Sat, 05 Jul 2008 03:58:42 BST CiteULike: matthewhflamm pde http://www.citeulike.org/user/matthewhflamm/tag/pde CiteULike.org en-gb Copyright © 2004-2008 citeulike.org http://www.citeulike.org/user/matthewhflamm/article/2602872 <i>Journal of Computational Physics, Vol. 194, No. 2. (1 March 2004), pp. 677-696.</i><br /><br />A numerical method for the simulation of the effect of melt flow on the three-dimensional growth of a dendrite is described. The method is an extension of the technique for two-dimensional flow described in Al-Rawahi and Tryggvason [J. Comput. Phys. 180 (2002) 471] and is based on the explicit tracking of connected marker points that describe the liquid-solid interface. An explicit projection method is used to solve the energy and the Navier-Stokes equations on a regular stationary grid and the solidified region is represented by setting the velocities in the solid phase to zero. The latent heat released during solidification is calculated using the normal temperature gradient near the interface. The method is validated by a comparison with an exact solution for a Stefan problem and a grid refinement study. The simulations show that the speed of a dendrite arm growing into the flow is increased due to an increase in the temperature gradient on the upstream side and the formation of side branches is promoted, as in two-dimensions. The effect of the flow on the growth of dendrite arms growing in the downstream direction is smaller than in two-dimensions, due to a smaller wake. Numerical simulation of dendritic solidification with convection: Three-dimensional flow Nabeel Al-Rawahi Gretar Tryggvason doi:10.1016/j.jcp.2003.09.020 Journal of Computational Physics, Vol. 194, No. 2. (1 March 2004), pp. 677-696. 2008-03-27T18:09:19-00:00 2004 Journal of Computational Physics 194 2 677 696 convection dendritic_growth flow pde http://www.citeulike.org/user/matthewhflamm/article/2599485 <i>Physical Review E, Vol. 69, No. 3. (30 March 2004), 036704.</i><br /><br />Simulations of heat and mass transport may require complex nonlinear boundary conditions to describe the flow of mass and energy across an interface. Although stochastic methods do not suffer from the numerical diffusion of grid-based methods; they typically lose accuracy in the vicinity of interfacial boundaries. In this work we introduce ideas and algorithms to account for mass (or energy) transfer at reactive interfaces; with accuracies comparable to the bulk phase. We show how to introduce particles into the system with the correct distribution near the interface; as well as the correct flux through the interface. The algorithms have been tested in a channel flow; for which accurate numerical solutions can be independently calculated. Stochastic boundary conditions to the convection-diffusion equation including chemical reactions at solid surfaces P Szymczak AJC Ladd doi:10.1103/PhysRevE.69.036704 Physical Review E, Vol. 69, No. 3. (30 March 2004), 036704. 2008-03-26T18:50:15-00:00 2004 Physical Review E 69 3 036704 American Physical Society boundary_condition flow pde stochastic http://www.citeulike.org/user/matthewhflamm/article/2599477 <i>Physical Review E, Vol. 68, No. 3. (2003), 036704.</i><br /><br />Stochastic methods offer an attractively simple solution to complex transport-controlled problems; and have a wide range of physical; chemical; and biological applications. Stochastic methods do not suffer from the numerical diffusion that plagues grid-based methods; but they typically lose accuracy in the vicinity of interfacial boundaries. In this work we introduce some ideas and algorithms that can be used to implement boundary conditions in stochastic simulations of the convection-diffusion equation with accuracies comparable to the bulk phase. The algorithms have been tested in two-dimensional channel flows over a range of Peclet numbers; and compared with independent finite-difference calculations. Boundary conditions for stochastic solutions of the convection-diffusion equation P Szymczak AJC Ladd doi:10.1103/PhysRevE.68.036704 Physical Review E, Vol. 68, No. 3. (2003), 036704. 2008-03-26T18:46:55-00:00 2003 Physical Review E 68 3 036704 American Physical Society boundary_condition flow pde stochastic