Fully resolved scalar transport for high Prandtl number flows using adaptive mesh refinement

In multiphase systems, boundary layers occur at fluid-fluid or fluid-solid interfaces. In a direct numerical simulation, the grid requirements are often dictated by the thickness of these boundary layers. Systems that are characterized by high Prandtl (or Schmidt number) exhibit temperature (or mass) boundary layers that are much thinner than the momentum boundary layers. In this paper, a hybrid computational approach is presented that uses a fixed Cartesian grid for the Navier-Stokes and continuity equations and an adaptive mesh for scalar transport, thus reducing the memory and CPU requirements tremendously while resolving all boundary layers. We describe the key aspects that need to be addressed in this hybrid approach, related to discretization, grid mapping, velocity interpolation along with detailed verification tests. Finally, the robustness and accuracy of our hybrid methodology is demonstrated for forced-convection heat transfer over stationary spherical particles at high Prandtl numbers.