Development and Validation of a High-Order Fully-Implicit DNS/LES Algorithm for Transitional and Turbulent Buoyant Flows with Heat Transfer

A high-order, finite-volume algorithm specially designed for simulating low-Mach number, variable-density, buoyancy- and thermally-driven, transitional and turbulent flows with or without heat transfer is proposed. For this purpose, the fully-implicit, non-dissipative, discrete kinetic energy-conserving Direct Numerical Simulation (DNS) algorithm is combined with high-order, symmetric/central-differencing finite-volume approximations. The Wall-Adapting Local Eddy-viscosity (WALE) model is also utilized for subgrid-scale (SGS) modeling. To validate the proposed algorithm, two types of flows are considered; the turbulent Rayleigh-Benard Convection (RBC) and the Rayleigh-Taylor Instability (RTI). The selected problems include various mechanisms and multiple scales such as baroclinic vorticity, diffusion, mixing, interface interactions, density gradients, buoyancy and thermal forces. All those effects drive the flows into a transitional regime that eventually results in a relative turbulent state. As the first aim of this ongoing study, the proposed algorithm is successfully validated against the two challenging test cases. The results show its efficiency on coarse grids. Additionally, the wall-clock time of the computations are only 10-15% higher than the lower-order ones and unlike the many other high-order methods such as spectral, compact, WENO-type or DG, the proposed one is easy to implement into an existing code, relatively low-cost, robust, extendable to complex geometries and not seriously limited by flow physics or numerical constraints, due to inherently advanced properties of the base algorithm. The very small discrepancies observed near walls in RBC may point out that a more careful treatment of boundaries with walls might be required with the higher-order scheme.