NUMERICAL SOLUTIONS OF NATURAL CONVECTION IN A SQUARE CAVITY BY GENERALISED DIFFERENTIAL QUADRATURE

Abstract

For the first time, this report presents the computation of the two-dimensional incompressible Navier-Stokes equations with primitive variable form by using the GDQ method. The spatial derivatives of the governing equations for the natural convection in a square cavity are discretised using the GDQ method. The numerical results are obtained by using the SIMPLE method and the pressure-correction equation is solved by using the SOR method. It is proven that the numerical result obtained by the GDQ method using fewer grid points is more accurate and efficient than the standard FD method. It is also proven that updating the pressure at the boundary enhances both the accuracy and the convergence rate of the simulation. In addition, the numerical results are obtained by using the SIMPLER and PISO methods. It is found that the SIMPLER method is more efficient than the PISO and SIMPLE methods in such problem.