Local wavelet adaptation of cartesian grids in computational fluid dynamics

A method for dynamic local adaptation of graded Cartesian trees for the numerical solution of fluid dynamics problems is presented. Local wavelet analysis of a gas-dynamic field based on nonuniform B-splines is applied independently to each cell of the computational grid and makes it possible to identify nonsmooth or significantly nonlinear sections of the solution (or, vice versa, sufficiently smooth and linear ones) and modify the grid to calculate the next time step so that nonuniformly scaled flow features had adequate grid resolution. In combination with other computational fluid dynamics methods, such as the free boundary method, the presented technique allows one to effectively solve nonstationary problems involving flow around moving bodies. The operation of the proposed version of wavelet adaptation is demonstrated using a number of such problems.