Efficient high-order discontinuous Galerkin schemes with first-order hyperbolic advection-diffusion system approach

JOURNAL OF COMPUTATIONAL PHYSICS

卷:321

Article

Mazaheri, Alireza¹  Nishikawa, Hiroaki² 

[1] NASA, Langley Res Ctr, Hampton, VA 23681 USA

[2] Natl Inst Aerosp, Hampton, VA 23666 USA

关键词: High-order;    Discontinuous Galerkin (DG);    DG with hyperbolic first-order system (DG-H);    Advection-diffusion;    WENO;    Interior Penalty (IP);   

DOI  :  10.1016/j.jcp.2016.06.006

来源: Elsevier

【 摘 要 】

We propose arbitrary high-order discontinuous Galerkin (DG) schemes that are designed based on a first-order hyperbolic advection-diffusion formulation of the target governing equations. We present, in details, the efficient construction of the proposed high-order schemes (called DG-H), and show that these schemes have the same number of global degrees-of-freedom as comparable conventional high-order DG schemes, produce the same or higher order of accuracy solutions and solution gradients, are exact for exact polynomial functions, and do not need a second-derivative diffusion operator. We demonstrate that the constructed high-order schemes give excellent quality solution and solution gradients on irregular triangular elements. We also construct a Weighted Essentially Non-Oscillatory (WENO) limiter for the proposed DG-H schemes and apply it to discontinuous problems. We also make some accuracy comparisons with conventional DG and interior penalty schemes. A relative qualitative cost analysis is also reported, which indicates that the high-order schemes produce orders of magnitude more accurate results than the low-order schemes for a given CPU time. Furthermore, we show that the proposed DG-H schemes are nearly as efficient as the DG and Interior-Penalty (IP) schemes as these schemes produce results that are relatively at the same error level for approximately a similar CPU time. Published by Elsevier Inc.

【 授权许可】

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