A fast numerical scheme for the Godunov–Peshkov–Romenski model of continuum mechanics

Jackson, Haran

doi:10.1016/j.jcp.2017.07.055

Cited by 8 publications

(13 citation statements)

References 24 publications

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“…Under circumstances in which the flow is compressed heavily in one direction relative to the other directions, it should be noted that the linearization assumption (53) used to derive the approximate analytical solver may break down. As discussed in Jackson [14], this is due to the fact that one of the singular values of the distortion tensor will be much larger than the others, and the mean of the squares of the singular values will be distant to the geometric mean. The subsequent linearization of the ODE governing the mean of the singular values will then fail.…”

Section: Discussionmentioning

confidence: 99%

A numerical scheme for non-Newtonian fluids and plastic solids under the GPR model

Jackson

Nikiforakis

2019

Journal of Computational Physics

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A method for modeling non-Newtonian fluids (dilatants and pseudoplastics) by a power law under the Godunov-Peshkov-Romenski model is presented, along with a new numerical scheme for solving this system. The scheme is also modified to solve the corresponding system for power-law elastoplastic solids.The scheme is based on a temporal operator splitting, with the homogeneous system solved using a finite volume method based on a WENO reconstruction, and the temporal ODEs solved using an analytical approximate solution. The method is found to perform favorably against problems with known exact solutions, and numerical solutions published in the open literature. It is simple to implement, and to the best of the authors' knowledge it is currently the only method for solving this modified version of the GPR model.

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Section: Discussionmentioning

confidence: 99%

A numerical scheme for non-Newtonian fluids and plastic solids under the GPR model

Jackson

Nikiforakis

2019

Journal of Computational Physics

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“…In our formulation, these variables act through the source systems for distortion and heat conduction. As a result, the assumptions of Jackson's semi-analytic ODE solvers [27] will no longer hold in the current case. We work around this by using the odeint library of numerical ODE solvers from Boost 1.71.0.0 for this problem.…”

Section: Viscous Heating-induced Detonationmentioning

confidence: 99%

“…The reactive ODE is solved using an explicit fourth order Runge-Kutta method. The distortion and thermal impulse equations (70b), (70c) are solved using the semi-analytic ODE solver of Jackson [27,28].…”

Section: Ode Solvermentioning

confidence: 99%

“…The PSL acts through a possibly stiff relaxation source term in the evolution equation of the distortion tensor. This stiffness, along with the quasi-conservative nature of the model poses a challenge for its numerical solution, which has been the subject of a number of papers, for example [25,26,27,28]. When compared against the requirements of our formulation, this unified theory of continuum modelling seems promising.…”

Section: Introductionmentioning

confidence: 99%

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A unified multi-phase and multi-material formulation for combustion modelling

Nikodemou,

Michael,

Nikiforakis

2021

Preprint

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The motivation of this work is to produce an integrated formulation for material response (e.g. elastoplastic, viscous, viscoplastic etc.) due to detonation wave loading. Here, we focus on elastoplastic structural response. In particular, we are interested to capture miscible and immiscible behaviour within condensed-phase explosives arising from the co-existence of a reactive carrier mixture of miscible materials, and several material interfaces due to the presence of immiscible impurities such as particles or cavities. The dynamic and thermodynamic evolution of the explosive is communicated to one or more inert confiners through their shared interfaces, which may undergo severe topological change. We also wish to consider elastic and plastic structural response of the confiners, rather than make a hydrodynamic assumption for their behaviour. Previous work by these authors has met these requirements by means of the simultaneous solution of appropriate systems of equations for the behaviour of the condensed-phase explosive and the elastoplastic behaviour of the confiners. To that end, both systems were written in the same mathematical form as a system of inhomogeneous hyperbolic partial differential equations which were solved on the same discrete space using the same algorithms, as opposed to coupling fluid and solid algorithms (co-simulation).In the present work, we employ a single system of partial differential equations (PDEs) proposed by Peshkov and Romenski, which is able to account for different states of matter by means of generalising the concept of distortion tensors beyond solids. We amalgamate that formulation with a single system of PDEs which meets the requirement of co-existing miscible and immiscible explosive mixtures. We present the mathematical derivation and construct appropriate algorithms for its solution. The resulting model is validated against exact solutions for several use-cases, including mechanically-and thermally-induced, inviscid and viscous detonations. Results indicate that the model can accurately simulate a very broad range of problems involving the nonlinear interaction between reactive and inert materials within a single framework.

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“…These convergence criteria are chosen so that the variables required to be less than T OL are dimensionless. At every iteration, (81b) is solved using the ODE solvers presented in [32,33].…”

Section: Boundary Conditionsmentioning

confidence: 99%

A unified Eulerian framework for multimaterial continuum mechanics

Jackson

Nikiforakis

2020

Journal of Computational Physics

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A framework for simulating the interactions between multiple different continua is presented. Each constituent material is governed by the same set of equations, differing only in terms of their equations of state and strain dissipation functions. The interfaces between any combination of fluids, solids, and vacuum are handled by a new Riemann Ghost Fluid Method, which is agnostic to the type of material on either side (depending only on the desired boundary conditions).The Godunov-Peshkov-Romenski (GPR) model is used for modeling the continua (having recently been used to solve a range of problems involving Newtonian and non-Newtonian fluids, and elastic and elastoplastic solids), and this study represents a novel approach for handling multimaterial problems under this model.The resulting framework is simple, yet capable of accurately reproducing a wide range of different physical scenarios. It is demonstrated here to accurately reproduce analytical results for known Riemann problems, and to produce expected results in other cases, including some featuring heat conduction across interfaces, and impact-induced deformation and detonation of combustible materials. The framework thus has the potential to streamline development of simulation software for scenarios involving multiple materials and phases of matter, by reducing the number of different systems of equations that require solvers, and cutting down on the amount of theoretical work required to deal with the interfaces between materials.

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A fast numerical scheme for the Godunov–Peshkov–Romenski model of continuum mechanics

Cited by 8 publications

References 24 publications

A numerical scheme for non-Newtonian fluids and plastic solids under the GPR model

A numerical scheme for non-Newtonian fluids and plastic solids under the GPR model

A unified multi-phase and multi-material formulation for combustion modelling

A unified Eulerian framework for multimaterial continuum mechanics

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