An interface-capturing Godunov method for the simulation of compressible solid-fluid problems

Barton, Philip T.

doi:10.1016/j.jcp.2019.03.044

Cited by 36 publications

(79 citation statements)

References 48 publications

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“…In particular, in this paper, we couple the GPR model with a simple diffuse interface approach, see [173,59,91,126]. For example, very interesting computational results with similar diffuse interface approaches and level set techniques for compressible multi-material flows have been obtained for example in [95,85,84,144,51,139,119,12]. Finally, we demonstrate that the ADER family of schemes is capable to resolve the GPR model in both solid and fluid regimes.…”

Section: Introduction and Review Of The Ader Approachmentioning

confidence: 84%

High Order ADER Schemes for Continuum Mechanics

et al. 2020

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In this paper we first review the development of high order ADER finite volume and ADER discontinuous Galerkin schemes on fixed and moving meshes, since their introduction in 1999 by Toro et al. We show the modern variant of ADER based on a space-time predictor-corrector formulation in the context of ADER discontinuous Galerkin schemes with a posteriori subcell finite volume limiter on fixed and moving grids, as well as on space-time adaptive Cartesian AMR meshes. We then present and discuss the unified symmetric hyperbolic and thermodynamically compatible (SHTC) formulation of continuum mechanics developed by Godunov, Peshkov and Romenski (GPR model), which allows to describe fluid and solid mechanics in one single and unified first order hyperbolic system. In order to deal with free surface and moving boundary problems, a simple diffuse interface approach is employed, which is compatible with Eulerian schemes on fixed grids as well as direct Arbitrary-Lagrangian-Eulerian methods on moving meshes. We show some examples of moving boundary problems in fluid and solid mechanics.

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Section: Introduction and Review Of The Ader Approachmentioning

confidence: 84%

High Order ADER Schemes for Continuum Mechanics

et al. 2020

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“…Firstly, the full multi-material base system of equations and its thermodynamics will be briefly outlined. The base system has been laid out in detail in previous works [2,33,34] and is not affected by the later additions of a rigid body, so shall not be repeated here in depth. Subsequently, the additional components required for the rigid body will be introduced.…”

Section: Governing Theorymentioning

confidence: 99%

“…The base system, devised by Barton [2], is an Allaire-type [1] multi-material diffuse interface system, capable of accounting for an arbitrary mixture of both fluids and elastoplastic solids. The state of any material l is characterised by its phasic density ρ (l) , volume fraction φ (l) , symmetric left unimodular stretch tensor V e , velocity vector u, and internal energy E .…”

Section: Base System 211 Evolution Equationsmentioning

confidence: 99%

“…where E = E +|u|/2 denotes the specific total energy, σ denotes the Cauchy stress tensor, β j = ∂V e k j /∂x k , and Φ represents the contribution from plastic effects (details of which can be found in Barton [2]). Some multi-physics closure models introduce a dependence on material history variables.…”

Section: Base System 211 Evolution Equationsmentioning

confidence: 99%

“…Mixture rules must be provided to represent the state of regions containing multiple materials in a thermodynamically consistent way. The following mixture rules are applied [1,2]:…”

Section: Thermodynamicsmentioning

confidence: 99%

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A unified diffuse interface method for the interaction of rigid bodies with elastoplastic solids and multi-phase mixtures

Wallis,

Barton,

Nikiforakis

2021

Preprint

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This work outlines a new multi-physics-compatible immersed rigid body method for Eulerian finite-volume simulations. To achieve this, rigid bodies are represented as a diffuse scalar field and an interface seeding method is employed to mediate the interface boundary conditions. The method is based on an existing multi-material diffuse interface method that is capable of handling an arbitrary mix of fluids and elastoplastic solids. The underlying method is general and can be extended to a range of different applications including high-strain rate deformation in elastoplastic solids and reactive fluid mixtures. As such, the new method presented here is thoroughly tested through a variety of problems, including fluid-rigid body interaction, elastoplastic-rigid body interaction, and detonation-structure interaction. Comparison is drawn between both experimental work and previous numerical results, with excellent agreement in both cases. The new method is straightforward to implement, highly local, and parallelisable. This allows the method to be employed in three dimensions with multiple levels of adaptive mesh refinement using complex immersed geometries. The rigid body field can be static or dynamic, with the THINC interface reconstruction method being used to keep the interface sharp in the dynamic case.

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