A parallel implementation of an implicit discontinuous Galerkin finite element scheme for fluid flow problems

Vimmr, Jan; Bublík, Ondřej; Pecka, Aleš

doi:10.1016/j.advengsoft.2016.11.007

Cited by 7 publications

(7 citation statements)

References 18 publications

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“…The discontinuous Galerkin (DG) method [3,13,18] is a very stable and robust solution for a compressible fluid flow modelling. In the field of CFD, it is the main competitor for the finite volume method -still the most commonly used method in the industry.…”

Section: Spatial Discretizationmentioning

confidence: 99%

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Curvilinear element of the discontinuous Galerkin method designed to capture the labyrinth seal geometry exactly

Bublík

Pecka

Vimmr

2022

ACM

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The present study applies the discontinuous Galerkin finite element method to a numerical simulation of a compressible fluid flow through a labyrinth seal. This paper is proposes a curvilinear hexahedral element, which is deformed in such a way that it matches the rotated walls of the labyrinth seal exactly. A numerical study is performed on the staggered labyrinth seal with two teeth on the rotor and one tooth on the stator. For numerical simulation, three computational meshes with different refinement are considered. All of the numerical simulations are performed for both stationary rotor and for rotor rotating at 50 Hz. The obtained numerical results are compared with results computed by the commercial CFD software Ansys Fluent.

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Section: Spatial Discretizationmentioning

confidence: 99%

“…The advantage of the DG method is its stability, robustness, low artificial damping and the ability to achieve a highorder of spatial accuracy, see e.g. [3,13,18]. The key part of this study is the transformation of the reference element onto the physical element in such a way, that it matches the geometry of the labyrinth seal exactly.…”

Section: Introductionmentioning

confidence: 99%

Curvilinear element of the discontinuous Galerkin method designed to capture the labyrinth seal geometry exactly

Bublík

Pecka

Vimmr

2022

ACM

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“…(1) Initialize the level set function, velocity, and pressure (2) For n � 0, ... , N (t � 0 ⟶ T) (a) Solve equations (18) and (19)…”

Section: Computational Processmentioning

confidence: 99%

“…As for the capturing of free surface, the simple and efficient level set method [16,17] is utilized. We employ the implicit discontinuous Galerkin method [18,19] to handle the level set and its reinitialization equations for the accuracy and stability. With a view to the main drawback of the level set method [20], a correction technique [21,22] is also added to preserve the mass conservation property.…”

Section: Introductionmentioning

confidence: 99%

The Finite Element Numerical Investigation of Free Surface Newtonian and Non-Newtonian Fluid Flows in the Rectangular Tanks

Gao

2020

Mathematical Problems in Engineering

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In this paper, we develop a new computational framework to investigate the sloshing free surface flow of Newtonian and non-Newtonian fluids in the rectangular tanks. We simulate the flow via a two-phase model and employ the fixed unstructured mesh in the computation to avoid the mesh distortion and reconstruction. As for the solution of Navier–Stokes equation, we utilize the SUPG finite element method based on the splitting scheme. The same order interpolation functions are then used for velocity and pressure. Moreover, the moving interface is captured via the concise level set method. We take advantage of the implicit discontinuous Galerkin method to handle the solution of level set and its reinitialization equations. A mass correction technique is also added to ensure the mass conservation property. The dam break-free surface flow is simulated firstly to demonstrate the validity of our mathematical model. In addition, the sloshing Newtonian fluid in the tank with flat and rough bottoms is considered to illustrate the feasibility and robustness of our computational scheme. Finally, the development of free surface for non-Newtonian fluid is also studied in the two tanks, and the influence of power-law index on the sloshing fluid flow is analyzed.

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“…The system is completed by the Spalart-Allmaras turbulence model [2] for transport equation of eddy viscosity. The discontinuous Galerkin finite element method (DGFEM) is used for the spatial discretization of the system of equations [3,4]. The advantages of the method are high order of spatial accuracy and low artificial dissipation.…”

Section: Fig 2 Model Of the Bypass System Of The Valve 3 Modelling mentioning

confidence: 99%

The computational study in the unloading slot of the control valve

et al. 2018

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The flow in the unloading system of the control valve is modelled using the numerical simulation. The proportional flow values for various widths of the slot and openings are evaluated. The changes of the pressure and Mach number in the space of the valve are recorded for the selected pressure ratios. The influence of the length of the slot on the mass flow changes is assessed. The results are compared with the experimental findings.

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A parallel implementation of an implicit discontinuous Galerkin finite element scheme for fluid flow problems

Cited by 7 publications

References 18 publications

Curvilinear element of the discontinuous Galerkin method designed to capture the labyrinth seal geometry exactly

Curvilinear element of the discontinuous Galerkin method designed to capture the labyrinth seal geometry exactly

The Finite Element Numerical Investigation of Free Surface Newtonian and Non-Newtonian Fluid Flows in the Rectangular Tanks

The computational study in the unloading slot of the control valve

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