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How to satisfy GCL in FD method

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Old   March 10, 2003, 04:15
Default How to satisfy GCL in FD method
Xiong Yan
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I want to compute unsteady flow around flying bird and insect. The bird or insect's wing is flexible. So the computed meshs are flexible deformation. The bird or insect's flow Re Number is very slow(<1000). The solved N-S equations is incompressible, now i can compute incompressible flow with Rogers's method(Steady and Unsteady Solutions of the Incompressible Navier-Stokes Equations Vol.29, No.4, April 1991 AIAA Journal). If i want to compute flexible wing's flow, the Rogers's solver must be satisfy GCL. But i don't how to let Rogers's incompressible solver satify GCL. Would u give me some advice about GCL, 3x

--Thanks for your time!
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Old   March 10, 2003, 15:28
Default Re: How to satisfy GCL in FD method
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The classic reference is a paper by Thomas and Lombard (don't have the citation with me, should be an AIAA Journal article or paper), but the essence of the approach is the following, assuming you have cast your equations in body-fitted coordinates so the transformation metrics are carried in the system of equations-

Apply the coninuity equation to a uniform freestream.

Expand out derivatives, i.e.

d(q/J)/dx = 1/J*dq/dx - q/J**2*dJ/dx

Recognize that all terms like dq/dx -> 0, and what is left is a differential equation for the evolution of the Jacobian in time that must be satisfied at each timestep as part of your overall system.

A more general approach is laid out by Marcel Vinokur, but again I don't have the citation handy. Try doing a google on Vinokur - the paper deals with a comparison of finite difference and finite volume methods.
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