Solving phase field equations using a meshless method. (English) Zbl 1109.65087
Summary: The phase field equation is solved by using a meshless reproducing kernel particle method for the very first time. The 1D phase field equation is solved using different grid sizes and various time steps at a given grid size. The method can give accurate solutions across the interface, and allows a larger time step than explicit finite-difference method. The 2D phase field equation is computed by the present method and a classic shrinking of a circle is simulated. This shows the powerfulness and the potential of the method to treat more complicated problems.
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 35Q72 | Other PDE from mechanics (MSC2000) |
Keywords:
phase field equation; meshless method; comparison of methods; numerical examples; Cahn-Hilliard equation; Allen-Cahn equation; reproducing kernel particle method; finite-difference methodReferences:
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