Abdullah Shah | COMSATS Institute of Information Technology (original) (raw)

Papers by Abdullah Shah

Research paper thumbnail of Fully decoupled pressure projection scheme for the numerical solution of diffuse interface model of two-phase flow

Communications in Nonlinear Science and Numerical Simulation, Sep 1, 2022

Research paper thumbnail of Numerical solution of coupled Cahn–Hilliard Navier–Stokes equations for two‐phase flows having variable density and viscosity

Mathematical Methods in The Applied Sciences, Aug 2, 2023

This work is concerned with the implementation of a decoupled diffuse interface approach for the ... more This work is concerned with the implementation of a decoupled diffuse interface approach for the numerical solution of two‐phase flows with a moving interface. The underlying two‐phase flow model consists of a mass‐preserving Cahn–Hilliard (CH) equation coupled with the incompressible Navier–Stokes equations (NSEs) through surface tension. Due to the higher order nonlinearity and stiff nature of the CH equation, its numerical solution is very challenging. We have used the decoupled pressure projection method for the numerical simulation of the governing equations. The spatial variables are discretized using the finite difference scheme on the staggered grids, while the explicit Euler method is used for time discretization. Four examples include the coalescence of inline rising bubbles, the obliques coalescence of two rising bubbles, and the deformation of single and two different‐sized bubbles in a shear flow field is numerically simulated. It is observed that the scheme is capable of tracking the interface accurately and respecting mass conservation and energy dissipation. Moreover, the scheme is efficient, easily implementable, energy stable, and fully decoupled.

Research paper thumbnail of Simulation of Incompressible Flow in Two Sided Lid Driven Cavity using Upwind Compact Scheme

CFD Letters, Jul 10, 2013

In this paper, the flow inside the two sided lid driven cavity is simulated using third order upw... more In this paper, the flow inside the two sided lid driven cavity is simulated using third order upwind compact finite difference scheme based on flux difference splitting in combination with artificial compressibility approach. The results are compared with alternate direction implicit finite difference scheme. Unlike single lid driven cavity, there is free shear layer and two symmetric secondary eddies growing in size directly with Reynolds numbers for parallel wall motion. However, for anti parallel wall motion the eddy structure changes, the secondary eddies appear in upper left and lower right corners

Research paper thumbnail of A One-Parameter Memoryless DFP Algorithm for Solving System of Monotone Nonlinear Equations with Application in Image Processing

Mathematics, Mar 2, 2023

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Research paper thumbnail of An Operator Splitting Scheme for Numerical Simulation of Spinodal Decomposition and Microstructure Evolution of Binary Alloys

Research paper thumbnail of Modified optimal Perry conjugate gradient method for solving system of monotone equations with applications

Applied Numerical Mathematics, Feb 1, 2023

Research paper thumbnail of A projection-based derivative free DFP approach for solving system of nonlinear convex constrained monotone equations with image restoration applications

Journal of Applied Mathematics and Computing

Research paper thumbnail of A Numerical Method for Two-Phase Flow with its Application to the Kelvin Helmholtz Instability Problem

Research paper thumbnail of Scaled Three-Term Conjugate Gradient Methods for Solving Monotone Equations with Application

Symmetry

In this paper, we derived a modified conjugate gradient (CG) parameter by adopting the Birgin and... more In this paper, we derived a modified conjugate gradient (CG) parameter by adopting the Birgin and Marti´nez strategy using the descent three-term CG direction and the Newton direction. The proposed CG parameter is applied and suggests a robust algorithm for solving constrained monotone equations with an application to image restoration problems. The global convergence of this algorithm is established using some proper assumptions. Lastly, the numerical comparison with some existing algorithms shows that the proposed algorithm is a robust approach for solving large-scale systems of monotone equations. Additionally, the proposed CG parameter can be used to solve the symmetric system of nonlinear equations as well as other relevant classes of nonlinear equations.

Research paper thumbnail of Numerical solution of a phase field model for incompressible two-phase flows based on artificial compressibility

Computers & Fluids, 2011

This article appeared in a journal published by Elsevier. The attached copy is furnished to the a... more This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/copyright

Research paper thumbnail of Solution of a System of Nonlinear Convex Constrained Monotone Equations using BFGS Method of Projection Approach with Application in Motion Control

This paper presents the scaling memoryless Broyden-Fletcher-Goldfarb-Shanno (BFGS) method for sol... more This paper presents the scaling memoryless Broyden-Fletcher-Goldfarb-Shanno (BFGS) method for solving a system of nonlinear convex constrained monotone equations. The optimal value of the scaling parameter is obtained by minimizing the condition number. A derivative-free memoryless BFGS projection-based algorithm is proposed. The global convergence of the algorithm is obtained analytically and some test problems are solved numerically. The computed results are compared with the available results in the literature. It is observed that the proposed algorithm performs well in terms of CPU time, number of iterations and function evaluations. Furthermore, the proposed method is successfully applied to robot manipulator motion control.

Research paper thumbnail of Effect of Couple Stresses on Flow of Third Grade Fluid between Two Parallel Plates using Homotopy Perturbation Method

International Journal of Nonlinear Sciences and Numerical Simulation, 2009

In this paper, an analytical analysis of the steady flow of an incompressible, third grade fluid ... more In this paper, an analytical analysis of the steady flow of an incompressible, third grade fluid between two parallel plates is carried out where the effect of couple stresses is taken into account. Depending on the relative motion of the plates, four different problems are studied: Couette flow, Plug flow, plane Poiseuille flow and generalized plane Couette flow. The solutions are obtained for the developed non-linear equations using the traditional perturbation method as well as the recently introduced homotopy perturbation method. Analytical expressions are given for the velocity field. It is observed that the homotopy perturbation method is more well-organized and flexible than the traditional perturbation method.

Research paper thumbnail of Simulation of different flow regimes in a narrow-gap spherical Couette flow

Applied Mathematics and Computation, 2022

Research paper thumbnail of Numerical simulation of flow past rectangular cylinders with different aspect ratios using the incompressible lattice Boltzmann method

Journal of Mechanical Science and Technology, 2012

Research paper thumbnail of Flux-difference splitting-based upwind compact schemes for the incompressible Navier-Stokes equations

International Journal for Numerical Methods in Fluids, 2009

Research paper thumbnail of Upwind compact finite difference scheme for time-accurate solution of the incompressible Navier–Stokes equations

Applied Mathematics and Computation, 2010

Research paper thumbnail of A comparison of different numerical schemes in spherical Couette flow simulation

AIP Advances

We compare the performance of line Gauss-Seidel (LGS), point Gauss-Seidel (PGS), and alternating ... more We compare the performance of line Gauss-Seidel (LGS), point Gauss-Seidel (PGS), and alternating direction implicit (ADI) linear solvers used in the artificial compressibility method for the numerical solution of the three-dimensional incompressible Navier-Stokes equations. Spatial discretization is carried out using a fifth-order WENO scheme for the convective terms and a second-order central difference scheme for the viscous terms. A comparison is made by simulating the spherical Couette flow problem, with only the inner sphere rotating and the outer one fixed. OpenMP is used for numerical computation in parallel for the three schemes. First, we compare the numerical efficiency of the solvers by computing 0-vortex flow for a medium-gap σ = (R 2 − R 1)/R 1 = 0.25. Second, we make a residual comparison for a steadystate flow calculation based on the CFL number and artificial compressibility factor. Finally, we compare the three solvers for unsteady flow computations based on the artificial compressibility factor. The results show that the LGS solver is more reliable than the PGS and the ADI solvers. To show the accuracy of the LGS scheme, we compute different flow modes for an intermediate-gap clearance ratio σ = (R 2 − R 1)/R 1 = 0.14. The computed results have good agreement with the existing numerical results.

Research paper thumbnail of An Explicit Analytical Solution of a Slider Bearing with a Third Grade Non-Newtonian Fluid as Lubricant

This paper presents an analytical solution of an inclined slider bearing consisting of connected ... more This paper presents an analytical solution of an inclined slider bearing consisting of connected surfaces lubricated with a third grade (non-Newtonian) fluid. Dimension analysis and by order of magnitude comparison with the full Navier-Stokes equations give rise to a nonlinear lubrication equation in the film region. The homotopy analysis method (HAM) for strongly nonlinear problems is used to give explicit analytic solution of the problem. Both the velocity profile and pressure distribution are calculated approximately using this method and plotted graphically using different parameter values. The load carrying capacity of the bearing is discussed for a range of bearing parameters. The boundary layer effect developed near the lower wall is also presented.

Research paper thumbnail of An Implicit Numerical Scheme for Solution of Incompressible Navier-Stokes Equations on Curvilinear Grids

This article deals with implementation of a high-order finite difference scheme for numerical sol... more This article deals with implementation of a high-order finite difference scheme for numerical solution of the incompressible NavierStokes equations on curvilinear grids. The numerical scheme is based on pseudo-compressibility approach. A fifth-order upwind compact scheme is used to approximate the inviscid fluxes while the discretization of metric and viscous terms is accomplished using sixth-order central compact scheme. An implicit Euler method is used for discretization of the pseudotime derivative to obtain the steady-state solution. The resulting block tridiagonal matrix system is solved by approximate factorization based alternating direction implicit scheme (AF-ADI) which consists of an alternate sweep in each direction for every pseudo-time step. The convergence and efficiency of the method are evaluated by solving some 2D benchmark problems. Finally, computed results are compared with numerical results in the literature and a good agreement is observed.

Research paper thumbnail of Steady viscous flow inside deep, shallow and skewed cavities by an implicit Navier-Stokes solver

International Journal of Advanced and Applied Sciences, 2018

Article history: Received 9 August 2017 Received in revised form 20 November 2017 Accepted 30 Nov... more Article history: Received 9 August 2017 Received in revised form 20 November 2017 Accepted 30 November 2017 In this paper, accurate and efficient calculations of the flow inside different types of cavities are presented. The incompressible Navier-Stokes equations are expressed in generalized curvilinear coordinates using artificial compressibility method. The governing equation in conservative form is solved numerically using an upwind compact finite difference scheme. The solution algorithm for solving the resulting linear system of equation is approximate factorization based ADI scheme. The computed results are compared with the results in the literature and the agreement is good. Also the presence of multiple solution and critical value of aspect ratio and Reynolds number for two sided cavity calculated and compared.

Research paper thumbnail of Fully decoupled pressure projection scheme for the numerical solution of diffuse interface model of two-phase flow

Communications in Nonlinear Science and Numerical Simulation, Sep 1, 2022

Research paper thumbnail of Numerical solution of coupled Cahn–Hilliard Navier–Stokes equations for two‐phase flows having variable density and viscosity

Mathematical Methods in The Applied Sciences, Aug 2, 2023

This work is concerned with the implementation of a decoupled diffuse interface approach for the ... more This work is concerned with the implementation of a decoupled diffuse interface approach for the numerical solution of two‐phase flows with a moving interface. The underlying two‐phase flow model consists of a mass‐preserving Cahn–Hilliard (CH) equation coupled with the incompressible Navier–Stokes equations (NSEs) through surface tension. Due to the higher order nonlinearity and stiff nature of the CH equation, its numerical solution is very challenging. We have used the decoupled pressure projection method for the numerical simulation of the governing equations. The spatial variables are discretized using the finite difference scheme on the staggered grids, while the explicit Euler method is used for time discretization. Four examples include the coalescence of inline rising bubbles, the obliques coalescence of two rising bubbles, and the deformation of single and two different‐sized bubbles in a shear flow field is numerically simulated. It is observed that the scheme is capable of tracking the interface accurately and respecting mass conservation and energy dissipation. Moreover, the scheme is efficient, easily implementable, energy stable, and fully decoupled.

Research paper thumbnail of Simulation of Incompressible Flow in Two Sided Lid Driven Cavity using Upwind Compact Scheme

CFD Letters, Jul 10, 2013

In this paper, the flow inside the two sided lid driven cavity is simulated using third order upw... more In this paper, the flow inside the two sided lid driven cavity is simulated using third order upwind compact finite difference scheme based on flux difference splitting in combination with artificial compressibility approach. The results are compared with alternate direction implicit finite difference scheme. Unlike single lid driven cavity, there is free shear layer and two symmetric secondary eddies growing in size directly with Reynolds numbers for parallel wall motion. However, for anti parallel wall motion the eddy structure changes, the secondary eddies appear in upper left and lower right corners

Research paper thumbnail of A One-Parameter Memoryless DFP Algorithm for Solving System of Monotone Nonlinear Equations with Application in Image Processing

Mathematics, Mar 2, 2023

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Research paper thumbnail of An Operator Splitting Scheme for Numerical Simulation of Spinodal Decomposition and Microstructure Evolution of Binary Alloys

Research paper thumbnail of Modified optimal Perry conjugate gradient method for solving system of monotone equations with applications

Applied Numerical Mathematics, Feb 1, 2023

Research paper thumbnail of A projection-based derivative free DFP approach for solving system of nonlinear convex constrained monotone equations with image restoration applications

Journal of Applied Mathematics and Computing

Research paper thumbnail of A Numerical Method for Two-Phase Flow with its Application to the Kelvin Helmholtz Instability Problem

Research paper thumbnail of Scaled Three-Term Conjugate Gradient Methods for Solving Monotone Equations with Application

Symmetry

In this paper, we derived a modified conjugate gradient (CG) parameter by adopting the Birgin and... more In this paper, we derived a modified conjugate gradient (CG) parameter by adopting the Birgin and Marti´nez strategy using the descent three-term CG direction and the Newton direction. The proposed CG parameter is applied and suggests a robust algorithm for solving constrained monotone equations with an application to image restoration problems. The global convergence of this algorithm is established using some proper assumptions. Lastly, the numerical comparison with some existing algorithms shows that the proposed algorithm is a robust approach for solving large-scale systems of monotone equations. Additionally, the proposed CG parameter can be used to solve the symmetric system of nonlinear equations as well as other relevant classes of nonlinear equations.

Research paper thumbnail of Numerical solution of a phase field model for incompressible two-phase flows based on artificial compressibility

Computers & Fluids, 2011

This article appeared in a journal published by Elsevier. The attached copy is furnished to the a... more This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/copyright

Research paper thumbnail of Solution of a System of Nonlinear Convex Constrained Monotone Equations using BFGS Method of Projection Approach with Application in Motion Control

This paper presents the scaling memoryless Broyden-Fletcher-Goldfarb-Shanno (BFGS) method for sol... more This paper presents the scaling memoryless Broyden-Fletcher-Goldfarb-Shanno (BFGS) method for solving a system of nonlinear convex constrained monotone equations. The optimal value of the scaling parameter is obtained by minimizing the condition number. A derivative-free memoryless BFGS projection-based algorithm is proposed. The global convergence of the algorithm is obtained analytically and some test problems are solved numerically. The computed results are compared with the available results in the literature. It is observed that the proposed algorithm performs well in terms of CPU time, number of iterations and function evaluations. Furthermore, the proposed method is successfully applied to robot manipulator motion control.

Research paper thumbnail of Effect of Couple Stresses on Flow of Third Grade Fluid between Two Parallel Plates using Homotopy Perturbation Method

International Journal of Nonlinear Sciences and Numerical Simulation, 2009

In this paper, an analytical analysis of the steady flow of an incompressible, third grade fluid ... more In this paper, an analytical analysis of the steady flow of an incompressible, third grade fluid between two parallel plates is carried out where the effect of couple stresses is taken into account. Depending on the relative motion of the plates, four different problems are studied: Couette flow, Plug flow, plane Poiseuille flow and generalized plane Couette flow. The solutions are obtained for the developed non-linear equations using the traditional perturbation method as well as the recently introduced homotopy perturbation method. Analytical expressions are given for the velocity field. It is observed that the homotopy perturbation method is more well-organized and flexible than the traditional perturbation method.

Research paper thumbnail of Simulation of different flow regimes in a narrow-gap spherical Couette flow

Applied Mathematics and Computation, 2022

Research paper thumbnail of Numerical simulation of flow past rectangular cylinders with different aspect ratios using the incompressible lattice Boltzmann method

Journal of Mechanical Science and Technology, 2012

Research paper thumbnail of Flux-difference splitting-based upwind compact schemes for the incompressible Navier-Stokes equations

International Journal for Numerical Methods in Fluids, 2009

Research paper thumbnail of Upwind compact finite difference scheme for time-accurate solution of the incompressible Navier–Stokes equations

Applied Mathematics and Computation, 2010

Research paper thumbnail of A comparison of different numerical schemes in spherical Couette flow simulation

AIP Advances

We compare the performance of line Gauss-Seidel (LGS), point Gauss-Seidel (PGS), and alternating ... more We compare the performance of line Gauss-Seidel (LGS), point Gauss-Seidel (PGS), and alternating direction implicit (ADI) linear solvers used in the artificial compressibility method for the numerical solution of the three-dimensional incompressible Navier-Stokes equations. Spatial discretization is carried out using a fifth-order WENO scheme for the convective terms and a second-order central difference scheme for the viscous terms. A comparison is made by simulating the spherical Couette flow problem, with only the inner sphere rotating and the outer one fixed. OpenMP is used for numerical computation in parallel for the three schemes. First, we compare the numerical efficiency of the solvers by computing 0-vortex flow for a medium-gap σ = (R 2 − R 1)/R 1 = 0.25. Second, we make a residual comparison for a steadystate flow calculation based on the CFL number and artificial compressibility factor. Finally, we compare the three solvers for unsteady flow computations based on the artificial compressibility factor. The results show that the LGS solver is more reliable than the PGS and the ADI solvers. To show the accuracy of the LGS scheme, we compute different flow modes for an intermediate-gap clearance ratio σ = (R 2 − R 1)/R 1 = 0.14. The computed results have good agreement with the existing numerical results.

Research paper thumbnail of An Explicit Analytical Solution of a Slider Bearing with a Third Grade Non-Newtonian Fluid as Lubricant

This paper presents an analytical solution of an inclined slider bearing consisting of connected ... more This paper presents an analytical solution of an inclined slider bearing consisting of connected surfaces lubricated with a third grade (non-Newtonian) fluid. Dimension analysis and by order of magnitude comparison with the full Navier-Stokes equations give rise to a nonlinear lubrication equation in the film region. The homotopy analysis method (HAM) for strongly nonlinear problems is used to give explicit analytic solution of the problem. Both the velocity profile and pressure distribution are calculated approximately using this method and plotted graphically using different parameter values. The load carrying capacity of the bearing is discussed for a range of bearing parameters. The boundary layer effect developed near the lower wall is also presented.

Research paper thumbnail of An Implicit Numerical Scheme for Solution of Incompressible Navier-Stokes Equations on Curvilinear Grids

This article deals with implementation of a high-order finite difference scheme for numerical sol... more This article deals with implementation of a high-order finite difference scheme for numerical solution of the incompressible NavierStokes equations on curvilinear grids. The numerical scheme is based on pseudo-compressibility approach. A fifth-order upwind compact scheme is used to approximate the inviscid fluxes while the discretization of metric and viscous terms is accomplished using sixth-order central compact scheme. An implicit Euler method is used for discretization of the pseudotime derivative to obtain the steady-state solution. The resulting block tridiagonal matrix system is solved by approximate factorization based alternating direction implicit scheme (AF-ADI) which consists of an alternate sweep in each direction for every pseudo-time step. The convergence and efficiency of the method are evaluated by solving some 2D benchmark problems. Finally, computed results are compared with numerical results in the literature and a good agreement is observed.

Research paper thumbnail of Steady viscous flow inside deep, shallow and skewed cavities by an implicit Navier-Stokes solver

International Journal of Advanced and Applied Sciences, 2018

Article history: Received 9 August 2017 Received in revised form 20 November 2017 Accepted 30 Nov... more Article history: Received 9 August 2017 Received in revised form 20 November 2017 Accepted 30 November 2017 In this paper, accurate and efficient calculations of the flow inside different types of cavities are presented. The incompressible Navier-Stokes equations are expressed in generalized curvilinear coordinates using artificial compressibility method. The governing equation in conservative form is solved numerically using an upwind compact finite difference scheme. The solution algorithm for solving the resulting linear system of equation is approximate factorization based ADI scheme. The computed results are compared with the results in the literature and the agreement is good. Also the presence of multiple solution and critical value of aspect ratio and Reynolds number for two sided cavity calculated and compared.