In recent years,Fourier spectral methods have emerged as competitive numerical methods for large-scale phase field simulations of microstructures in computational materials sciences.To further improve their effectiven...In recent years,Fourier spectral methods have emerged as competitive numerical methods for large-scale phase field simulations of microstructures in computational materials sciences.To further improve their effectiveness,we recently developed a new adaptive Fourier-spectral semi-implicit method(AFSIM)for solving the phase field equation by combining an adaptive moving mesh method and the semi-implicit Fourier spectral algorithm.In this paper,we present the application of AFSIM to the Cahn-Hilliard equation with inhomogeneous,anisotropic elasticity.Numerical implementations and test examples in both two and three dimensions are considered with a particular illustration using the well-studied example of mis-fitting particles in a solid as they approach to their equilibrium shapes.It is shown that significant savings in memory and computational time is achieved while accurate solutions are preserved.展开更多
The coarsening kinetics of a two-phase mixture with a large diffusional mobility disparity between the two phases is studied using a variable-mobility Cahn Hilliard equation.The semi-implicit spectral numerical techni...The coarsening kinetics of a two-phase mixture with a large diffusional mobility disparity between the two phases is studied using a variable-mobility Cahn Hilliard equation.The semi-implicit spectral numerical technique was employed,and a number of interpolation functions are considered for describing the change in diffusion mobility across the interface boundary from one phase to another.The coarsening rate of domain size was measured using both structure and pair correlation functions as well as the direct computation of particle sizes in real space for the case that the coarsening phase consists of dispersed particles.We discovered that the average size(R)versus time(t)follows the R^(10/3)∝t law,in contrast to the conventional LSW theory,R^(3)∝t,and the interface-diffusion dominated two-phase coarsening,R^(4)∝t.展开更多
基金This work has been supported by the National Science Foundation Information Technol-ogy Research Project(NSF-ITR)through Grant DMR-0205232The work of Qiang Du is also supported by NSF-DMS 0712744.
文摘In recent years,Fourier spectral methods have emerged as competitive numerical methods for large-scale phase field simulations of microstructures in computational materials sciences.To further improve their effectiveness,we recently developed a new adaptive Fourier-spectral semi-implicit method(AFSIM)for solving the phase field equation by combining an adaptive moving mesh method and the semi-implicit Fourier spectral algorithm.In this paper,we present the application of AFSIM to the Cahn-Hilliard equation with inhomogeneous,anisotropic elasticity.Numerical implementations and test examples in both two and three dimensions are considered with a particular illustration using the well-studied example of mis-fitting particles in a solid as they approach to their equilibrium shapes.It is shown that significant savings in memory and computational time is achieved while accurate solutions are preserved.
基金the financial supports from the National Science Foundation under the grant number DMR-0710483(Chen)NSF-DMS 0712744(Du)+1 种基金DMR-0510180(Liu)DMR-0710484(K.G.Wang).
文摘The coarsening kinetics of a two-phase mixture with a large diffusional mobility disparity between the two phases is studied using a variable-mobility Cahn Hilliard equation.The semi-implicit spectral numerical technique was employed,and a number of interpolation functions are considered for describing the change in diffusion mobility across the interface boundary from one phase to another.The coarsening rate of domain size was measured using both structure and pair correlation functions as well as the direct computation of particle sizes in real space for the case that the coarsening phase consists of dispersed particles.We discovered that the average size(R)versus time(t)follows the R^(10/3)∝t law,in contrast to the conventional LSW theory,R^(3)∝t,and the interface-diffusion dominated two-phase coarsening,R^(4)∝t.
