# mix-derivatives?

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 December 14, 1999, 02:25 mix-derivatives? #1 Mohammad kermani Guest   Posts: n/a 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

 December 14, 1999, 02:48 Re: mix-derivatives? #2 John C. Chien Guest   Posts: n/a (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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