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Old   December 14, 1999, 02:25
Default mix-derivatives?
  #1
Mohammad kermani
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Hi there:

I need to compute the mix-derivatives in the viscous part of the Navier Stokes. In general a mix derivative looks like:

d( A d(u)/dx )/dy; where A is a general function of x and y.

I wonder if someone can help or introduce a reference?

Thanks

Mohammad Kermani Fax: 613-520-5715

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Old   December 14, 1999, 02:48
Default Re: mix-derivatives?
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John C. Chien
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(1). d(A*(du/dx))/dy = A(x,y)*d(du/dx)/dy + (dA/dy)*(du/dx)= A(x,y)*( (du/dx)at(j+1) - (du/dx)at(j-1) )/(y(j+1)-y(j-1)) + (A(j+1)-A(j-1))/(y(j+1)-y(j-1))*(u(i+1)-u(i-1))/(x(i+1)-x(i-1)), where (du/dx)at(j+1)=(u(i+1,j+1)-u(i-1,j+1))/(x(i+1)-x(i-1)),... (2). CRC math Handbook should have the finite difference formula included. (3). You can also apply the same method directly to the original derivative term.
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