Extension of weakly compressible approximations to incompressible thermal flows

Weakly compressible and advection approximations of incompressible isothermal flows were developed and tested in (Commun. Numer. Methods Eng. 2006; 22:831-847). In this paper, we extend the method to solve equations governing incompressible thermal flows. The emphasis is again on the reconstruction of unconditionally stable numerical scheme such that, restriction on time steps, projection procedures, solution of linear system of algebraic equations and staggered grids are completely avoided in its implementation. These features are achieved by combining a low-Mach asymptotic in compressible flow equations with a semi-Lagrangian method for the weakly compressible approach. The time integration is carried out using an explicit Runge-Kutta with variable stages. The method is applied to the natural convection flows in a squared cavity for both steady and transient computations. The numerical results demonstrate high resolution of the proposed method and confirm its capability to provide accurate and efficient simulations for thermal flow problems. Copyright (c) 2006 John Wiley & Sons, Ltd.