A parallel domain decomposition algorithm for the incompressible Navier-Stokes equations

1994 ◽  
pp. 743-752 ◽  
Author(s):  
E. Brakkee ◽  
A. Segal
Keyword(s):  
Domain Decomposition ◽  
Stokes Equations ◽  
Decomposition Algorithm ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Domain Decomposition Algorithm

A Parallel Domain Decomposition Algorithm for Simulating Blood Flow with Incompressible Navier-Stokes Equations with Resistive Boundary Condition

2012 ◽  
Vol 11 (4) ◽  
pp. 1279-1299
Author(s):  
Yuqi Wu ◽  
Xiao-Chuan Cai
Keyword(s):  
Boundary Condition ◽  
Blood Flow ◽  
Domain Decomposition ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Outflow Boundary Condition ◽  
Outflow Boundary ◽  
Domain Decomposition Algorithm ◽  
Fully Coupled

AbstractWe introduce and study a parallel domain decomposition algorithm for the simulation of blood flow in compliant arteries using a fully-coupled system of nonlinear partial differential equations consisting of a linear elasticity equation and the incompressible Navier-Stokes equations with a resistive outflow boundary condition. The system is discretized with a finite element method on unstructured moving meshes and solved by a Newton-Krylov algorithm preconditioned with an overlapping restricted additive Schwarz method. The resistive outflow boundary condition plays an interesting role in the accuracy of the blood flow simulation and we provide a numerical comparison of its accuracy with the standard pressure type boundary condition. We also discuss the parallel performance of the implicit domain decomposition method for solving the fully coupled nonlinear system on a supercomputer with a few hundred processors.

scholarly journals Dynamic Domain Decomposition Strategy Coupling Lattice Boltzmann Methods With Finite Differences Approximations of the Navier-Stokes Equations to Study Bodies in Current

2015 ◽  
Author(s):  
Giuseppina Colicchio ◽  
Claudio Lugni ◽  
Marilena Greco ◽  
Odd M. Faltinsen
Keyword(s):  
Domain Decomposition ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Dynamic Change ◽  
Accurate Solution ◽  
The Body ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Coupling Strategy ◽  
Hybrid Solver

A Domain-Decomposition (DD) strategy is proposed for problems involving regions with slow variations of the flow (A) and others where the fluid features undergo rapid changes (B), like in the case of steady current past bodies with pronounced local unsteadiness connected with the vortex shedding from the structures. For an efficient and accurate solution of such problems, the DD couples a Finite Difference solver of the Navier-Stokes equations (FD-NS) with a Multiple Relaxation Time Lattice Boltzmann method (MRT-LBM). Regions A are handled by FD-NS, while zones B are solved by MRT-LBM and the two solvers exchange information within a strong coupling strategy. Present DD strategy is able to deal with a dynamic change of the sub-domains topology. This feature is needed when regions with vorticity shed from the body vary in time for a more flexible and reliable solution strategy. Its performances in terms of accuracy and efficiency have been successfully assessed by comparing the hybrid solver against a full FD-NS solution and experimental data for a 2D circular cylinder in an impulsively started flow.

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