An efficient nonlinear solver and convergence analysis for a viscoplastic flow model

08/19/2021
by   Sara Pollock, et al.
0

This paper studies a finite element discretization of the regularized Bingham equations that describe viscoplastic flow. Convergence analysis is provided, as we prove optimal convergence with respect to the spatial mesh width but depending inversely on the regularization parameter ε, and also suboptimal (by one order) convergence that is independent of the regularization parameter. An efficient nonlinear solver for the discrete model is then proposed and analyzed. The solver is based on Anderson acceleration (AA) applied to a Picard iteration, and we prove accelerated convergence of the method by applying AA theory (recently developed by authors) to the iteration, after showing sufficient smoothness properties of the associated fixed point operator. Numerical tests of spatial convergence are provided, as are results of the model for 2D and 3D driven cavity simulations. For each numerical test, the proposed nonlinear solver is also tested and shown to be very effective and robust with respect to the regularization parameter as it goes to zero.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

04/14/2020

Acceleration of nonlinear solvers for natural convection problems

This paper develops an efficient and robust solution technique for the s...
10/27/2021

Convergence of Restricted Additive Schwarz with impedance transmission conditions for discretised Helmholtz problems

The Restricted Additive Schwarz method with impedance transmission condi...
05/25/2021

An efficient iterative method for solving parameter-dependent and random diffusion problems

This paper develops and analyzes a general iterative framework for solvi...
12/23/2021

Multigrid solvers for isogeometric discretizations of the second biharmonic problem

We develop a multigrid solver for the second biharmonic problem in the c...
02/29/2020

Preconditioning nonlocal multi-phase flow

We propose an efficient solver for saddle point problems arising from fi...
08/02/2020

Improving accuracy in the Leray model for incompressible non-isothermal flows via adaptive deconvolution-based nonlinear filtering

This paper considers a Leray regularization model of incompressible, non...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.