Efficient simulation of one-dimensional two-phase flow with a high-order h-adaptive space-time Discontinuous Galerkin method

Efficient simulation of one-dimensional two-phase flow with a high-order h-adaptive space-time Discontinuous Galerkin method

van Zwieten, J.S.B. (TU Delft Numerical Analysis)
Sanderse, B. (Shell Technology Centre, Amsterdam; Centrum Wiskunde & Informatica (CWI))
Hendrix, M.H.W. (TU Delft Fluid Mechanics)
Vuik, Cornelis (TU Delft Numerical Analysis)
Henkes, R.A.W.M. (TU Delft Fluid Mechanics; Shell Technology Centre, Amsterdam)

2017-06-15

One-dimensional models for multiphase flow in pipelines are commonly discretised using first-order Finite Volume (FV) schemes, often combined with implicit time-integration methods. While robust, these methods introduce much numerical diffusion depending on the number of grid points. In this paper we propose a high-order, space-time Discontinuous Galerkin (DG) Finite Element method with h-adaptivity to improve the efficiency of one-dimensional multiphase flow simulations. For smooth initial boundary value problems we show that the DG method converges with the theoretical rate and that the growth rate and phase shift of small, harmonic perturbations exhibit superconvergence. We employ two techniques to accurately and efficiently represent discontinuities. Firstly artificial diffusion in the neighbourhood of a discontinuity suppresses spurious oscillations. Secondly local mesh refinement allows for a sharper representation of the discontinuity while keeping the amount of work required to obtain a solution relatively low. The proposed DG method is shown to be superior to FV.

Discontinuous Galerkin method
h-adaptive
Two-fluid model

http://resolver.tudelft.nl/uuid:9f5e432e-844e-4428-b61e-82cbe88f2bb6

https://doi.org/10.1016/j.compfluid.2017.06.010

2019-07-03

0045-7930

Computers & Fluids, 156, 34-47

Author accepted manuscript

Institutional Repository

journal article

© 2017 J.S.B. van Zwieten, B. Sanderse, M.H.W. Hendrix, Cornelis Vuik, R.A.W.M. Henkes