Moving mesh simulations of pitting corrosion

Abu Naser Sarker; Ronald D. Haynes; Michael D. Robertson; Abu Naser Sarker; Ronald D. Haynes; Michael D. Robertson

doi:10.3934/math.20241682

AIMS Mathematics

2024, Volume 9, Issue 12: 35401-35431. doi: 10.3934/math.20241682

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Moving mesh simulations of pitting corrosion

1.
Scientific Computing Program, Memorial University, St. John's, NL, A1C 5S7, Canada
2.
Department of Mathematics and Statistics, Memorial University, St. John's, NL, A1C 5S7, Canada
3.
Department of Physics, Acadia University, Wolfville, NS, B4P 2R6, Canada

Received: 15 March 2023 Revised: 20 November 2023 Accepted: 17 January 2024 Published: 19 December 2024
MSC : 65M50

Damages due to pitting corrosion of metals cost industry billions of dollars per year and can put human lives at risk. The design and implementation of an adaptive moving mesh method is provided for a moving boundary problem related to pitting corrosion. The adaptive mesh is generated automatically by solving a mesh PDE coupled to the nonlinear potential problem. The moving mesh approach is shown to enable initial mesh generation, provide automatic mesh adjustment (or recovery) and is able to smoothly tackle changing pit geometry. Materials with varying crystallography are considered. Changing mesh topology due to the merging of pits is also handled. The evolution of the pit shape, the pit depth, and the pit width are computed and compared to existing results in the literature. Mesh quality results are also included.
- pitting corrosion,
- adaptive moving mesh,
- MMPDE,
- FEM,
- crystallography
Citation: Abu Naser Sarker, Ronald D. Haynes, Michael D. Robertson. Moving mesh simulations of pitting corrosion[J]. AIMS Mathematics, 2024, 9(12): 35401-35431. doi: 10.3934/math.20241682

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Abstract

Damages due to pitting corrosion of metals cost industry billions of dollars per year and can put human lives at risk. The design and implementation of an adaptive moving mesh method is provided for a moving boundary problem related to pitting corrosion. The adaptive mesh is generated automatically by solving a mesh PDE coupled to the nonlinear potential problem. The moving mesh approach is shown to enable initial mesh generation, provide automatic mesh adjustment (or recovery) and is able to smoothly tackle changing pit geometry. Materials with varying crystallography are considered. Changing mesh topology due to the merging of pits is also handled. The evolution of the pit shape, the pit depth, and the pit width are computed and compared to existing results in the literature. Mesh quality results are also included.

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