Print Email Facebook Twitter Efficient simulation of one-dimensional two-phase flow with a new high-order Discontinuous Galerkin method Title Efficient simulation of one-dimensional two-phase flow with a new high-order Discontinuous Galerkin method Author Van Zwieten, J.S.B. Sanderse, B. Hendrix, M.H.V. Vuik, C. Henkes, R.A.W.M. Faculty Electrical Engineering, Mathematics and Computer Science Department Delft Institute of Applied Mathematics Date 2015-12-31 Abstract 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. To reference this document use: http://resolver.tudelft.nl/uuid:87c62cf3-1dc3-48a7-ae5f-4adca43206e8 Publisher Delft University of Technology, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft Institute of Applied Mathematics ISSN 1389-6520 Source Reports of the Delft Institute of Applied Mathematics, 15-07 Part of collection Institutional Repository Document type report Rights © 2015 The Author(s) Files PDF 326437.pdf 1.25 MB Close viewer /islandora/object/uuid:87c62cf3-1dc3-48a7-ae5f-4adca43206e8/datastream/OBJ/view