Here, higher order methods are developed for this type of applications, since the discretization error decreases very fast when choosing a finer grid. Thus, not as many gridpoints are needed to obtain a good approximation, saving computer time and memory. When using higher order methods, one usually encounters problems near the boundary of the domain. To avoid this, compact finite difference methods are used.
The project is a joint work with the Department of Mechanics at KTH, Stockholm and the Division of Aeronautics at the Swedish Defence Research Agency.