An Arbitrary Lagrangian-Eulerian Reconstructed Discontinuous Galerkin method for Compressible Multiphase flows

Pandare, Aditya; Wang, Chuanjin; Luo, Hong

doi:10.2514/6.2016-4270

Cited by 10 publications

(10 citation statements)

References 17 publications

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“…Another class of methods which can also be considered under the geometric interface tracking type are the Arbitrary Lagrangian-Eulerian (ALE) methods, which can alleviate mesh tangling problems. ALE methods have been extensively used to simulate multi-material hydrodynamics [7,8,9], where the mesh is moved with the material interface to enable sharp interface tracking.…”

Section: Numerical Methods For Multi-materials Hydrodynamicsmentioning

confidence: 99%

“…The benefit of the least-squares rDG(P n P m ) method is that the compactness of the stencil is retained. Studies of the rDG methods both on Eulerian compressible [29,30], incompressible [31] and ALE/Lagrangian systems [9] indicate that they can achieve design order of accuracy in space, in addition to significantly improving the accuracy of the underlying DG(P n ) solution.…”

Section: Discontinuous Galerkin Methodsmentioning

confidence: 99%

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A reconstructed discontinuous Galerkin method for multi‐material hydrodynamics with sharp interfaces

Pandare

Waltz

Bakosi

2020

Numerical Methods in Fluids

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Discontinuous Galerkin (DG) methods have been well established for single material hydrodynamics. However, consistent DG discretizations for non-equilibrium multi-material (more than two materials) hydrodynamics have not been extensively studied. In this work, a novel reconstructed discontinuous Galerkin (rDG) method for the single-velocity multi-material system is presented. The multi-material system being considered assumes stiff velocity relaxation, but does not assume pressure and temperature equilibrium between the multiple materials. A second-order DG(P 1 ) method and a third-order least-squares based rDG(P 1 P 2 ) are used to discretize this system in space, and a third-order TVD Runge-Kutta method is used to integrate in time. A well-balanced DG discretization of the non-conservative system is presented, and is verified by numerical test problems. Further, a consistent interface treatment is implemented, which ensures strict conservation of material masses and total energy. Numerical tests indicate that the DG and rDG methods are indeed second-and third-order accurate. Comparisons with the second-order finite volume method show that the DG and rDG methods are able to capture the interfaces more sharply. The DG and rDG methods are also more accurate in the single-material regions of the flow. This work focuses on the general multidimensional rDG formulation of the non-equilibrium multi-material system and a study of properties of the method via one-dimensional numerical experiments. The results from this research will be the foundation for a multi-dimensional high-order rDG method for multi-material hydrodynamics.

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Section: Numerical Methods For Multi-materials Hydrodynamicsmentioning

confidence: 99%

Section: Discontinuous Galerkin Methodsmentioning

confidence: 99%

A reconstructed discontinuous Galerkin method for multi‐material hydrodynamics with sharp interfaces

Pandare

Waltz

Bakosi

2020

Numerical Methods in Fluids

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“…The discontinuous Galerkin methods [1,2,3,4,5,8,9,25,26,27] have recently become popular for the solution of systems of conservation laws. Originally introduced in 1973 by Reed and Hill [2] in the framework of transport of neutrons, nowadays they are widely used in computational fluid dynamics, computational acoustics, and computational magnetohydrodynamics.…”

Section: Introductionmentioning

confidence: 99%

A p -adaptive Discontinuous Galerkin Method for Compressible Flows Using Charm++

Luo

Pandare

et al. 2020

AIAA Scitech 2020 Forum

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A parallel p-adaptive discontinuous Galerkin (DG) method was presented for compressible flows on 3D tetrahedral grids. Hierarchical orthogonal basis functions are adopted to facilitate the p-adaptation. Unlike the traditional data parallelism implemented by MPI, our parallel algorithm implemented in a new adaptive CFD code Quinoa * is based on the combination of task parallelism and data parallelism so that it fit in the framework of Charm++ library. This naturally enables asynchronous communications and dynamic load balancing techniques by the use of Charm++. A number of numerical experiments are conducted to demonstrate the performance of the developed p-adaptive DG method. The numerical results obtained indicate that using an appropriate load balancing strategy, Charm++ library provides an effective tool to achieve the dynamic load balancing for the p-adaptive DG method and consequently, the developed p-adaptive DG method can significantly reduce the total execution time comparison with the uniformly standard DG method.

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“…remapping) of physical variables between different meshes. For example, Luo et al [24] introduce second-order direct ALE HLLCE and Godunov schemes to solve the problems of multi-material flows while high-order direct ALE finite volume and discontinuous Galerkin (DG) schemes are proposed in [5,6] and [29,30], respectively. Unlike their traditional counterparts, which can readily handle free boundary domains in the Lagrangian phase and allow the mesh to move arbitrarily in the rezone phase, these direct ALE methods are not considered to deal with free boundary problems where the boundary moves at the flow velocity (which is part of the solutions to be sought) and therefore cannot be purely Lagrangian [6,29].…”

Section: Introductionmentioning

confidence: 99%

“…The scheme can be viewed as a new direct ALE method. Indeed, like the existing direct ALE methods [5,6,24,29,30], MMCC scheme does not need the remapping of physical variables between different meshes. But it also possesses a unique feature that other direct ALE methods do not have, that is, it can be degenerated to a purely Lagrangian scheme.…”

Section: Introductionmentioning

confidence: 99%

A third-order moving mesh cell-centered scheme for one-dimensional elastic-plastic flows

Cheng¹,

Huang²,

Jiang³

et al. 2017

Journal of Computational Physics

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A third-order moving mesh cell-centered scheme without the remapping of physical variables is developed for the numerical solution of one-dimensional elastic-plastic flows with the Mie-Grüneisen equation of state, the Wilkins constitutive model, and the von Mises yielding criterion. The scheme combines the Lagrangian method with the MMPDE moving mesh method and adaptively moves the mesh to better resolve shock and other types of waves while preventing the mesh from crossing and tangling. It can be viewed as a direct arbitrarily Lagrangian-Eulerian method but can also be degenerated to a purely Lagrangian scheme. It treats the relative velocity of the fluid with respect to the mesh as constant in time between time steps, which allows high-order approximation of free boundaries. A time dependent scaling is used in the monitor function to avoid possible sudden movement of the mesh points due to the creation or diminishing of shock and rarefaction waves or the steepening of those waves. A two-rarefaction Riemann solver with elastic waves is employed to compute the Godunov values of the density, pressure, velocity, and deviatoric stress at cell interfaces. Numerical results are presented for three examples. The third-order convergence of the scheme and its ability to concentrate mesh points around shock and elastic rarefaction waves are demonstrated. The obtained numerical results are in good agreement with those in literature. The new scheme is also shown to be more accurate in resolving shock and rarefaction waves than an existing third-order cell-centered Lagrangian scheme.

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An Arbitrary Lagrangian-Eulerian Reconstructed Discontinuous Galerkin method for Compressible Multiphase flows

Cited by 10 publications

References 17 publications

A reconstructed discontinuous Galerkin method for multi‐material hydrodynamics with sharp interfaces

A reconstructed discontinuous Galerkin method for multi‐material hydrodynamics with sharp interfaces

A p -adaptive Discontinuous Galerkin Method for Compressible Flows Using Charm++

A third-order moving mesh cell-centered scheme for one-dimensional elastic-plastic flows

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