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- W4301207169 abstract "In this paper we consider discontinuous Galerkin (DG) methods for the incompressible Navier-Stokes equations in the framework of projection methods. In particular we employ symmetric interior penalty DG methods within the second-order rotational incremental pressure correction scheme. The major focus of the paper is threefold: i) We propose a modified upwind scheme based on the Vijayasundaram numerical flux that has favourable properties in the context of DG. ii) We present a novel postprocessing technique in the Helmholtz projection step based on $H(text{div})$ reconstruction of the pressure correction that is computed locally, is a projection in the discrete setting and ensures that the projected velocity satisfies the discrete continuity equation exactly. As a consequence it also provides local mass conservation of the projected velocity. iii) Numerical results demonstrate the properties of the scheme for different polynomial degrees applied to two-dimensional problems with known solution as well as large-scale three-dimensional problems. In particular we address second-order convergence in time of the splitting scheme as well as its long-time stability." @default.
- W4301207169 created "2022-10-05" @default.
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- W4301207169 date "2016-12-02" @default.
- W4301207169 modified "2023-09-26" @default.
- W4301207169 title "A Stable and High-Order Accurate Discontinuous Galerkin Based Splitting Method for the Incompressible Navier-Stokes Equations" @default.
- W4301207169 doi "https://doi.org/10.48550/arxiv.1612.00657" @default.
- W4301207169 hasPublicationYear "2016" @default.
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