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Laboratory for Scientific Computing

 

Lab SC PhD student Tim Wallis completed his MPhil in Scientific Computing in 2019. His research focused on multi-phase, multi-physics diffuse interface modelling for coupled compressible fluid and elastoplastic solid systems. Originally formatted as a poster, here is a summary.

Outline

This work develops a purely diffuse interface computational framework that can model compressible elastoplastic solids and multi-phase reactive fluids in one all-encompassing system. THINC interface reconstruction keeps material interfaces sharp, overcoming the previous drawbacks of diffuse interface methods, while keeping computational costs down. The model has excellent agreement with experiment and previous simulation, whilst also having better conservation properties than other techniques.

Background
Multi-material modelling requires extra techniques to stably and accurately capture the interfaces between very different materials.

  • Previously this has been done with Ghost Fluid methods, but these have conservation errors and do not lend themselves well to physically mixing fluids such as those produced by detonations.

  • Diffuse interface methods have better conservation properties and can be applied naturally to fluid mixtures, but have not previously been applied systems with solids and detonating reactive fluids: this work accomplishes this.

Formulation
The method combines the reactive multi-fluid model of Michael and Nikiforakis, the elastoplastic model of Barton and the THINC interface reconstruction of Deng et al. Diffuse interface methods work by allowing a computational cell to contain any amount of any material, measured by the volume fraction that material occupies in the cell. It is best to make the implicit interfaces in these methods as thin as possible to prevent them becoming smeared and inaccurate. THINC interface reconstruction is used for this, where the volume fraction and other related quantities are fitted to a sub-cell tanh function.

Figure 1: A propagating contact wave between two ideal gases, showing how THINC reconstruction helps to keep interfaces sharp.

Figure 2: Rod impact test. An elastoplastic rod surrounded by air collides with a wall at 373 ms^-1. The colourbar shows the accumulated plastic strain. The initial/final length ratio is in excellent agreement with experiment, validating the elastoplastic parts of the model.

Figure 3: Richtmyer-Meshkov instability test from Luo et al. for THINC validation. A shock wave hits a square block of SF_6. This is a strenuous test of the THINC method as the instability produces thin tendrils. (above) simulation, (below) experiment.

Figure 4: One dimensional multi-material test of the reactive fluid and elastoplastic solid components. A ZND detonation wave impacts quiescent copper.

Figure 5: The impact-induced detonation test from Schoch et al., now in a fully diffuse interface framework. An explosive filled cylinder is hit from the left at 400 ms^-1 with a projectile, igniting a detonation wave. The top of each image shows pressure and the bottom shows density. We see excellent coupling of the elastoplastic solid and reactive fluid.

[1] R. P. Fedkiw et al. eng. Journal of Computational Physics 152.2 (1999).
[2] L. Michael and N. Nikiforakis. eng. Journal of Computational Physics 316 (2016).
[3] P. T. Barton. Journal of Computational Physics (2019).
[4] X. Deng et al. eng. Journal of Computational Physics 371 (2018).
[5] X. Luo et al. Journal of Fluid Mechanics 773 (2015).
[6] S. Schoch, K. Nordin-Bates, and N. Nikiforakis. eng. Journal of Computational Physics 252 (2013).

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