discretization of a gradient term in FVM
Hi,
In the finite volume method, are there any other ways of discretizing a dv/dx term other than central differencing i.e. for instance (dv/dx) at east face = (v_E  v_p )/(x_E x_p ), where p and E are the central and east nodes of a structured grid. I am looking for a method of the same order as the CDS method above. Thanks! 
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If you use FV approach, then you must discretize the surface integral of the normal component of the flux. That means: Integral [S] n . Grad f dS can be written in a FV manner, for example on a 2D structured Cartesian grid as: Int [dy/2, + dy/2] (df/dx_i+1/2  df/dx_i1/2) dy + Int [dx/2, + dx/2] (df/dy_j+1/2  df/dy_j1/2) dx Now you can discretize the integral with the mean value formula and the derivative with second order central formula, getting a global second order of accuracy. If you want to increase the accuracy, you can use the Simpon rule for the integral and a third degree polynomial interpolation for the derivatives, as we explained in http://adsabs.harvard.edu/abs/2003IJNMF..43..431I 
I don't want to use any higher order method that involve cells other than the neighbouring cells.

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ok, then you have two choice, Lagrangian linear interpolation for a second order accuracy or implicit Padè interpolation for higher 
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