An Efficient Interface Capturing Method for Allen-Cahn and Cahn-Hilliard Type Equations Based on a Flow Map Approach in Lagrangian Coordinates
Host
Department of Applied Mathematics
Speaker
Qing Cheng
Department of Applied Mathematics, Illinois Institute of Technology
www.iit.edu/directory/people/qing-cheng
Description
We develop a Lagrangian numerical method (the flow dynamic approach (FDA)), based on the Energetic Variational Approach (EnVarA), motivated by Rayleigh and Onsager. The method posses advantages in capturing the sharp interface, comparing with numerical methods in Eulerian coordinates. As demonstrations we derive the equation of trajectory in Lagrangian coordinate for Allen-Cahn and Cahn-Hilliard type equation under the flow map and energy dissipative laws. Several corresponding numerical schemes are designed for these equations of trajectory in Lagrangian coordinate. These numerical schemes automatically obey the energy dissipative law and variational structures. Numerical simulations are provided to show relating fewer points (in fact less than 10) are enough to resolve sharp interfaces by using our Lagrangian numerical method for Allen-Cahn type equation.
Event Topic
Stochastic & Multiscale Modeling and Computation