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

Abstract

a b s t r a c tOne-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.

Simulation of Unconfined Aquifer Flow Based on Parallel Adaptive Mesh Refinement

“…Mesh refinement can be grouped into three broad categories (Mitchell & McClain, 2011). (a) r‐refinement methods (Beckett et al., 2006; Hénap & Szabó, 2017; Lang et al., 2003) increase or decrease the density of the mesh by relocating the mesh vertices, (b) h‐refinement (Kardani et al., 2012; van Zwieten et al., 2017) add new points or remove existing points from the previous mesh to increase or decrease the mesh density, and (c) p‐refinement (Panourgias et al., 2014) where the element order changes (e.g.,. from linear to quadratic to cubic etc.)…”

Advanced two phase flow model for transient molten salt receiver system simulation

“…However, in vertical receiver tubes we can assume locally identical velocities and temperatures of the phases and thus eliminate two differential equations. This leads to a homogeneous model, in which the flow is treated like the flow of a single phase (Francke, 2014;van Zwieten et al, 2015). The assumption of the identical velocity would not be valid for sections with horizontal flow, but an accurate representation of the two-phase flow is only necessary in the vertical absorber tubes of the receiver.…”

Entropy stable DGSEM for nonlinear hyperbolic systems in nonconservative form with application to two-phase flows

“…Computations are done with the entropy stable numerical scheme (45) and fourth-order accuracy, p = 3. The limiter (54) is applied at the end of each stage unless stated otherwise.…”

“…The limiter (54) guaranties a discrete maximum principle on the void fractions m α i j ≤ α0≤k≤p,n+1 i, j ≤ M α i j and keeps the entropy inequality (4) at the discrete level in the sense that [14, Lemma 3.1] for η convex we have…”

“…Some works rely on the discontinuous Galerkin approximation of nonconservative systems in the fields of either the shallow water flows [28,22,47], or magnetohydrodynamics (MHD) [34,22], or two-phase flows [54,25,26,40,30,48,27,22], etc. Note that the works in [28] and [34] use the DGSEM as discretization method and derive, respectively, high-order entropy conservative and well balanced discretization of the shallow water equations through skew-symmetric splitting techniques, and entropy stable schemes for the ideal compressible MHD equations by using two-point numerical fluxes from [13] at element interfaces and treating the nonconservative product as source terms without particular treatment.…”