Wildcat04
Nov10-09, 02:58 PM
1. The problem statement, all variables and given/known data
I am trying to write an excel spreadsheet to show the f, f', f'', and f''' for \eta = 0 - 8.8 and I just wanted to check my formulas if someone wouldn't mind as my results are slightly off from the tables in my fluid mechanics book
2. Relevant equations
Equation:
f''' + \frac {1}{2} f f''' = 0
Boundary Conditions:
f(0) = f'(0) = 0
f'(\eta \rightarrow \infty) = 1
\Delta\eta = 0.2
Initial
f_{i2} = f_{i1} + \Delta\eta * \frac {f'_{i1} + f'_{k1}} {2}
f'_{i2} = f'_{i1} + \Delta\eta * \frac {f''_{i1} + f''_{k1}} {2}
f''_{i2} = f''_{i1} + \Delta\eta * \frac {f'''_{i1} + f'''_{k1}} {2}
f'''_{i2} = -\frac {1} {2} f_{i2} * f''_{i2}
Predictor
f_{k2} = f_{i2}+ \Delta\eta * f'_{i2}
f'_{k2} = f'_{i2}+ \Delta\eta * f''_{i2}
f''_{k2} = f''_{i2}+ \Delta\eta * f'''_{i2}
f'''_{k2} = -\frac {1} {2} f_{k2} * f''_{k2}
3. The attempt at a solution
Thanks in advance!
Just a note, I couldn't get i-1 and k-1 subscripted, so i2, k2 is current and i1, k1 is the previous result. Initial boundary conditions are set at i0, for f, f', f'', and f'''.
I am trying to write an excel spreadsheet to show the f, f', f'', and f''' for \eta = 0 - 8.8 and I just wanted to check my formulas if someone wouldn't mind as my results are slightly off from the tables in my fluid mechanics book
2. Relevant equations
Equation:
f''' + \frac {1}{2} f f''' = 0
Boundary Conditions:
f(0) = f'(0) = 0
f'(\eta \rightarrow \infty) = 1
\Delta\eta = 0.2
Initial
f_{i2} = f_{i1} + \Delta\eta * \frac {f'_{i1} + f'_{k1}} {2}
f'_{i2} = f'_{i1} + \Delta\eta * \frac {f''_{i1} + f''_{k1}} {2}
f''_{i2} = f''_{i1} + \Delta\eta * \frac {f'''_{i1} + f'''_{k1}} {2}
f'''_{i2} = -\frac {1} {2} f_{i2} * f''_{i2}
Predictor
f_{k2} = f_{i2}+ \Delta\eta * f'_{i2}
f'_{k2} = f'_{i2}+ \Delta\eta * f''_{i2}
f''_{k2} = f''_{i2}+ \Delta\eta * f'''_{i2}
f'''_{k2} = -\frac {1} {2} f_{k2} * f''_{k2}
3. The attempt at a solution
Thanks in advance!
Just a note, I couldn't get i-1 and k-1 subscripted, so i2, k2 is current and i1, k1 is the previous result. Initial boundary conditions are set at i0, for f, f', f'', and f'''.