Study of a non-overlapping domain decomposition method: Steady Navier–Stokes equations

2005 ◽  
Vol 55 (1) ◽  
pp. 100-124 ◽  
Author(s):  
Tomás Chacón Rebollo ◽  
Eliseo Chacón Vera
Keyword(s):  
Domain Decomposition ◽  
Decomposition Method ◽  
Stokes Equations ◽  
Domain Decomposition Method ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Overlapping Domain Decomposition

scholarly journals A domain decomposition method for the Navier–Stokes equations with stochastic input

2021 ◽  
Vol 40 (5) ◽  
Author(s):  
Junxiang Lu ◽  
Jin Su
Keyword(s):  
Constrained Optimization ◽  
Domain Decomposition ◽  
Gradient Method ◽  
Decomposition Method ◽  
Stokes Equations ◽  
Optimization Problems ◽  
Domain Decomposition Method ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stochastic Input

AbstractThe paper is committed to studying the domain decomposition method for the incompressible Navier–Stokes equations(NSEs) with stochastic input. The stochastic input is represented spectrally by employing orthogonal polynomial functionals from the Askey scheme as trial basis to represent the random space, and the stochastic NSEs system are transformed into deterministic ones via the polynomial chaos expansion. The corresponding deterministic equations are transformed into the constrained optimization problem by minimizing the cost function on the common interface after the whole domain decomposed into two sub-domains. The constrained optimization problems are transformed into unconstrained problems by the Lagrange multiplier rule. A gradient method-based approach to the solutions of domain decomposition problem is proposed to solve the unconstrained optimality system. Finally, one numerical simulation experiment for square cavity flow problem with the stochastic boundary conditions are performed to demonstrate the feasibility and applicability of the gradient method.

A FICTITIOUS DOMAIN / DOMAIN DECOMPOSITION METHOD AND ITS APPLICATIONS

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1523-1526
Author(s):  
CHUNHUA ZHOU ◽  
YONGFENG YAO
Keyword(s):  
Domain Decomposition ◽  
Variational Formulation ◽  
Decomposition Method ◽  
Stokes Equations ◽  
Domain Decomposition Method ◽  
Operator Splitting ◽  
Time Discretization ◽  
Navier Stokes ◽  
Fictitious Domain ◽  
Navier Stokes Equations

In this article, the combination of fictitious domain and domain decomposition has been presented. First, we construct an equivalent variational formulation for the Dirichlet problem of linear elliptic operators and discuss the space approximation. Then the approach is applied to the incompressible Navier-Stokes equations, including construction of the variational formulation and time discretization by operator splitting. Finally, some numerical results are presented to validate our approach.

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