Key words. adaptive mesh refinement, buoyant plumes, large eddy simulation

Numerical simulation of turbulent buoyancy driven plumes is characterized by two distinct length and time scales. Buoyancy induces large scale mixing of air and other species, forming a plume which can persist as an organized structure over large length scales. These large scale vortical structures have a puffing frequency that is inversely proportional to the square root of the length scales of these structures. The small scales tend to reduce the buoyant force by local mixing phenomena. Global refinement to capture the details at smaller length scales is not practical in many applications. Local mesh refinement provides an efficient alternative to global refinement. Motivation to simulate buoyant plumes and capture the salient flow features in the regions where small scale mixing occurs led us to develop a code with the capability of Adaptive Mesh Refinement (AMR). The coupled AMR, Large Eddy Simulation (LES) procedure allows us to capture the information at the scales of the large structures with a higher fidelity and also the details which require a sub grid scale LES model.

Our approach uses a filtered form for the variable density incompressible flow equations that conserves both mass and momentum. We use a collocated grid for our computations. The projection formulation used avoids any velocity – pressure decoupling. The method is based on a projection formulation for momentum equations in which we first solve the advection – diffusion equations to predict intermediate velocities. We then project the velocities after interpolating them on to the faces to enforce the continuity constraint. This projection method successfully handles “large density” variations of ten to one observed in buoyant plume applications. This approach is implemented in SAMRAI (Structured Adaptive Mesh Refinement Application Infrastructure), an AMR framework from Lawrence Livermore National Laboratory (LLNL) developed for structured hierarchical grids. For solving the pressure poisson equation on a composite mesh, we use Fast Adaptive Composite (FAC) solver in SAMRAI, which is a multilevel solver. The FAC solver interfaces with HYPRE [developed at LLNL] linear solvers on the coarsest level. The time integration algorithm is a recursive procedure for each level of refinement. For this study, the criteria used for grid refinement is the gradient of the mass fraction of a specie.

Verification and Validation of our method is done to assess its accuracy and reliability. Verification tests are carried out by using the analytical solutions for Eulers equation and Navier Stokes equations on a periodic box. These test examples demonstrate the accuracy and convergence properties of the algorithm. Validation of the code is carried out by demonstrating the performance of the method on a more relevant problem, in which a jet of light density fluid like Helium mixes in ambient air in the computational domain.