A Parallel Particle-Grid Method for the study of Scalar Advection in Turbulent Flows

The advection-diffusion equation in turbulent flows is a phenomenon that appears in various situation such as heat transfer or pollutants dispersion. Passively advected
scalars mainly differ by their diffusivity properties characterized by their Schmidt number, the viscosity-to-diffusivity ratio. The case of scalars with high Schmidt numbers is still a challenge for numerical simulation. Indeed, the scalar dynamics occurs at scales smaller than the Kolmogorov scale. As a consequence, the accurate treatment of scalar advection-diffusion at high Schmidt numbers requires a finer mesh for the scalar than for the momentum. This is why numerical studies are still restricted to moderate Schmidt numbers. We developed and implemented a method to overcome those difficulties. We will also show its limitations and propose some improvements of the method.