Paper Info
Title
Dual Dynamically Orthogonal approximation of incompressible Navier Stokes equations with random boundary conditions.
Abstract
In this paper we propose a method for the strong imposition of random Dirichlet boundary conditions in the Dynamical Low Rank (DLR) approximation of parabolic PDEs and, in particular, incompressible Navier Stokes equations. We show that the DLR variational principle can be set in the constrained manifold of all S rank random fields with a prescribed value on the boundary, expressed in low rank format, with rank smaller then S. We characterize the tangent space to the constrained manifold by means of a Dual Dynamically Orthogonal (Dual DO) formulation, in which the stochastic modes are kept orthonormal and the deterministic modes satisfy suitable boundary conditions, consistent with the original problem. The Dual DO formulation is also convenient to include the incompressibility constraint, when dealing with incompressible Navier Stokes equations. We show the performance of the proposed Dual DO approximation on two numerical test cases: the classical benchmark of a laminar flow around a cylinder with random inflow velocity, and a biomedical application for simulating blood flow in realistic carotid artery reconstructed from MRI data with random inflow conditions coming from Doppler measurements.
Year
DOI
Venue
2018
10.1016/j.jcp.2017.09.061
Journal of Computational Physics
Keywords
Field
DocType
Uncertainty quantification,Dynamical low rank approximation,Dynamically orthogonal approximation,Reduced basis method,Time dependent Navier Stokes,Random boundary conditions
Boundary value problem,Mathematical optimization,Random field,Mathematical analysis,Dirichlet boundary condition,Variational principle,Orthonormal basis,Mathematics,Tangent space,Parabola,Navier–Stokes equations
Journal
Volume
ISSN
Citations 
354
0021-9991
0
PageRank 
References 
Authors
0.34
7
2
Name
Order
Citations
PageRank
Eleonora Musharbash100.34
Fabio Nobile233629.63