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.

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.

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.

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