A Wavelet-Adaptive Method for Multiscale Simulation of Turbulent Flows in Flying Insects (Communications in Computational Physics, 2021)
We present a wavelet-based adaptive method for computing 3D multiscaleflows in complex, time-dependent geometries, implemented on massively parallel computers. While our focus is on simulations of flapping insects, it can be used for otherflow problems. We model the incompressible fluid with an artificial compressibilityapproach in order to avoid solving elliptical problems. No-slip and in/outflow boundary conditions are imposed using volume penalization. The governing equations arediscretized on a locally uniform Cartesian grid with centered finite differences, andintegrated in time with a Runge–Kutta scheme, both of 4th order. The domain ispartitioned into cubic blocks with different resolution and, for each block, biorthogonal interpolating wavelets are used as refinement indicators and prediction operators. Thresholding the wavelet coefficients allows to generate dynamically evolvinggrids, and an adaption strategy tracks the solution in both space and scale. Blocks aredistributed among MPI processes and the grid topology is encoded using a tree-likedata structure. Analyzing the different physical and numerical parameters allows usto balance their errors and thus ensures optimal convergence while minimizing computational effort. Different validation tests score accuracy and performance of our newopen source code, WABBIT. Flow simulations of flapping insects demonstrate its applicability to complex, bio-inspired problems.
Keywords: Adaptive numerical method; wavelets; volume penalization; artificial compressibility; flapping flight.