A NEW SOLVER FOR NON-ISOTHERMAL FLOWS IN NATURAL AND MIXED CONVECTION

Abstract

Most thermal fluid flow of real-life practical problems fall in the category of low Mach-number or incompressible flow (e.g., industrial flows inside ducts, or around stationary/moving objects, flows in biological/biomedical problems, or atmospheric flows). Several numerical techniques have been proposed for simulation of thermal flows, Finite Difference (FDM), Finite Element (FEM), Finite Volume (FVM) and Lattice Boltzmann (LBM) methods. Unlike the FVMs and FEMs, the classical FDMs show some difficulties in handling irregular geometries. Conventional formulation of FEMs (e.g., Galerkin FEMs) suffers from the lack of local mass balance, recovered by modified formulations (Narasimhan & Witherspoon, 1976). In the Discontinuous Galerkin FEMs (DG-FEMs) high-order accuracy is achieved using discontinuous high-order polynomial approximation within the computational elements. The main drawback of DG-FEMs are the high computational cost and variable storage requirement, compared to the classical FEMs and FVMs. LBMs were originally proposed to simulate weakly compressible flows, and only recently they have been applied to incompressible flows (e.g., Guo et al., 2000). We present a new FVM solver for the solution of incompressible non-isothermal flows in natural and mixed convection over unstructured triangular meshes. The Incompressible Navier-Stokes Equations (INSEs) are solved along with the Energy Conservation Equation (ECE). Fluid velocity and temperature are coupled in the buoyancy term of the momentum equations, assuming small variations of the fluid density due to temperature, according to the Oberbeck–Boussinesq approximation (e.g., Patel & Chhabra, 2019). Two numerical procedures, recently proposed to solve 1) the INSEs (Aricò et al., 2021) and 2) the transport problem of a passive scalar (Aricò & Tucciarelli, 2007), are adjusted to solve the governing equations of the present problem. Unstructured meshes easily discretize irregular geometries, and do not require interpolation operations between the underlying Cartesian mesh and the irregular boundaries as in the Immersed Boundary methods. Local refinements can be easily performed, avoiding unnecessary mesh refining in large portions of the domain.