Discrete energy conservation in numerical flow simulations with local grid refinement
| PhD ceremony: | Mr A.J.A. Kort |
| When: | January 08, 2016 |
| Start: | 16:15 |
| Supervisors: | prof. dr. A.E.P. (Arthur) Veldman, prof. dr. ir. R.W.C.P. (Roel) Verstappen |
| Co-supervisor: | dr. ir. F.W. (Fred) Wubs |
| Where: | Academy building RUG |
| Faculty: | Science and Engineering |
Discrete energy conservation in numerical flow simulations with local grid refinement
The behaviour of fluids is studied through the Navier-Stokes equations. Computer models are used to solve these equations in practical situations. However, for many practically interesting applications, computer simulations still take too much time to be useful. To increase the feasibility of simulations in these situations in the future, the speed of computers and the efficiency of the models and calculation methods can be increased.
A way to improve the efficiency of the models is tuning the resolution of a calculation grid in such a way that the number of grid points is minimal. Lately, the so-called method of local grid refinement is receiving a lot of attention in this field. It uses jumps in resolution for the transition from coarse to fine grid parts and vice versa.
Implementation of fundamental conservation laws is not trivial on grids with local refinement. Typically, solution methods consider only the laws of conservation of mass and momentum and ignore the law of conservation of energy. But since conservation of energy is crucial to obtain stable simulations without artificial diffusion, extension of local grid refinement with this fundamental law is the main theme of this thesis.
The research in this thesis shows how energy conservation can be achieved theoretically and demonstrates through simulation results that the proposed method indeed yields stable solutions without artificial diffusion.