Computing singular solutions of the Navier-Stokes equations with the Chebyshev-collocation method

2001 ◽  
Vol 36 (2) ◽  
pp. 125-163 ◽  
Author(s):  
O. Botella ◽  
R. Peyret
Keyword(s):  
Collocation Method ◽  
Stokes Equations ◽  
Singular Solutions ◽  
Navier Stokes ◽  
Chebyshev Collocation Method ◽  
Navier Stokes Equations ◽  
Chebyshev Collocation

scholarly journals Instability of Rayleigh-Bernard Convection Affected by Upper Wall Temperature Variation

2020 ◽  
Author(s):  
Sadoon Ayed ◽  
Keyword(s):  
Energy Equation ◽  
Stokes Equations ◽  
Time Discretization ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Chebyshev Collocation Method ◽  
Step Method ◽  
Navier Stokes Equations ◽  
Numeric Simulation ◽  
Pseudo Spectral

This paper represents the analysis of Rayleigh-Bernard convection between two parallel plates. Lower wall is being cooled while upper is heated according to periodic spatial distribution. This process has been modeled using Navier-Stokes equations, equation of continuity and energy equation. Solution of the differential equations has been obtained using pseudo spectral numeric method. For discretization in homogeneous direction, Fourier-Galerkin model has been used, while for discretization in inhomogeneous direction Chebyshev collocation method is applied. Time discretization has been performed using Adams-Bashworth two step method of second order. The results of numeric simulation have been presented by figures where vorticity fields, stream-function and velocity are shown for six different time steps.

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