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:
- 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.
- ui+1 = eD Δx
- E ui = ui+1
- Definitions
Some definitions for differences and mean values between points exist like Shift operator E.
- 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.