Numerical Solutions Applied To Heat
Transfer And Fluid Mechanics Problems
Selection of Grid Pattern
Each equation to be solved needs a grid.
Consider the required accuracy of results
Finer Grid spacing Larger
Number of Nodes $
Select Grid Type
Cartesian Usually depends on boundary
Cylindrical configuration of region
How many grid patterns do we need?
Example: Primitive variable set of equations
Vector: x & y momentum
Scalar: pressure, temperature
You may wish to have 3 grids, one for scalars, and
one for each flow direction.
Formation of finite difference equation
Covered in future lectures. Considerations include:
accuracy in space and (were appropriate) time; stability; robustness; and
applicability to target computer architectures. Interior and Boundary nodes
require different difference forms.
Select a method for solving sets of algebraic equations
simultaneously. This may become a fairly complicated iterative procedure.
For flow calculations – must handle the coupling of
the various equations and the non-linear terms in the momentum equation.
Perform Auxiliary Calculations
Invert transformed variables if necessary
Calculate shear stresses and heat flux at boundaries
For transients audit mass and energy conservation
Summary of steps in problem solution
Determine appropriate mathematical model
Classification of partial differential equation
Transformation of mathematical model
Select grid pattern
Formation of finite difference equations
Perform auxiliary calculations
Created by Frank Schmidt
Maintained by John Mahaffy : email@example.com