Multiscale Finite-Difference-Diffusion-Monte-Carlo Method for Simulating Dendritic Solidification

@article{citeulike:2599521, abstract = {We present a novel hybrid computational method to simulate accurately dendritic solidification in the low undercooling limit where the dendrite tip radius is one or more orders of magnitude smaller than the characteristic spatial scale of variation of the surrounding thermal or solutal diffusion field. The first key feature of this method is an efficient multiscale diffusion Monte Carlo (DMC) algorithm which allows off-lattice random walkers to take longer and concomitantly rarer steps with increasing distance away from the solid-liquid interface. As a result, the computational cost of evolving the large-scale diffusion field becomes insignificant when compared to that of calculating the interface evolution. The second key feature is that random walks are only permitted outside of a thin liquid layer surrounding the interface. Inside this layer and in the solid, the diffusion equation is solved using a standard finite difference algorithm that is interfaced with the DMC algorithm using the local conservation law for the diffusing quantity. Here we combine this algorithm with a previously developed phase-field formulation of the interface dynamics and demonstrate that it can accurately simulate three-dimensional dendritic growth in a previously unreachable range of low undercoolings that is of direct experimental relevance.}, author = {Plapp, Mathis and Karma, Alain }, citeulike-article-id = {2599521}, doi = {10.1006/jcph.2000.6634}, journal = {Journal of Computational Physics}, keywords = {dendritic\_growth, dmc, multiscale}, month = {December}, number = {2}, pages = {592--619}, posted-at = {2008-03-26 19:02:15}, priority = {2}, title = {Multiscale Finite-Difference-Diffusion-Monte-Carlo Method for Simulating Dendritic Solidification}, url = {http://dx.doi.org/10.1006/jcph.2000.6634}, volume = {165}, year = {2000} }

TY - JOUR ID - citeulike:2599521 L3 - citeulike-article-id:2599521 TI - Multiscale Finite-Difference-Diffusion-Monte-Carlo Method for Simulating Dendritic Solidification JF - Journal of Computational Physics VL - 165 IS - 2 SP - 592 EP - 619 N2 - We present a novel hybrid computational method to simulate accurately dendritic solidification in the low undercooling limit where the dendrite tip radius is one or more orders of magnitude smaller than the characteristic spatial scale of variation of the surrounding thermal or solutal diffusion field. The first key feature of this method is an efficient multiscale diffusion Monte Carlo (DMC) algorithm which allows off-lattice random walkers to take longer and concomitantly rarer steps with increasing distance away from the solid-liquid interface. As a result, the computational cost of evolving the large-scale diffusion field becomes insignificant when compared to that of calculating the interface evolution. The second key feature is that random walks are only permitted outside of a thin liquid layer surrounding the interface. Inside this layer and in the solid, the diffusion equation is solved using a standard finite difference algorithm that is interfaced with the DMC algorithm using the local conservation law for the diffusing quantity. Here we combine this algorithm with a previously developed phase-field formulation of the interface dynamics and demonstrate that it can accurately simulate three-dimensional dendritic growth in a previously unreachable range of low undercoolings that is of direct experimental relevance. KW - dendritic_growth KW - dmc KW - multiscale AU - Plapp, Mathis AU - Karma, Alain PY - 2000/12/10/ UR - http://dx.doi.org/10.1006/jcph.2000.6634 ER -