Influence of biorthogonal wavelets on adaptive simulations of turbulent flows*

We present a wavelet-based adaptive approach for computing flows in complex geometries, in particular the aerodynamics of flapping insect flight. This approach is implemented in our open-source code WABBIT (Engels et al. Commun. Comput. Phys., doi:10.4208/cicp.OA-2020-0246). Dynamically evolving grids using regular Cartesian blocks allow significant reduction of memory and CPU time requirements while monitoring the precision of the computation. Distributing the blocks among MPI processes permits an efficient parallelization on large scale supercomputers. Our adaptation strategy is based on lifted interpolating biorthogonal wavelets, and in this talk we discuss how the choice of wavelet influences on the spatio-temporal dynamics of the flow. We demonstrate that an insufficient vanishing moments of the reconstructing wavelet results in a reduced convergence order. Applying lifting to the wavelets is therefore important for nonlinear problems. The classical three-vortex problem and the Taylor-Green vortex serve as test cases in 2D and 3D, respectively. Finally, we perform 3D simulations of a model bumblebee and discuss the impact of the wavelet on the vortical structures. We conclude with guidelines on the choice of wavelets for adaptive CFD simulations.