closed form; while the flood is coupled to the channel flow through th...
This article investigated the treatment effect on LDL-C and atherosclerotic blood flow through microchannel with heat and magnetic field. The study involved the formulation of mathematical models which represent the blood momentum equation, LDL-C concentration and Energy equation, we also remodeled the region of atherosclerosis in order to incorpor...
In this article, we proposed some mathematical models to investigate the treatment effect of low density lipoprotein-Concentration and atherosclerotic blood flow in a porous micro-channel with metabolic heat and magnetic field. The heat contribution was through the hydrolysis of adenosine which aid blood circulation, and the lipid concentration was...
This study proposes analytical solution to the problem of transport in a Newtonian fluid within a cylindrical domain. The flow is assumed to be dominated along the channel axis, and is taken to be axi-symmetric. No-slip boundary condition is considered for velocity while the temperature and concentration have Dirichlet boundary values. The resultin...
This study proposes a mathematical model and the numerical scheme, with rigorous stability and convergence analyses, for a channel flow problem incorporating a nonstandard variable cross-diffusion (Soret-Dufour effects), an unconventional nonlinear radiative heat flux, and time-dependent wall velocity and wall temperature. This led to a system of h...
An unconditionally stable difference scheme is proposed for convection-diffusion-reaction equations (CDREs) with nonlinear coefficients and sources. A key requirement in addition to high-order accuracy, com-pactness of stencil and efficiency, is the capability to simulate purely convection problems (at least over short duration) without compromisin...
The importance of numerical flux solvers (NFS) in constructing conservative methods is well known, but it is not always clear which solvers more suitable for given conservation laws. To elucidate this, we compare some NFS for some conservation laws. The finite volume method is adopted as the base scheme and the selected models include linear, nonli...
Developing robust numerical schemes through meticulous and judicious applications of insight gained by many years of teaching and research in mathematical analysis, that provide accurate answers to Nonlinear Mathematical Models in Fluid Mechanics.
This paper studies the theoretical analyses and applications of a convergent numerical algorithm to the problem of heat transfer in a convective channel flow. The model equations are derived under the assumption of exponentially varying solution-dependent suction, and temperature-dependent heat source. We propose a finite difference scheme which is...
Purpose :
The purpose of this paper is to formulate and analyse a convergent numerical scheme and apply it to investigate the coupled problem of fluid flow with heat and mass transfer in a porous channel with variable transport properties.
Design/methodology/approach:
This paper derives the model by assuming a fully developed Brinkman flow with...
We extend previous studies of channel flows to porous media flows with combined effects of both heat and mass transfer. We consider a temperature-dependent viscosity fluid and a concentration dependent diffusivity in an unsteady and pressure-driven non-isothermal Brinkman flow. This leads to the governing equations for velocity, concentration a...
A sequential implicit numerical scheme is proposed for a system of partial differential equations defining the transport of heat and mass in the channel flow of a variable-viscosity fluid. By adopting the backward difference scheme for time derivative and the central difference scheme for the spatial derivatives, an implicit finite difference schem...
This study investigates the fluid flow and transport in a vertical channel with an exponentially decaying suction and mobile wall. The governing equations are derived based on the assumptions of incompressible flow with buoyancy forces and viscous dissipation. A finite-difference scheme is formulated and implemented. The numerical results are prese...
We investigate the heat and mass transfer in a variable-viscosity channel flow simultaneously accounting for viscous dissipation, external pollutant injection and Soret-Dufour effects. By adopting the Boussinesq approximation and assuming a fully developed uni-direction flow, the set of governing equations are presented. We formulate a finite diffe...
We propose a second-order finite difference scheme to study the flow of a viscous fluid in a stationary horizontal channel with porous walls. Following conservation principles, we obtain the governing equation in the form of a convection-diffusion problem. Naive discretization leads to either oscillatory solutions or low order accurate schemes. So...
Aims/ Objectives: To investigate the influence of a model parameter on the convergence of two finite difference schemes designed for a convection-diffusion-reaction equation governing the pressure-driven flow of a Newtonian fluid in a rectangular channel. Methodology: By assuming a uni-directional and incompressible channel flow with an exponential...
We investigate the effects of moving channel wall, thermal radiation and variable-thermal conductivity on the flow of a non-Newtonian fluid in a porous channel. The effects on fluid temperature variations are also studied. By assuming that both the fluid viscosity and thermal conductivity are temperature-dependent, and incorporating viscous dissipa...
This study investigates the fluid flow and transport in a vertical channel with an exponentially decaying suction and mobile wall. The governing equations are derived based on the assumptions of incompressible flow with buoyancy forces and viscous dissipation. A finite-difference scheme is formulated and implemented. The numerical results are prese...
This work investigates the free convection boundary layer flow in a rotating MHD fluid past a vertical porous medium with thermal radiation. The dimensionless coupled governing boundary layer partial differential equations under the Boussinesq and Rosseland approximations are transformed into ordinary differential equation by the perturbation techn...
This report describes the response to the 'hydraulic modelling of collection networks for civil engineering applications' challenge set by Sweco at the second Environmental Modelling in Industry Study Group. The solution was developed in workshops hosted by the Turing Gateway to Mathematics at the Newton Institute in Cambridge on 3-6 April 2017. Th...
A brief presentation of my research.
In this paper, we propose a novel approach for coupling 2D/1D shallow water flow models. Efficiently coupling these models is vital for simulating the flow and flooding of open channels. Currently, existing methods couple the models either at the channel lateral boundaries (lateral methods) or at the location, along the channel flow direction, wher...
One dimensional (1D) simulations of the flow and flooding of open channels are known to be inaccurate as the flow is multi-dimensional in nature, especially at the flooded regions. However, multi-dimensional simulations, even in two dimensions (2D), are computationally expensive, hence the problem of efficiently coupling 2D and 1D simulations for t...
This is the code architecture for the software I developed during my PhD. I used it for all the simulations in my PhD thesis.
Integral calculus is easy and accessible by integration by parts, but it is tedious and time-consuming. Nedu's theorem for integration is proposed and proved strictly, the new theorem is especially useful for an integrand involving products of a polynomial and an integrable function. The theorem can be also used as basic tool for Laplace transform...
This paper investigates the problem of MHD free convection and oscillatory flow of an optically thin fluid bounded by two horizontal porous parallel walls under the influence of an external imposed transverse magnetic field in a porous medium. By taking the radiative heat flux in the differential form and imposing an oscillatory time-dependent pert...
This paper investigates the problem of ground temperature under a vegetative cover with time dependent suction and radiative heat transfer. By assuming that the ground radiates heat from its' surface and that the radiative heat flux takes a differential form which follows that of Tarkhar et al [1], the problem was formulated. By imposing a regular...
This study presents the flow of an electrically conducting and radiating fluid over a moving heated porous plate in the presence of an induced magnetic field. By taking the radiative heat flux in the differential form of the optically thinness and imposing a time – dependent sinusoidal perturbation, the coupled non-linear partial differential equat...
This paper investigates the problem of MHD free convection and oscillatory flow of an optically thin fluid bounded by two horizontal porous parallel walls under the influence of an external imposed transverse magnetic field in a porous medium. By taking the radiative heat flux in the differential form and imposing an oscillatory time-dependent pert...
Questions
Questions (47)
I am using radial basis functions for a current problem, but these basis functions do not satisfy the kronecker-delta condition like the finite element basis functions. I would like to have a discussion on the efficient and state-of-art ideas on handling them for optimum performance.
Thank you in advance.
Chinedu
I need a collaborator with experience in code development and, if possible, numerical analysis too.
I am currently developing an open source code in python that can be used to solve different kinds of Integral Equations.
In the last one and half years I have done some work in numerical Algorithms for integral equations with some papers already published. It has culminated to several python codes which I have used to produce the results.
The codes are all private but the results are published so I am inclined to make these codes publicly available so that others can use them at no cost and minimum effort.
I, therefore, need a fellow Researcher who has good skills in software engineering and numerical analysis to join me in this line.
A minimum requirement is the knowledge of git and python.
You can email me at nwaigwe.chinedu@ust.edu.ng
The Banach fixed point theorem provides an iterative scheme (the Picard) for the fixed point of contraction maps and also close form expressions for the errors committed in the approximation.
I am wondering if there is a similar error estimate for the Krasnoselskij iteration which approximates the fixed point of non-expansive maps. I appreciate your help in advance.
The complete flow equations for a third grade flow can be derived from the differential representation of the stress tensor. Has anyone ever obtained any results, experimentally or otherwise, that indicate the space-invariance (constancy) of the velocity gradient, especially for 1D shear flow in the presence of constant wall-suction velocity? Under what conditions were the results obtained?
I have a 2D finite difference scheme to implement. I use C++ but do not want to write my own 2D grid as I would like to reuse the code for many other problems. Hence, I want to use a well-established code that provides all the functionalities that I may need. Deall ii fits this purpose but since deal is meant for FEM, I want to know if it is advisable to also use it for FDM.
Your thoughts are highly welcomed.
I need to multiply the inverse of a matrix A to another matrix B. If B were to be a vector, I would simply solve a linear system Ax = B to get the product x=inv(A)B. With B being a matrix, I don't know the most efficient way|method to compute inv(A)B.
Kindly share your experience.
