A numerical framework for low-speed flows with large thermal variations

Abstract

In the numerical simulation of fluid dynamic problems there are situations in which low-speed flows exhibit a non-negligible density variation driven by thermal or compositional distributions. A new method for solving the Low Mach Number equations governing such flows is developed. The basis of the formulation is the semi-implicit scheme build on the Non-oscillatory Forward-in-Time integrator encompassing Multidimensional Positive Definite Advection Transport Algorithm and a robust Krylov solver. The spatial discretisation is constructed using the median dual finite volumes and the method is second-order-accurate in space and time. A collocated arrangement of all flow variables is implemented. The validity of the presented method is evaluated using the Differentially Heated Cavity flows. Three-dimensional simulations demonstrate its efficacy and ability to capture the Non-Oberbeck–Boussinesq effects. Ideally, a numerical method should be able to treat different flow regimes without strong limitations. When implemented, it is shown that in the limit of small density variations the new formulation correctly reproduces simulations of incompressible flows subject to the Oberbeck–Boussinesq approximation. Furthermore, the three-dimensional computations set to the quasi-two-dimensional cases are in excellent agreement with the established two-dimensional Differentially Heated Cavity benchmarks.