A Computational Study with Finite Difference Methods for Second Order Quasilinear Hyperbolic Partial Differential Equations in Two Independent Variables

Stampolidis, Pavlos; Gousidou-Koutita, M.

doi:10.4236/am.2018.911079

Cited by 5 publications

(3 citation statements)

References 21 publications

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“…The effect of buoyancy which is characterized by a rise and fall in an enclosed path was crucial in the movement of the fluid. Stampolidis et al show a significant difference between dynamic viscosity enhancement and thermal conductivity was found to be useful [27]. The authors discussed the error, stability, and consistency of different methods in line with the results obtained.…”

Section: Introductionmentioning

confidence: 85%

Numerical Investigation of Fin Shape Optimization and Entropy of Magnetohydrodynamics Natural Convection Nanofluid Flow in a Cavity

2023

EOA

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The purpose of the investigation is to analyze the effect of fin length and position in terms of rotational angle on heat transmission and entropy generation. Different parameters such as Prandtl numbers, Hartmann numbers, Rayleigh numbers, and particle volume fractions are used to analyze nanofluid laminar flow behavior and temperature distribution. The fin has a significant impact on both the isotherm and the streamlines. Findings revealed that increasing the rotational angle of a spinning heat exchanger might result in more consistent temperature distribution along isotherms; larger fins, on the other hand, frequently provide greater heat dissipation due to increased surface area. Furthermore, when Rayleigh numbers increase, so does the temperature distribution between the fins and the surrounding fluid. The presence of a magnetic field affects fluid dynamics and contributes to the generation of entropy. Higher Prandtl numbers can result in the enhancement heat transfer phenomena and the generation of entropy.

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Section: Introductionmentioning

confidence: 85%

Numerical Investigation of Fin Shape Optimization and Entropy of Magnetohydrodynamics Natural Convection Nanofluid Flow in a Cavity

2023

EOA

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“…Experiment 2. Solve u tt − 2 2 u xx = 0 for x ∈ [0,1] and t ∈ [0,1] with initial conditions u(x, 0) = sin(πx) and u t (x, 0) = 0, and boundary conditions u(0, t) = u(1, t) = 0 [12].…”

Section: Numerical Experimentsmentioning

confidence: 99%

CTCS Schemes for Second Order Wave Equation: Numerical Results and Spectral Analysis

Appadu

Waal

2021

JERA

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IIn this paper, two finite difference methods are used to solve the one-dimensional second order wave equation with constant coefficients subject to specified initial and boundary conditions. Two numerical experiments are considered. The two methods are Central in Time and Central in Space scheme with second order accuracy in both time and space, abbreviated as CTCS (2,2) and Central in Time and Central in Space scheme with second order accuracy in time and fourth order accuracy in space, abbreviated as CTCS (2,4). Properties such as consistency and stability are studied. We also perform spectral analysis of dispersive and dissipative properties of the two methods. Two numerical experiments are considered, and the numerical results are displayed.

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“…The C-N implicit scheme combined with time efficient ADI combined using iterative methods produces even more efficient numerical solution model [15]. The central difference approximations of the C-N implicit scheme applied on initial value problems (IVP) of the quasi linear parabolic PDEs and hyperbolic PDEs produce more accurate numerical results than forward difference approximations with decreased steps sizes [4,17].…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of the Navier-Stokes Equations for Incompressible Fluid Flow by Crank-Nicolson Implicit Scheme

Charles¹,

John²,

Daniel³

2021

ACM

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The Navier-Stokes (N-S) equations for incompressible fluid flow comprise of a system of four nonlinear equations with five flow fields such as pressure P, density ρ and three velocity components u, v, and w. The system of equations is generally complex due to the fact that it is nonlinear and a mixture of the three classes of partial differential equations (PDEs) each with distinct solution methods. The N-S equations fully describe the unsteady fluid flow behaviour of laminar and turbulent types. Previous studies have shown existence of general solutions of fluid flow models but little has been done on numerical solution for velocity of flow in N-S equation of incompressible fluid flow by Crank-Nicolson implicit scheme. In practice, real fluid flows are compressible due to the inevitable variations in density caused by temperature changes and other physical factors. Numerical approximations of the general system of Navier-Stokes equations were made to develop numerical solution model for incompressible fluid flow. Adequate solutions of the latter produce numerical solutions applicable in numerical simulation of fluid flows useful in engineering and science. Non-dimensionalization of variables involved was done. Crank-Nicolson (C.N) implicit scheme was implemented to discretize partial derivatives and appropriate approximation made at the boundaries yielded a linear system of N-S equations model. The linear numerical system was then expressed in matrix form for computation of velocity field by Computational fluid dynamics (CFD) approach using MATLAB software. Numerical results for velocity field in two dimensional space, u(x,y,t) and v(x,y,t) generated in uniform 32×32 grids points of the square flow domains, 0≤x≤1.0 and 0≤y≤1.0 were presented in three dimensional figures. Results showed that the velocity in two dimensional space does not change suddenly for any change in spatial levels, x and y. Therefore, C-N implicit Scheme applied to solve the N-S equations for fluid flow is consistent.

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A Computational Study with Finite Difference Methods for Second Order Quasilinear Hyperbolic Partial Differential Equations in Two Independent Variables

Cited by 5 publications

References 21 publications

Numerical Investigation of Fin Shape Optimization and Entropy of Magnetohydrodynamics Natural Convection Nanofluid Flow in a Cavity

Numerical Investigation of Fin Shape Optimization and Entropy of Magnetohydrodynamics Natural Convection Nanofluid Flow in a Cavity

CTCS Schemes for Second Order Wave Equation: Numerical Results and Spectral Analysis

Numerical Solution of the Navier-Stokes Equations for Incompressible Fluid Flow by Crank-Nicolson Implicit Scheme

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