16:00 - 17:00
online
Title: Dynamical boundary conditions for the water hammer problem.
Abstract: We are using hyperbolic balanced laws to model the fluid flow in the water pipes, and specifically the partial differential equation (PDE) used is a 1d Euler system with a semi-linear friction term. This coupled system in divergence form with semi-linearity is otherwise known as the isothermal Euler or Saint-Venant equations with friction. In [1] a switched differential algebraic equation (sDAE) model is used to approximate the water hammer model, however the approximation accuracy has not been investigated there. Therefore, the goal of this article is to show that a class of the solutions of the sDAE model for the water hammer problem converges to a nonlinear PDE solution under some stringent assumptions on the water density.
[1] R. Kausar and S. Trenn, Water hammer modeling for water networks via hyperbolic PDEs and switched DAEs, 2018.
The colloquium will take place online in Google Meet. You can email the organizer for a link to the meeting.