In flow assurance, the simulation of multiphase flow in pipes is important. The profile of the pipe is a sensitive input parameter to the simulation. Close to the horizontal, fractions of degrees can change the flow in the pipes significantly. Often, only a echo sounding image of the ocean surface is available. This echo sounding image has a resolution of typically 1 meter in the horizontal direction and 1 cm in the vertical direction. The pipe is a stiff object which will only touch the seabed at some points. We want to be able to compute the profile of the pipe based on the echo image, and a stiffness description of the pipe.

The project:

In this project the student should develop a simulator that computes the solution of this minimization problem. It is suitable to study the problem in 1D with e.g. a finite difference or finite element method.

Student backgound:

The obstacle problem is typically rephrased as a nonlinear problem involving partial differential equations. Hence, the student needs a mathematical background. Furthermore, the simulator should be developed in Python and the student therefore needs basic programming skills, although experience with Python is not required.