Output-based space–time mesh adaptation for the compressible Navier–Stokes equations

Fidkowski, Krzysztof J.; Luo, Yuxing

doi:10.1016/j.jcp.2011.03.059

Cited by 46 publications

(40 citation statements)

References 35 publications

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“…[20][21][22] In our previous work we have employed space-time discontinuous Galerkin (DG) and hybridized discontinuous Galerkin (HDG) 23-28 finite element discretizations using time slabs and an approximate space-time solver. 13,29 Output-based methods rely on an adjoint solution, which for unsteady problems is typically obtained by reverse time-integration and linearization about a stored primal state. Figure 1(a) shows a schematic of the adaptive process, in which the unsteady simulation is run multiple times, starting with a coarse space-time mesh that is successively improved.…”

Section: Iia Output-based Methods For Unsteady Flowsmentioning

confidence: 99%

Output Error Estimation for Chaotic Flows

Shimizu

Fidkowski

2016

46th AIAA Fluid Dynamics Conference

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This paper presents two methods for estimating the effect of numerical discretization error on statistical output accuracy in chaotic unsteady flow simulations: (1) an extension of recent advances in least-squares shadowing sensitivity calculations (LSS), and (2) an approximate time-windowing approach with individual adjoint solutions on each time window. Both methods rely on output adjoints, a direct application of which is not possible for chaotic systems, in which sensitivities to initial conditions and single-point discretization errors grow exponentially. This paper shows results for two prototypical chaotic systems: the Lorenz oscillator and the modified ergodic Kuramoto-Sivashinksy partial differential equation (MEKS). In addition it presents results for a low-Reynolds number Navier-Stokes flow to demonstrate the effectivity of the error estimates. Preliminary adaptive results are also included, in which spatially-localized forms of the error estimates drive static mesh adaptation to reduce errors in statistical outputs.

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Section: Iia Output-based Methods For Unsteady Flowsmentioning

confidence: 99%

Output Error Estimation for Chaotic Flows

Shimizu

Fidkowski

2016

46th AIAA Fluid Dynamics Conference

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“…Fidkowski and Luo [16] describe an adjoint based adaptive space-time DG scheme for the compressible Navier-Stokes equations. The space-time mesh is the tensor product of an unstructured spatial mesh and time-slabs.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2017

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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.

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“…There are only a few papers dealing with it, let us mention [30], which uses the so-called goal-oriented a posteriori error estimation for stationary compressible Navier-Stokes equations based on the approach [31], see also [32]. A similar idea was developed in [33,34] for the space-time discontinuous Galerkin method applied to the Navier-Stokes equations.…”

Section: Introductionmentioning

confidence: 99%