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Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

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An Interface-Fitted Finite Element Level Set Method with Application to Solidification and Solvation.

Bo Li¹, John Shopple

¹Department of Mathematics and the NSF Center for Theoretical Biological Physics, University of California, San Diego, 9500 Gilman Drive, Mail code: 0112. La Jolla, CA 92093-0112, USA. bli@math.ucsd.edu.

Communications in Computational Physics

|September 24, 2013

Summary

This summary is machine-generated.

A novel finite element level set method accurately simulates interface motion using an interface-fitted mesh. This approach enhances diffusion equation solutions and captures complex phenomena like dendrite formation and molecular solvation interfaces.

Keywords:

curvature approximation dendrites finite element interface-fitted mesh level set method molecular solvation reinitialization solidification variational implicit-solvent models velocity extension

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Area of Science:

Computational fluid dynamics
Numerical analysis
Materials science

Background:

Simulating interface motion is crucial for various scientific and engineering problems.
Existing methods often struggle with accuracy and computational efficiency for complex geometries.
Accurate modeling of diffusion processes across interfaces is essential for understanding material behavior.

Purpose of the Study:

To develop a new finite element level set method for simulating interface motion.
To improve the accuracy of interface representation and diffusion equation solutions.
To apply the method to problems in solidification and molecular solvation.

Main Methods:

Development of a finite element level set method.
Utilizing an interface-fitted finite element mesh for accurate interface tracking.
Implementation of novel finite element techniques for curvature approximation, normal velocity extension, and level set reinitialization.
Application to solidification and molecular solvation problems.

Main Results:

The method accurately simulates interface motion influenced by local geometry and external forces.
The interface-fitted mesh allows for precise calculation of diffusion equation solutions.
Successful application to capture dendrites in solidification and determine optimal solute-solvent interfaces in solvation systems.

Conclusions:

The developed finite element level set method provides an accurate and efficient approach for interface motion simulation.
The interface-fitted mesh is key to achieving high accuracy in diffusion calculations.
The method shows broad applicability in diverse scientific domains, including materials science and molecular modeling.