Analysis of Phase-Field Models and Discretizations

In this talk, I will address several issues related to numerical and mathematical aspects of phase-field models and their numerical simulations. For the two-phase Allen-Cahn and Cahn Hilliard model, I will demonstrate that (1) the popular convex splitting schemes are fully implicit schemes in disguise but with a much delayed time; (2) by using energy minimization, an fully implicit scheme can be made unconditionally stable; and (3) an unconditionally stable scheme is not necessarily better than a conditionally stable scheme. When the number of phases is more than 2, I will discuss some phase-field models involving the pairwise surface tension as a coefficient matrix in the energy density function, prove the unisolvent and symmetric positive property of the coefficient matrix, and analyze the energy stability and convexity property of different discretization schemes.

Event Topic

Stochastic & Multiscale Modeling and Computation