A new solver for incompressible non-isothermal flows in natural and mixed convection over unstructured grids

In the present paper we propose a new numerical methodology for the solution of 2D non-isothermal incompressible flows for natural and mixed convection in irregular geometries. The governing equations are the Incompressible Navier-Stokes equations and the energy conservation equation. Fluid velocity and temperature are coupled in the buoyancy term of the momentum equations according to the Oberbeck-Boussinesq approximation. The governing equations are discretized over unstructured triangular meshes satisfying the Delaunay property. Thanks to the Oberbeck-Boussinesq hypothesis, the flow and energy problems are solved in an uncoupled way, and two fractional time step procedures are sequentially applied to solve each problem. The prediction steps of both procedures are solved applying a Marching in Space and Time (MAST) numerical Eulerian scheme, which explicitly handles the non-linear terms in the momentum equations of the fluid problem, and allows numerical stability for Courant numbers greater than one. An analytical solution is applied for the prediction thermal problem. The correction steps of the two fractional time step procedures involve the solution of large linear systems, whose matrices are sparse and symmetric and have the “M” property if the mesh satisfies the Delaunay condition. This allows a well performing condition number. The matrix coefficients are constant in time, so that they are calculated and factorized only once, before the simulations loop starts, saving a lot of computational time. We present four numerical applications. For the first test, an analytical solution is available, and this makes it possible to analyze the spatial convergence order of the numerical solver. In the other applications, we investigate the capability of the proposed algorithm to handle irregular geometries, and we compare the computed results with experimental data and the outputs of literature models. A study of the required computational costs is also presente