 enabling a waveletGalerkin turbulent flow field representation with expansion coefficients in identical physical & wavelet space
“When Fourier meets Navier” in a physical H(1/2) energy Hilbert space there is a global unique H(1/2) solution of the corresponding weak variation equation of the nonlinear, nonstationary NavierStokes equations ("solution"). The standard numerical approximation method for PDE is the RitzGalerkin method which is usually equipped with finite element approximation spaces (FEM). In case of negative scaled Hilbert spaces the RitzGalerkin method accompanied by finte element approximation spaces becomes a boundary element method (BEM) related to the underlying singular equation representation. The required finite (boundary) element approximation properties of the BEM face some challenges in case of nonlinearity and/or nonperiodic boundary conditions. The wavelet extension method is used to represent functions that have discontinuities and sharp peaks, and for accurately deconstructing and reconstructing finite, nonperiodic and/or nonstationary signals, (MeM). Here we go with a collection of some useful supporting tool sets:
