70
T. Torsvik
Fig. 3.3 Discretization of a continuous function
forcing field at the boundary of the model domain. The FV method is applicable
for unstructured as well as structured grids. The main strength of the FV method is
to maintain global conservation of mass, momentum and energy within the model
domain. Maintaining these conservation properties is often vital for an accurate description of the flow problem. This method is mainly used when the equations of
motion can be written in the form of conservation equations. In principle, the FV
approximation is discontinuous at cell borders, but it is usually possible to visualize the solution by specifying the cell average values at the cell centres and make a
linear interpolation between these centre points. However, the interpolated solution
constructed in this way will in general not have the same conservation properties as
the underlying cell averaged FV solution.
The FE method has its origin within the field of complex elasticity and structural
analysis problems, but has also found its use within CFD applications. The method
works by reformulating the given differential equations in an equivalent variational
form, and then solves a minimization problem in terms of a given set of basis functions. The main advantages of the FE method are that it is easy to apply for complicated geometry as it works nicely with unstructured grids, and that it is based
on a mathematical theory that facilitates error estimation for the numerical solution.
When comparing the FE and FV methods, which can both work with unstructured
grids, the traditional view has been that the FE method is more computationally demanding, but the difference in performance is highly dependent on the particular
implementation of each method.
It is not easy to give general advice on which method to choose. Different applications have different requirements in terms of computational efficiency, geometrical complexity, conservation properties and error sensitivity, and no single tool
will be best for all applications. GCMs have usually used the FD method for discretization, but there is a trend towards increasing use of the FV method within this
particular field of research.
There is an extensive literature available on numerical methods and CFD, both
as introduction and reference level textbooks. As introductions to CFD, the books
T. Torsvik
Fig. 3.3 Discretization of a continuous function
forcing field at the boundary of the model domain. The FV method is applicable
for unstructured as well as structured grids. The main strength of the FV method is
to maintain global conservation of mass, momentum and energy within the model
domain. Maintaining these conservation properties is often vital for an accurate description of the flow problem. This method is mainly used when the equations of
motion can be written in the form of conservation equations. In principle, the FV
approximation is discontinuous at cell borders, but it is usually possible to visualize the solution by specifying the cell average values at the cell centres and make a
linear interpolation between these centre points. However, the interpolated solution
constructed in this way will in general not have the same conservation properties as
the underlying cell averaged FV solution.
The FE method has its origin within the field of complex elasticity and structural
analysis problems, but has also found its use within CFD applications. The method
works by reformulating the given differential equations in an equivalent variational
form, and then solves a minimization problem in terms of a given set of basis functions. The main advantages of the FE method are that it is easy to apply for complicated geometry as it works nicely with unstructured grids, and that it is based
on a mathematical theory that facilitates error estimation for the numerical solution.
When comparing the FE and FV methods, which can both work with unstructured
grids, the traditional view has been that the FE method is more computationally demanding, but the difference in performance is highly dependent on the particular
implementation of each method.
It is not easy to give general advice on which method to choose. Different applications have different requirements in terms of computational efficiency, geometrical complexity, conservation properties and error sensitivity, and no single tool
will be best for all applications. GCMs have usually used the FD method for discretization, but there is a trend towards increasing use of the FV method within this
particular field of research.
There is an extensive literature available on numerical methods and CFD, both
as introduction and reference level textbooks. As introductions to CFD, the books