A Combined Analytic and Numerical Procedure for Stagnation-Point Flow
Applied and Computational Mathematics
Volume 6, Issue 2, April 2017, Pages: 75-82
Received: Jan. 8, 2017; Accepted: Feb. 7, 2017; Published: Mar. 14, 2017
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Okey Oseloka Onyejekwe, Computational Science Program, Faculty of Natural Science, Addis Ababa University, Arat-Kilo Campus, Addis Ababa, Ethiopia
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The two dimensional vector form of the Navier-Stokes equation is reduced to a fourth–order equation for the streamfunction. Boundary conditions arise from considerations of the no-slip constraint at the surface as well the interaction of viscous flow with potential-flow at the edge of the boundary layer. By employing a separation of variables technique and introducing certain dimensionless variables, the stream function equation is converted into its dimensionless analog with appropriate boundary conditions. The resulting quasi-linear third-order ordinary differential equation facilitates the numerical computation of the velocity and the pressure terms. This is achieved by solving the nonlinear two-point boundary-value problem with a time-marching method involving a Crank-Nicolson and Newton-linearization schemes until steady-state solution is obtained. The velocity, stream-function and pressure profiles are discussed with reference to various computation parameters and are found to be in good agreement with the physics of the problem. It was also found that there is no penalty in accuracy for a broad range of CFL numbers. However as the CFL number exceeds a certain threshold, the approach to convergence becomes erratic as indicated by the spurious results produced by the solution residuals.
Navier-Stokes Equation, Streamfunction, CFL Number, Fourth-Order Equation, Quasi-Linear Third-Order Differential Equation, Crank-Nicolson, Newton-Linearization
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Okey Oseloka Onyejekwe, A Combined Analytic and Numerical Procedure for Stagnation-Point Flow, Applied and Computational Mathematics. Vol. 6, No. 2, 2017, pp. 75-82. doi: 10.11648/j.acm.20170602.12
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