A fourth-order compact finite difference method for solving natural convection in rectangular enclosures

A new fourth order compact finite difference method for solving transient natural convection in rectangular enclosures is developed. First, finite difference approximations based on Padé schemes are developed to discretize spatial derivatives in the advection-diffusion equations of vorticity and tem...

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Bibliographic Details
Main Authors: Leonard, Christopher, Harahap, Caesar Ondolan
Format: Conference Proceeding
Language:English
Subjects:
Advection-diffusion equation
Enclosures
Finite difference method
Free convection
Mathematical analysis
Numerical methods
Poisson equation
Runge-Kutta method
Vorticity
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Summary:A new fourth order compact finite difference method for solving transient natural convection in rectangular enclosures is developed. First, finite difference approximations based on Padé schemes are developed to discretize spatial derivatives in the advection-diffusion equations of vorticity and temperature. Then, a different fourth-order compact finite difference method was utilized to solve the Poisson’s equation for the stream function. The system of equations is then time-marched using a fourth-order Runge-Kutta method. The numerical method is then validated by applying it to the natural convection in a square cavity problem. It is shown that good agreement with results of the benchmark solution can be obtained with much fewer grid points.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0188442