An Immersed Boundary Method for Simulation of Wind Flow Over Complex Terrain

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
S. Jafari ◽  
N. Chokani ◽  
R. S. Abhari
Keyword(s):  
Immersed Boundary Method ◽  
Complex Terrain ◽  
Stokes Equations ◽  
Ground Level ◽  
Rectangular Domain ◽  
Immersed Boundary ◽  
Test Case ◽  
Wind Flow ◽  
Wall Functions ◽  
Boundary Method

The accurate modeling of the wind resource over complex terrain is required to optimize the micrositing of wind turbines. In this paper, an immersed boundary method that is used in connection with the Reynolds-averaged Navier–Stokes equations with k-ω turbulence model in order to efficiently simulate the wind flow over complex terrain is presented. With the immersed boundary method, only one Cartesian grid is required to simulate the wind flow for all wind directions, with only the rotation of the digital elevation map. Thus, the lengthy procedure of generating multiple grids for conventional rectangular domain is avoided. Wall functions are employed with the immersed boundary method in order to relax the stringent near-wall grid resolution requirements as well as to allow the effects of surface roughness to be accounted for. The immersed boundary method is applied to the complex terrain test case of Bolund Hill. The simulation results of wind speed and turbulent kinetic energy show good agreement with experiments for heights greater than 5 m above ground level.

Terrain Effects on Wind Flow: Simulations With an Immersed Boundary Method

2011 ◽  
Author(s):  
S. Jafari ◽  
N. Chokani ◽  
R. S. Abhari
Keyword(s):  
Boundary Condition ◽  
Immersed Boundary Method ◽  
Flow Simulation ◽  
Rectangular Domain ◽  
Immersed Boundary ◽  
Wind Flow ◽  
Generation Process ◽  
Wind Rose ◽  
Boundary Method ◽  
Arbitrary Topography

The modelling of the wind resource over arbitrary topography is required to optimize the micrositing of wind turbines. Most solvers use classical body-fitted grid for simulations. In such an approach, to cover the wind rose using a rectangular domain, a dedicated mesh must be generated for each direction. Moreover, over complex terrain, additional numerical errors are introduced in the solver due to coordinate transformations. To overcome these challenges and to facilitate the grid generation process, an immersed boundary method is developed in connection with a RANS solver in order to simulate turbulent atmospheric flows over arbitrary topography. In this method, a Cartesian grid is used and the boundary condition on the terrain surface is modelled within the solver using a “direct forcing” approach. With the immersed boundary method a rectangular grid can be used to simulate the flow field for all wind directions and only a rotation of the digital elevation map is required. Ghost cells are used to enforce the desired boundary condition at the immersed surface. The immersed boundary method developed in this work is used to simulate the flow in connection with both Baldwin-Lomax and kω turbulence models. The performance of the method is examined for the flow over a two-dimensional hill. Results are compared with experimental data as well as a classical body-fitted grid to isolate the effect of the boundary conditions. The comparisons show good agreement among all the results. The results for the three-dimensional wind flow simulation over the Askervein Hill test case are also presented, and show the capability of the immersed boundary method in a full-scale scenario.

FINITE ELEMENT APPROACH TO IMMERSED BOUNDARY METHOD WITH DIFFERENT FLUID AND SOLID DENSITIES

2011 ◽  
Vol 21 (12) ◽  
pp. 2523-2550 ◽  
Author(s):  
DANIELE BOFFI ◽  
NICOLA CAVALLINI ◽  
LUCIA GASTALDI
Keyword(s):  
Finite Element ◽  
Immersed Boundary Method ◽  
Stokes Equations ◽  
Numerical Procedure ◽  
Biological Tissues ◽  
Immersed Boundary ◽  
Fluid Structure ◽  
Finite Element Approach ◽  
Boundary Method ◽  
Element Approach

The Immersed Boundary Method (IBM) has been designed by Peskin for the modeling and the numerical approximation of fluid-structure interaction problems, where flexible structures are immersed in a fluid. In this approach, the Navier–Stokes equations are considered everywhere and the presence of the structure is taken into account by means of a source term which depends on the unknown position of the structure. These equations are coupled with the condition that the structure moves at the same velocity of the underlying fluid. Recently, a finite element version of the IBM has been developed, which offers interesting features for both the analysis of the problem under consideration and the robustness and flexibility of the numerical scheme. Initially, we considered structure and fluid with the same density, as it often happens when dealing with biological tissues. Here we study the case of a structure which can have a density higher than that of the fluid. The higher density of the structure is taken into account as an excess of Lagrangian mass located along the structure, and can be dealt with in a variational way in the finite element approach. The numerical procedure to compute the solution is based on a semi-implicit scheme. In fluid-structure simulations, nonimplicit schemes often produce instabilities when the density of the structure is close to that of the fluid. This is not the case for the IBM approach. In fact, we show that the scheme enjoys the same stability properties as in the case of equal densities.

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.

Sign in / Sign up

Export Citation Format

Share Document