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SPECIAL SECTION ON CFD METHODS

# Adaptive Wavelet Method for Incompressible Flows in Complex Domains

[+] Author and Article Information
Damrongsak Wirasaet

Department of Aerospace and Mechanical Engineering,  University of Notre Dame Notre Dame, Indiana 46556dwirasae@nd.edu

Samuel Paolucci

Department of Aerospace and Mechanical Engineering,  University of Notre Dame Notre Dame, Indiana 46556paolucci@nd.edu

J. Fluids Eng 127(4), 656-665 (Apr 06, 2005) (10 pages) doi:10.1115/1.1949650 History: Received September 22, 2004; Revised April 06, 2005

## Abstract

An adaptive wavelet-based method provides an alternative means to refine grids according to local demands of the physical solution. One of the prominent challenges of such a method is the application to problems defined on complex domains. In the case of incompressible flow, the application to problems with complicated domains is made possible by the use of the Navier-Stokes–Brinkman equations. These equations take into account solid obstacles by adding a penalized velocity term in the momentum equation. In this study, an adaptive wavelet collocation method, based on interpolating wavelets, is first applied to a benchmark problem defined on a simple domain to demonstrate the accuracy and efficiency of the method. Then the penalty technique is used to simulate flows over obstacles. The numerical results are compared to those obtained by other computational approaches as well as to experiments.

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## Figures

Figure 1

Evolution of streamlines and dynamically adaptive grids for Re=1000 at t=2.5, 5.0, 7.5, 12.5, and steady state. The associated number of collocation points at each time are respectively N=3378, 3910, 4075, 4180, and 4372

Figure 2

Streamlines and dynamically adaptive grids at steady state for Re=1000 and 3200

Figure 3

Comparison of steady state velocity profiles u(0.5,y) and v(x,0.5) with those of 35 for Re=400

Figure 4

Comparison of steady state velocity profiles u(0.5,y) and v(x,0.5) with those of 35 for Re=1000

Figure 5

Comparison of steady state velocity profiles u(0.5,y) and v(x,0.5) with those of 35 for Re=3200

Figure 6

(a) Vorticity field and (b) dynamically adaptive grid for flow past a tandem pair of circular cylinders with gap L=1.5D at t=200 for Re=200

Figure 7

(a) Vorticity field and (b) dynamically adaptive grid for flow past a tandem pair of circular cylinders with gap L=3D at t=200 for Re=200

Figure 8

(a) Vorticity field and (b) dynamically adaptive grid for flow past a tandem pair of circular cylinders with gap L=4D at t=200 for Re=200

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