Parallelized Domain Decomposition Techniques for Multiphase Flow

Volume 3 ◽  
2004 ◽  
Author(s):  
Eray Uzgoren ◽  
Wei Shyy ◽  
Marc Garbey
Keyword(s):  
Domain Decomposition ◽  
Immersed Boundary Method ◽  
Stokes Equations ◽  
Domain Decomposition Method ◽  
Computational Cost ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Pressure Poisson Equation ◽  
Boundary Method ◽  
Additive Schwarz Method

Direct simulation of multiphase flows is a challenging task due to the moving interface and property variations between phases. In this study, a parallel domain decomposition method is implemented for such flows to lower the computing cost. Specifically, the approach consists of the additive Schwarz method for domain decomposition, the projection method for the Navier-Stokes equations, the immersed boundary method for treating the interfacial dynamics, and the multigrid method to expedite the solution of the pressure Poisson equation. The issues related to load balancing, communication and computation, scalability in regard to grid size and the number of processors, and interface shape deformation, are studied using both SGI Altix and Linux-based Beowulf systems. As the number of processors increases, as expected, the domain decomposition technique results in modest decrease in convergence rate, while the multigrid technique is effective in reducing the computational cost. The additional computational cost incurred by the immersed boundary method for tracking the interface is not significant.

scholarly journals A Stress Mapping Immersed Boundary Method for Viscous Flows

2021 ◽  
Vol 87 (3) ◽  
pp. 1-20
Author(s):  
Karim M. Ali ◽  
Mohamed Madbouli ◽  
Hany M. Hamouda ◽  
Amr Guaily
Keyword(s):  
Immersed Boundary Method ◽  
Stokes Equations ◽  
Cross Flow ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Element Formulation ◽  
Navier Stokes Equations ◽  
Boundary Method ◽  
Background Grid ◽  
Dimensional Simulation

This work introduces an immersed boundary method for two-dimensional simulation of incompressible Navier-Stokes equations. The method uses flow field mapping on the immersed boundary and performs a contour integration to calculate immersed boundary forces. This takes into account the relative location of the immersed boundary inside the background grid elements by using inverse distance weights, and also considers the curvature of the immersed boundary edges. The governing equations of the fluid mechanics are solved using a Galerkin-Least squares finite element formulation. The model is validated against a stationary and a vertically oscillating circular cylinder in a cross flow. The results of the model show acceptable accuracy when compared to experimental and numerical results.

An Immersed Boundary Method for Compressible Flows with Complex Boundaries

2013 ◽  
Vol 477-478 ◽  
pp. 281-284
Author(s):  
Jie Yang ◽  
Song Ping Wu
Keyword(s):  
Immersed Boundary Method ◽  
Compressible Flows ◽  
Stokes Equations ◽  
Splitting Method ◽  
Linear Interpolation ◽  
High Order Accuracy ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Central Difference ◽  
Boundary Method

An immersed boundary method based on the ghost-cell approach is presented in this paper. The compressible Navier-Stokes equations are discretized using a flux-splitting method for inviscid fluxes and second-order central-difference for the viscous components. High-order accuracy is achieved by using weighted essentially non-oscillatory (WENO) and Runge-Kutta schemes. Boundary conditions are reconstructed by a serial of linear interpolation and inverse distance weighting interpolation of flow variables in fluid domain. Two classic flow problems (flow over a circular cylinder, and a NACA 0012 airfoil) are simulated using the present immersed boundary method, and the predictions show good agreement with previous computational results.

scholarly journals Immersed Boundary Method Application as a Way to Deal with the Three-Dimensional Sudden Contraction

Computation ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 50
Author(s):  
Jonatas Borges ◽  
Marcos Lourenço ◽  
Elie Padilla ◽  
Christopher Micallef
Keyword(s):  
Immersed Boundary Method ◽  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Immersed Boundary ◽  
Fractional Step Method ◽  
Central Difference ◽  
Boundary Method ◽  
Contraction Ratio ◽  
Sudden Contraction

The immersed boundary method has attracted considerable interest in the last few years. The method is a computational cheap alternative to represent the boundaries of a geometrically complex body, while using a cartesian mesh, by adding a force term in the momentum equation. The advantage of this is that bodies of any arbitrary shape can be added without grid restructuring, a procedure which is often time-consuming. Furthermore, multiple bodies may be simulated, and relative motion of those bodies may be accomplished at reasonable computational cost. The numerical platform in development has a parallel distributed-memory implementation to solve the Navier-Stokes equations. The Finite Volume Method is used in the spatial discretization where the diffusive terms are approximated by the central difference method. The temporal discretization is accomplished using the Adams-Bashforth method. Both temporal and spatial discretizations are second-order accurate. The Velocity-pressure coupling is done using the fractional-step method of two steps. The present work applies the immersed boundary method to simulate a Newtonian laminar flow through a three-dimensional sudden contraction. Results are compared to published literature. Flow patterns upstream and downstream of the contraction region are analysed at various Reynolds number in the range 44 ≤ R e D ≤ 993 for the large tube and 87 ≤ R e D ≤ 1956 for the small tube, considerating a contraction ratio of β = 1 . 97 . Comparison between numerical and experimental velocity profiles has shown good agreement.

scholarly journals Immersed boundary method combined with proper generalized decomposition for simulation of a flexible filament in a viscous incompressible flow

2017 ◽  
Vol 39 (2) ◽  
pp. 109-119
Author(s):  
Cuong Q. Le ◽  
H. Phan-Duc ◽  
Son H. Nguyen
Keyword(s):  
Immersed Boundary Method ◽  
Stokes Equations ◽  
Fluid Pressure ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Proper Generalized Decomposition ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Boundary Method ◽  
Fluid Filament

In this paper, a combination of the Proper Generalized  Decomposition (PGD) with the Immersed Boundary method (IBM) for solving  fluid-filament interaction problem is proposed. In this combination, a  forcing term constructed by the IBM is introduced to Navier-Stokes equations  to handle the influence of the filament on the fluid flow. The PGD is  applied to solve the Poission's equation to find the fluid pressure  distribution for each time step. The numerical results are compared with  those by previous publications to illustrate the robustness and  effectiveness of the proposed method.

scholarly journals An Immersed Boundary Method Based on Navier-Stokes Equations in Discrete Stream Function Formulation

2010 ◽  
Author(s):  
Xing Zhang ◽  
Shizhao Wang ◽  
Guowei He
Keyword(s):  
Stream Function ◽  
Immersed Boundary Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Simulation Code ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Boundary Method ◽  
New Variant

A new variant of Immersed Boundary method is proposed in the framework of discrete stream function approach for the Navier-Stokes equations. A parallelized flow solver is developed to simulate two and three-dimensional flow problems involving complex and moving boundaries. The parallel performance of the present flow solver is tested by varying the number of processors used in the simulation. Code validations and applications are also presented, in an order of increasing complexity.

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