A high-order vertex-centered quasi-Lagrangian discontinuous Galerkin method for compressible Euler equations in two-dimensions

Liu, Liqi; Shen, Zhijun; Zeng, Qinghong; Zhang, Jia

doi:10.1016/j.compfluid.2020.104678

Cited by 1 publication

(2 citation statements)

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“…Besides the SGH schemes and the CCH schemes, the vertex-centered hydrodynamics (VCH) has attracted more and more interests in recent years, see [35][36][37][38]. In this kind of schemes, the conserved variables (the mass, the momentum, and the total energy) are all stored at the nodes of mesh.…”

Section: Introductionmentioning

confidence: 99%

“…Aguirre et al [37] developed an upwind vertex-centered finite volume solver for Lagrangian solid dynamics. Liu et al [38] developed a vertexcentered DG method in the direct ALE form for compressible single-material flow, and the vertex control volumes of this scheme are constructed with curved edges. This scheme is third-order accurate both in space and time, and it is conservative for the mass, the momentum and the total energy.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Vertex-Centered Arbitrary Lagrangian-Eulerian Finite Volume Method with Sub-Cells for Two-Dimensional Compressible Flow

Zhao¹,

Yu²,

Zhang³

et al. 2024

AAMM

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In this paper, we present a new vertex-centered arbitrary Lagrangian-Eulerian (ALE) finite volume scheme for two-dimensional compressible flow. In our scheme, the momentum equation is discretized on the vertex control volume, while the mass equation and the energy equation are discretized on the sub-cells which are included in the vertex control volume. We attain the average of the fluid velocity on the vertex control volume directly by solving the conservation equations. Then we can obtain the fluid velocity at vertex with the reconstructed polynomial of the velocity. This fluid velocity is chosen as the mesh velocity, which makes the mesh move in a Lagrangian manner. Two WENO (Weighted Essentially Non-Oscillatory) reconstructions for the density (the total energy) and the velocity are used to make our scheme achieve the anticipated accuracy. Compared with the general vertexcentered schemes, our scheme with the new approach for the space discretization can simulate some multi-material flows which do not involve large deformations. In addition, our scheme has good robustness, and some numerical examples are presented to demonstrate the anticipated accuracy and the good properties of our scheme.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%