Thu, 24 Jul 2008 19:50:49 BST CiteULike: matthewhflamm stochastic http://www.citeulike.org/user/matthewhflamm/tag/stochastic CiteULike.org en-gb Copyright © 2004-2008 citeulike.org 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