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Solving one- and two-dimensional unsteady Burgers' equation using fully implicit finite difference schemes
Faculty
Engineering
Year:
2019
Type of Publication:
ZU Hosted
Pages:
Authors:
Norhan Alaaeldeen Mohamed Ali Hsan
Staff Zu Site
Abstract In Staff Site
Journal:
ARAB JOURNAL OF BASIC AND APPLIED SCIENCES Taylor & Francis Group
Volume:
Keywords :
Solving one- , two-dimensional unsteady Burgers' equation using
Abstract:
This paper introduces new fully implicit numerical schemes for solving 1D and 2D unsteady Burgers’ equation. The non-linear Burgers’ equation is discretized in the spatial direction by using second order Finite difference method which converts the Burgers’ equation to nonlinear system of ODEs. Then, the backward differentiation formula of order two (BDF-2) is employed to march the solution in the time direction. The non-linear term in the obtained system is linearized without any transformation; and it forms a system of linear algebraic equations that is solved by using Thomas’s algorithm. Accuracy and performance of the proposed schemes are studied by using four test problems with Dirichlet and Neumann boundary conditions. Comparing the numerical results with exact solutions and the solutions of other schemes shows that the proposed schemes are simple, efficient and accurate even for the cases with high Reynolds numbers.
Author Related Publications
Norhan Alaaeldeen Mohamed Ali Hsan , "A novel differential-integral quadrature method for the solution of nonlinear integro-differential equations", John Wiley & Sons Ltd, 2021
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Norhan Alaaeldeen Mohamed Ali Hsan , "Surface energy effects on the nonlinear free vibration of functionally graded Timoshenko nanobeams based on modified couple stress theory", World Scientific Publishing Company, 2019
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Norhan Alaaeldeen Mohamed Ali Hsan , "Effective numerical technique applied for Burgers' equation of (1 + 1)-, (2 + 1)-dimensional, and coupled forms", John Wiley & Sons, Ltd, 2021
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Norhan Alaaeldeen Mohamed Ali Hsan , "Effective numerical technique applied for Burgers' equation of (1+1)-, (2+1)-dimensional, and coupled forms", Wiley, 2021
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Norhan Alaaeldeen Mohamed Ali Hsan , "Free vibration analysis of nonlocal viscoelastic nanobeam with holes and elastic foundations by Navier analytical method", Techno-Press, 2023
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Department Related Publications
Salwa Amien Mohamed ebrhiem, "Adaptive FAS-Multigrid Method for Nonlinear Elliptic Equations on Unstructured Grids", لايوجد, 1900
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Amr Mohamed Salaheldeen Abdelaziem Mohamed, "Evaluation o Green's unction derivatives or exponentially graded elasticity", لايوجد, 1900
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Salwa Amien Mohamed ebrhiem, "Optimally efficient multigrid algorithms for incompressible Euler equations", Emerald Group Publishing Limited, 2008
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Salwa Amien Mohamed ebrhiem, "Adaptive FAS-multigrid method for nonlinear elliptic equations on unstructured grids", Wiley InterScience, 2007
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Rania Bahgat Mohamed Amer, "An Efficient Method To Solve Thermal Wave Equations", Published by Scientific Research Publishing, 2014
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