Hoang Tran
Afilliation: Department of Mathematics, University of Pittsburgh
Title: Explicitly Uncoupled VMS Stabilization of Fluid Flow
Abstract: Variational multiscale methods have proven to be an accurate and systematic approach to the simulation of turbulent flows. Many turbulent flows are
solved by legacy codes or by ones written by a team of programmers and of
great complexity so implementing a new approach to turbulence in such cases
can be daunting. We propose a new approach to inducing a VMS treatment of
turbulence in such cases. The method adds
a separate, uncoupled and modular postprocessing step to each time step. Adding this step requires the ability to solve a Stokes
problem either on the same mesh or to solve and interpolate between the
postprocessing step's mesh and the code's mesh. We prove stability and
convergence for the combination and quantify the VMS dissipation induced.
Numerical experiments confirming the theory are given. In particular, the
performance of the two step, modular VMS method is comparable to a
monolithic (fully coupled) VMS method for the benchmark problem of decaying
homogeneous turbulence.
