A Cartesian Embedded Boundary Method for the Compressible Navier-Stokes Equations

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.

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The use of dual reciprocity method for 2D laminar viscous flow

MATEC Web of Conferences ◽

10.1051/matecconf/202031000044 ◽

2020 ◽

Vol 310 ◽

pp. 00044

Author(s):

Juraj Mužík

Keyword(s):

Viscous Flow ◽

Flow Problem ◽

Stokes Equations ◽

Navier Stokes ◽

Singular Boundary ◽

Navier Stokes Equations ◽

Driven Cavity ◽

Boundary Method ◽

2D Flow ◽

Singular Boundary Method

The paper presents the use of the dual reciprocity multidomain singular boundary method (SBMDR) for the solution of the laminar viscous flow problem described by Navier-Stokes equations. A homogeneous part of the solution is solved using a singular boundary method with the 2D Stokes fundamental solution - Stokeslet. The dual reciprocity approach has been chosen because it is ideal for the treatment of the nonhomogeneous and nonlinear terms of Navier-Stokes equations. The presented SBMDR approach to the solution of the 2D flow problem is demonstrated on a standard benchmark problem - lid-driven cavity.

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An efficient semi-implicit immersed boundary method for the Navier–Stokes equations

Journal of Computational Physics ◽

10.1016/j.jcp.2008.07.005 ◽

2008 ◽

Vol 227 (20) ◽

pp. 8968-8991 ◽

Cited By ~ 33

Author(s):

Thomas Y. Hou ◽

Zuoqiang Shi

Keyword(s):

Immersed Boundary Method ◽

Stokes Equations ◽

Navier Stokes ◽

Immersed Boundary ◽

Navier Stokes Equations ◽

Boundary Method

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

Vietnam Journal of Mechanics ◽

10.15625/0866-7136/8120 ◽

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.

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