Domain decomposition methods for nonlinear problems in fluid dynamics
Abstract
The numerical solution of finite element approximations of complicated two and threedimensional nonlinear problems can be a most formidable task. In order to overcome this difficulty related to dimensionality, domainsplitting methods can be very effective, particularly in view of obtaining a fast and economical conjugate gradient solver, which can be used to precondition the solution of nonlinear problems by optimization methods via nonlinear least squares or weighted residual formulations. A new technique of this type will be introduced and analyzed and its efficiency will be discussed from numerical experiments concerning the numerical simulation of transonic flows for compressible inviscid fluids and incompressible viscous flows modeled by the NavierStokes equations.
 Publication:

Computer Methods in Applied Mechanics and Engineering
 Pub Date:
 September 1983
 DOI:
 10.1016/00457825(83)900452
 Bibcode:
 1983CMAME..40...27G
 Keywords:

 Computational Fluid Dynamics;
 Conjugate Gradient Method;
 Decomposition;
 Finite Element Method;
 Flow Equations;
 Nonlinear Equations;
 Boundary Value Problems;
 Convergence;
 Dirichlet Problem;
 Domains;
 Flow Geometry;
 Least Squares Method;
 NavierStokes Equation;
 Transonic Flow;
 Fluid Mechanics and Heat Transfer