Adaptive simulation of the subcritical flow past a sphere

Abstract

Adaptive DNS/LES (direct numerical simulation/large-eddy simulation) is used to compute the drag coefficient $c_D$ for the flow past a sphere at Reynolds number $\hbox{\it Re}\,{=}\,10^4$. Using less than $10^5$ mesh points, $c_D$ is computed to an accuracy of a few percent, corresponding to experimental precision, which is at least an order of magnitude cheaper than standard non-adaptive LES computations in the literature. Adaptive DNS/LES is a General Galerkin G2 method for turbulent flow, where a stabilized Galerkin finite element method is used to compute approximate solutions to the Navier–Stokes equations, with the mesh being adaptively refined until a stopping criterion is reached with respect to the error in a chosen output of interest, in this paper $c_D$. Both the stopping criterion and the mesh refinement strategy are based on a posteriori error estimates, in the form of a space–time integral of residuals multiplied by derivatives of the solution of an associated dual problem, linearized at the approximate solution, and with data coupling to the output of interest. There is no filtering of the equations, and thus no Reynolds stresses are introduced that need modelling. The stabilization in the numerical method is acting as a simple turbulence model.