Numerical approximation of statistical solutions of the incompressible Navier-Stokes Equations
Abstract
Statistical solutions, which are time-parameterized probability measures on spaces of square-integrable functions, have been established as a suitable framework for global solutions of incompressible Navier-Stokes equations (NSE). We compute numerical approximations of statistical solutions of NSE on two-dimensional domains with non-periodic boundary conditions and empirically investigate the convergence of these approximations and their observables. For the numerical solver, we use Monte Carlo sampling with an H(div)-FEM based deterministic solver. Our numerical experiments for high Reynolds number turbulent flows demonstrate that the statistics and observables of the approximations converge. We also develop a novel algorithm to compute structure functions on unstructured meshes.
Keywords
Cite
@article{arxiv.2107.06073,
title = {Numerical approximation of statistical solutions of the incompressible Navier-Stokes Equations},
author = {Pratyuksh Bansal},
journal= {arXiv preprint arXiv:2107.06073},
year = {2021}
}