A phase-field model of solidification with convection

Anderson, D M; McFadden, G B; Wheeler, A A

doi:10.6028/nist.ir.6237

Cited by 2 publications

(4 citation statements)

References 39 publications

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“…The phase-field framework is a mathematical approach to describe systems out of thermodynamic equilibrium (Anderson et al, 1998). It was first introduced in the context of solidification processes and phase transitions of pure or multi-component materials (Cahn & Hilliard, 1958;Boettinger et al, 2002).…”

Section: A Phase-field Model Of Lava Solidification 21 Model Equationsmentioning

confidence: 99%

“…It was first introduced in the context of solidification processes and phase transitions of pure or multi-component materials (Cahn & Hilliard, 1958;Boettinger et al, 2002). The framework evolves the solidification front as part of the solution to the system of partial differential equations, avoiding the need for explicit tracking of the moving interface as is traditionally done in the Stefan problem (Anderson et al, 1998). Here, we consider a simplified model of lava solidification where we track the binary solidification of lava through a phase variable, denoted φ (φ = 1 for the melt and φ = 0 for the solid phase), and the corresponding temperature (T ).…”

Section: A Phase-field Model Of Lava Solidification 21 Model Equationsmentioning

confidence: 99%

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Some Lava Flows May Not Have Been as Thick as They Appear

Katona

Mittal

et al. 2021

Geophysical Research Letters

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Continental flood basalt (CFB) province eruptions contain the largest (𝐴𝐴 𝐴 1,000 km 3 , Bryan & Ernst, 2008;Self et al., 2014) and longest (∼1,000 km; Self et al., 2008) lava flows. Since CFBs are frequently coeval with severe environmental perturbations including mass extinctions, ocean anoxic events, and hyperthermal events (Clapham & Renne, 2019), understanding the physical process and timescale of flow field emplacement would help quantify the release of volcanic gases that have environmental impacts (e.g., CO 2 , SO 2 ). However, despite decades of work, the tempo and style of CFB eruptions remain poorly quantified.CFB lava flow fields are composed of 5-100 m thick dominantly pāhoehoe lobes (Self et al., 1998(Self et al., , 2021. Given the general lack of large lava tubes in CFBs (Kale et al., 2020;Self et al., 1998), the primary process hypothesized for creating thick flows is the formation of pāhoehoe lobes by inflation (Hon et al., 1994). If the quasi-continuous magma flux into individual lava lobes is sufficient, the solidifying surface crust can continuously rise due to increasing pressure (Hoblitt et al., 2012;Hon et al., 1994). If the lateral magma pressure is large enough, the lobe can propagate laterally by sporadic breakouts (

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Section: A Phase-field Model Of Lava Solidification 21 Model Equationsmentioning

confidence: 99%

Section: A Phase-field Model Of Lava Solidification 21 Model Equationsmentioning

confidence: 99%

Some Lava Flows May Not Have Been as Thick as They Appear

Katona

Mittal

et al. 2021

Geophysical Research Letters

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“…Yet phase-field models stand out for combining several key benefits: They are physically motivated, introduced by Fix [22] and Langer [23] to model free energy near phase boundaries (following from Hohenburg and Halperin’s model C [24]).They generalize canonical models of phase separation, reducing to Allen–Cahn and Hele-Shaw flow (among others) in various asymptotic limits [25,26]. They are easily extensible to more general systems, including two-component alloys [27–30], convection [31,32] or multi-phase flows [20,33]. They can be made thermodynamically consistent [34–38].…”

Section: Introductionmentioning

confidence: 99%

“…They are easily extensible to more general systems, including two-component alloys [27–30], convection [31,32] or multi-phase flows [20,33].…”

Section: Introductionmentioning

confidence: 99%

Improved phase-field models of melting and dissolution in multi-component flows

et al. 2020

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We develop and analyse the first second-order phase-field model to combine melting and dissolution in multi-component flows. This provides a simple and accurate way to simulate challenging phase-change problems in existing codes. Phase-field models simplify computation by describing separate regions using a smoothed phase field. The phase field eliminates the need for complicated discretizations that track the moving phase boundary. However, standard phase-field models are only first-order accurate. They often incur an error proportional to the thickness of the diffuse interface. We eliminate this dominant error by developing a general framework for asymptotic analysis of diffuse-interface methods in arbitrary geometries. With this framework, we can consistently unify previous second-order phase-field models of melting and dissolution and the volume-penalty method for fluid–solid interaction. We finally validate second-order convergence of our model in two comprehensive benchmark problems using the open-source spectral code Dedalus.

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A phase-field model of solidification with convection

Abstract: We develop a phase-field model for

Cited by 2 publications

References 39 publications

Some Lava Flows May Not Have Been as Thick as They Appear

Some Lava Flows May Not Have Been as Thick as They Appear

Improved phase-field models of melting and dissolution in multi-component flows

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