FLOTHERM Advanced Training Course1-6

admin 2011-09-15

AdvancedTraining_6_Numerical_Solution.pdf
Numerical Solution

Numerical Solution
-Governing equations are partial differential equations
-Variables are fluid properties
-For numerical solution, equations must be transformed into algebraic form
-i.e. Equations must contain only numbers

Transformation
-Transformation of partial differential equations into algebraic form is called discretization
-Each term of equation must be transformed

Discretization
-Three major techniques:
-Finite volume
-Finite element
-Finite difference
-Flotherm uses finite volume method

Finite Volume
-Consider the simple case of steadystate 1-D diffusion
-Remove the convection and transient terms

Discretization
-Need to set up equations at each point in the domain
-At domain boundaries, use boundary conditions
-Upwind discretization is used by FLOTHERM
-Non-uniform grid leads to large range of matrix terms in solution
-But, need fine grid to resolve boundary layers
-False diffusion is consequence of upwind scheme of discretization

==================
AdvancedTraining_7_False_Diffusion.pdf
AdvancedTraining_8_Solver.pdf
AdvancedTraining_9_Initial_Conditions.pdf
AdvancedTraining_10_Radiation.pdf
AdvancedTraining_11_Compact_Models.pdf
AdvancedTraining_12_Compact_Component_Modelling.pdf