Application of Local Defect Correction in a 3d turbulent channel flow

To investigate the behavior of the concentration of a passive scalar in a turbulent flow with realistic high Schmidt numbers, one needs a very fine grid to capture all length-scales that are present in the concentration. An efficient method to increase the spatial resolution without a drastic raise of the computational costs is to apply a Local Defect Correction method. To compute the velocity field of a turbulent channel flow, a Direct Numerical Simulation is used that consists of a pseudo-spectral method in two periodic directions and a Chebyshev expansion in the wall-normal direction. The concentration equation for the passive scalar is solved using a finite volume method. The main concern with an LDC method in a hyperbolic time-dependent problem is the interpolation of the concentration when the refinement area is moved. The interpolated solution has to be smooth and continuous to ensure numerical stability. Using the mean averaged radius and the total surface area of the concentration, the behaviour of several numerical methods can be investigated