An optimal Robin-Robin domain decomposition method for Stokes equations

2021 ◽  
Author(s):  
Xuyang Na ◽  
Xuejun Xu
Keyword(s):  
Domain Decomposition ◽  
Decomposition Method ◽  
Stokes Equations ◽  
Domain Decomposition Method

scholarly journals Large Scale Simulation of Hydrogen Dispersion by a Stabilized Balancing Domain Decomposition Method

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Qing-He Yao ◽  
Xin Pan
Keyword(s):  
Domain Decomposition ◽  
Decomposition Method ◽  
Large Scale ◽  
Open Space ◽  
Stokes Equations ◽  
Domain Decomposition Method ◽  
Concentration Field ◽  
Numerical Results ◽  
Interface Problem ◽  
Balancing Domain Decomposition

The dispersion behaviour of leaking hydrogen in a partially open space is simulated by a balancing domain decomposition method in this work. An analogy of the Boussinesq approximation is employed to describe the connection between the flow field and the concentration field. The linear systems of Navier-Stokes equations and the convection diffusion equation are symmetrized by a pressure stabilized Lagrange-Galerkin method, and thus a balancing domain decomposition method is enabled to solve the interface problem of the domain decomposition system. Numerical results are validated by comparing with the experimental data and available numerical results. The dilution effect of ventilation is investigated, especially at the doors, where flow pattern is complicated and oscillations appear in the past research reported by other researchers. The transient behaviour of hydrogen and the process of accumulation in the partially open space are discussed, and more details are revealed by large scale computation.

scholarly journals Study of Indoor Ventilation Based on Large-Scale [DNS by a Domain Decomposition Method

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1416
Author(s):  
Jiang ◽  
Jiang ◽  
Kwan ◽  
Liu ◽  
Yao
Keyword(s):  
Domain Decomposition ◽  
Decomposition Method ◽  
Large Scale ◽  
Stokes Equations ◽  
Domain Decomposition Method ◽  
Numerical Data ◽  
Transient Behavior ◽  
Preconditioned Conjugate Gradient ◽  
Interface Problem ◽  
Indoor Airflow

This paper presents a large-scale Domain Decomposition Method (DDM) based Direct Numerical Simulation (DNS) for predicting the behavior of indoor airflow, where the aim is to design a comfortable and efficient indoor air environment of modern buildings. An analogy of the single-phase convection problems is applied, and the pressure stabilized domain decomposition method is used to symmetrize the linear systems of Navier-Stokes equations and the convection-diffusion equation. Furthermore, a balancing preconditioned conjugate gradient method is utilized to deal with the interface problem caused by domain decomposition. The entire simulation model is validated by comparing the numerical results with that of recognized experimental and numerical data from previous literature. The transient behavior of indoor airflow and its complexity in the ventilated room are discussed; the velocity and vortex distribution of airflow are investigated, and its possible influence on particle accumulation is classified.

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.

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