DNS of buoyancy-driven flows using EDAC formulation solved by high-order method.

Entropically Damped Artificial Compressibility (EDAC) equation-based solution method is investigated to simulate the incompressible Navier–Stokes equations for buoyancy-driven flows. The method introduces an evolution equation for pressure, which is used to close the system of equations. The resulting parabolic system removes the need to solve the traditional Poisson's equation at each time step. The energy equation with the Boussinesq approximation and the EDAC system of equations with the low Mach number approximation is solved for the thermal convection problem. This system is discretized using a sixth-order compact difference in space and advanced in time using an explicit fourth-order Runge–Kutta scheme. To investigate the suitability of the EDAC model for buoyancy flows, two widely used benchmark problems, namely: thermal cavity and Rayleigh–Bénard problems, are simulated. The simulation results are compared against the literature data. An excellent agreement is obtained, showing the feasibility and accuracy of the EDAC method in simulating buoyancy-driven flows. The EDAC pressure equation derived from entropy balance, together with the energy equation, are shown in this paper to model thermally dominant flows accurately. • Entropically Damped Artificial Compressibility (EDAC) method for simulating stratified flows. • Unsteady turbulent buoyancy-driven flow using EDAC. • Usage of high-order compact finite difference scheme. [ABSTRACT FROM AUTHOR]