A three-dimensional finite element arbitrary Lagrangian–Eulerian method for shock hydrodynamics on unstructured grids

Waltz, Jacob; Morgan, Nathaniel R.; Canfield, Thomas R.; Charest, Marc; Risinger, L. Dean; Wohlbier, J.G.

doi:10.1016/j.compfluid.2013.12.021

Cited by 46 publications

(41 citation statements)

References 44 publications

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“…The above equations are solved with a lumped mass, edge-based finite element method for linear tetrahedral cells 16 and a multistage explicit time stepping scheme, integrating the spatially discretized system The above equations are solved with a lumped mass, edge-based finite element method for linear tetrahedral cells 16 and a multistage explicit time stepping scheme, integrating the spatially discretized system…”

Section: Ale Formulationmentioning

confidence: 99%

“…Because the focus of this work is on the mesh motion procedure, the complete ALE algorithm is not presented here and the reader is referred to Waltz et al 16 for further details. The semidiscrete equations, including the coordinate equation, are integrated in time with a 2-step Runge-Kutta method.…”

Section: Ale Formulationmentioning

confidence: 99%

“…In typical Lagrange-plus-remap ALE methods, [2][3][4][5] the mesh moves with the fluid in the Lagrangian step and is then smoothed in a way that improves mesh quality. Mesh velocity smoothing also has been applied to shock hydrodynamics problems [16][17][18] : The mesh velocity is initially set equal to the fluid velocity and then smoothed to maintain mesh quality. A variant on the Lagrange-plus-remap method is to replace the smoothing step with a reconnection step.…”

Section: Introductionmentioning

confidence: 99%

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Improved ALE mesh velocities for complex flows

Bakosi

Waltz

Morgan

2017

Numerical Methods in Fluids

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Summary A key choice in the development of arbitrary Lagrangian‐Eulerian solution algorithms is how to move the computational mesh. The most common approaches are smoothing and relaxation techniques, or to compute a mesh velocity field that produces smooth mesh displacements. We present a method in which the mesh velocity is specified by the irrotational component of the fluid velocity as computed from a Helmholtz decomposition, and excess compression of mesh cells is treated through a noniterative, local spring‐force model. This approach allows distinct and separate control over rotational and translational modes. The utility of the new mesh motion algorithm is demonstrated on a number of 3D test problems, including problems that involve both shocks and significant amounts of vorticity.

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Section: Ale Formulationmentioning

confidence: 99%

Section: Ale Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Improved ALE mesh velocities for complex flows

Bakosi

Waltz

Morgan

2017

Numerical Methods in Fluids

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“…The SGH method stores the solution variables at different locations. Some finite element methods have been previously developed for hydrodynamic problems involving strong shocks [14][15][16][17][18][19][20][21]. In contrast to SGH, the CCH method is a collocated method where all solution variables are stored at the cell center.…”

Section: Introductionmentioning

confidence: 99%

A 3D finite element ALE method using an approximate Riemann solution

Chiravalle

Morgan

2016

Numerical Methods in Fluids

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Summary Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann‐like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann‐like problem. Two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well‐known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problem results are presented. Copyright © 2016 John Wiley & Sons, Ltd.

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“…Different approaches can be used for the solution of hydrodynamics equations: Eulerian [3,2], Lagrangian [14,7] or ALE [1,16]. In this work, a Lagrangian finite element approach is exploited to describe strong evolving material interfaces and shocks propagations.…”

Section: Introductionmentioning

confidence: 99%

A Lagrangian Finite Element Method for the Simulation of 3d Compressible Flows

Cremonesi¹,

Frangi²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. The numerical solution of compressible fluid flows is of paramount importance in many industrial and engineering applications. Compared to the classical fluid dynamics, the introduction of the fluid compressibility changes the formulation of the problem and consequently its computational treatment.Among the possible numerical solutions of compressible flow problems, the finite element method has always been privileged. However, the standard Eulerian approaches with fixed domain are not particularly suited to represent the strong shock waves and the significant movement of the external boundaries. On the contrary, in problems characterized by evolving surfaces, Lagrangian approaches can be very effective.The governing equations of compressible flow problems are mass, momentum and energy conservation. These equations are discretized in the spirit of the Lagrangian Particle Finite Element Method (PFEM). The strong distortions of the mesh, typical of the Lagrangian approaches, are managed with a continuous remeshing of the computational domain. The nodal unknowns are velocities, density and internal energy. To fully exploit the potential of continuous remeshing, only nodal variables are stored and consequently only linear interpolation are used. In addition, an artificial viscosity has been introduced to stabilize the formation and propagation of shock waves. Finally, explicit time integration of the governing equations enables a highly efficient solution of the discretized problem.The proposed approach has been validated against typical benchmarks of gas dynamics in the presence of strong shock waves. A very good agreement has been shown in all the tests proving the excellent accuracy and versatility of the proposed method.

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A three-dimensional finite element arbitrary Lagrangian–Eulerian method for shock hydrodynamics on unstructured grids

Cited by 46 publications

References 44 publications

Improved ALE mesh velocities for complex flows

Improved ALE mesh velocities for complex flows

A 3D finite element ALE method using an approximate Riemann solution

A Lagrangian Finite Element Method for the Simulation of 3d Compressible Flows

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