Further study on the geometric conservation law for finite volume method on dynamic unstructured mesh

Chang, Xinghua; Ma, Ruixuan; Zhang, Laiping; He, Xiao‐Gang; Li, Ming

doi:10.1016/j.compfluid.2015.07.023

Cited by 12 publications

(12 citation statements)

References 22 publications

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“…(43) are equivalent, but as with Eqs. (34), (25) and (29), these relationships are not satisfied upon discretization. Therefore, for reference purposes, results obtained using this discretization are referred to as being obtained with the "inconsistent" method.…”

Section: Methods 1 Methodsmentioning

confidence: 99%

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High-Order Stabilized Finite Elements on Dynamic Meshes

Anderson

Newman²

2018

2018 AIAA Aerospace Sciences Meeting

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The development of dynamic mesh capability for turbulent flow simulations using the Streamlined Upwind Petrov-Galerkin (SUPG) discretization is described. The current work extends previous research to include high-order spatial accuracy, including the satisfaction of the discrete geometric conservation law (GCL) on curved elements. Two closelyrelated schemes are described and the ability of these schemes to satisfy the GCL, while also maintaining temporal accuracy and conservation is assessed. Studies indicate that although one scheme discretizes the time derivative in conservative form, both schemes exhibit temporal conservation errors that decrease according to the expected design order of accuracy. The source of the temporal conservation errors is examined, and it is demonstrated that many finite-volume and finite-element schemes can also be expected to have difficulty strictly satisfying conservation in time. The effects on conservation are examined and, while present in the simulations, are seen to be negligible for the problems considered.

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Section: Methods 1 Methodsmentioning

confidence: 99%

“…35, the time derivative of (QJ) has been rewritten in a nonconservative form. While common, [28][29][30] this approach requires investigation to quantify potentially undesirable effects. Additionally, this relationship is similar to Eqs.…”

Section: ∂ ∂T ω(T)mentioning

confidence: 99%

High-Order Stabilized Finite Elements on Dynamic Meshes

Anderson

Newman²

2018

2018 AIAA Aerospace Sciences Meeting

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“…to satisfy the DGCL, the volume V * ,n+1 must be modified [21]. With the firstorder Euler time discretized scheme, Eq.…”

Section: Geometric Conservation Lawmentioning

confidence: 99%

“…As the DGCL scheme1 is much easy to implement, and only one time level (F n+1/2 ) is needed to calculate the flux at cell interface, it can natural couple with current ALE-type DUGKS. Though DGCL scheme2 and scheme3 are much complex, further improved ALE-type DUGKS framework such as highorder DUGKS [28] or multi-time-level implicit method [21] which the geometry information at intermediate time-levels are much difficult to define [29], these two schemes are the good choice. Besides, the scheme2 and scheme3 are the volume-constrained scheme, the face-constrained scheme [21] also can be used but not considered in this paper.…”

Section: Geometric Conservation Lawmentioning

confidence: 99%

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Arbitrary Lagrangian-Eulerian-type discrete unified gas kinetic scheme for low-speed continuum and rarefied flow simulations with moving boundaries

2019

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In this paper, the original discrete unified gas kinetic scheme (DUGKS) is extended to arbitrary Lagrangian-Eulerian (ALE) framework for simulating the low-speed continuum and rarefied flows with moving boundaries. For ALE method, the mesh moving velocity is introduced into the Boltzmann-BGK equation. The remapping-free scheme is adopted to develop the present ALE-type DUGKS, which avoids the complex rezoning and remapping process in traditional ALE method. As in some application areas, the large discretization errors will be introduced into the simulation if the geometric conservation is not guaranteed. Three compliant approaches of the geometric conservation law (GCL) are discussed and a uniform flow test case is conducted to validate these schemes. To illustrate the performance of present ALE-type DUGKS, four test cases are carried out. Two of them are the continuum flow cases, which are the flows around the oscillating circular cylinder and the pitching NACA0012 airfoil, respectively. Others are the rarefied flow cases, one is the moving piston driven by the rarefied gas, another is the flow caused by the plate oscillating in its normal direction. The results of all test cases are in good agreement with the other numerical and/or experimental results, demonstrating the capability of present ALE-type DUGKS to cope with the moving boundary problems at

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Numerical investigation on aerodynamic performance of a bionic flapping wing

Chang

Zhang

et al. 2019

Appl. Math. Mech.-Engl. Ed.

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Further study on the geometric conservation law for finite volume method on dynamic unstructured mesh

Cited by 12 publications

References 22 publications

High-Order Stabilized Finite Elements on Dynamic Meshes

High-Order Stabilized Finite Elements on Dynamic Meshes

Arbitrary Lagrangian-Eulerian-type discrete unified gas kinetic scheme for low-speed continuum and rarefied flow simulations with moving boundaries

Numerical investigation on aerodynamic performance of a bionic flapping wing

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