Global Coefficient Adjustment Method for Neumann Condition in Explicit Chebyshev Collocation Method and Its Application to Compressible Navier-Stokes Equations

1993 ◽  
Vol 107 (1) ◽  
pp. 160-175 ◽  
Author(s):  
Jian-Ping Wang ◽  
Yoshiaki Nakamura ◽  
Michiru Yasuhara
Keyword(s):  
Collocation Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Neumann Condition ◽  
Chebyshev Collocation Method ◽  
Navier Stokes Equations ◽  
Adjustment Method ◽  
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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