Numerical simulation of a mixing layer in an adaptive wavelet basis

This note presents an adaptive wavelet method to compute two-dimensional turbulent flows. The Navier–Stokes equations in vorticity–velocity form are discretized using a Petrov–Galerkin scheme. The vorticity field is developed into an orthogonal wavelet series where only the most significant coefficients are retained. The testfunctions are adapted to the linear part of the equation so that the resulting stiffness matrix turns out to be the identity. The nonlinear term is evaluated on a locally refined grid in physical space. This numerical scheme is applied to simulate a temporally developing mixing layer. A comparison with a classical pseudo-spectral method is used for validation of the new method. The results show that the formation of Kelvin–Helmholtz vortices is well captured and all scales of the flow are well represented.