Operator Theory

in the name of God

الثلاثاء, فیفرییه 23, 2016

03:25 ب.ظ

Fundamentals of CFD

 

Operator Theory

• To discretize a problem we need have 3 parameters to know or to obtain: DSO (Derivative number + Stencil + Order of Truncation error )

We know the Derivative number. Should deal with Stencil and Order of error

• Operator Theory contains 3 parts:
  1. Theory:

Is to convert order of derivatives and shift on mesh to power by two means of Taylor Series and Definition of Shift Operator E.

1. ui+1 = eD Δx
2. E ui = ui+1

2. Definitions

Some definitions for differences and mean values between points exist like Shift operator E.

3. Relations

Because we need to calculate the derivatives, we are to re-write the theory in a practical form:

We also need to calculate the derivative using other difference or mean value parameters:

 

So there are two ways to write D in terms of these operators.

So

 

• Review: it needs to be reviewed

And other Taylor essential series.