Boundary conditions for stochastic solutions of the convection-diffusion equation

by: P Szymczak, AJC Ladd

Physical Review E, Vol. 68, No. 3. (2003), 036704.

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Abstract

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.

@article{citeulike:2599477, abstract = {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.}, author = {Szymczak, P. and Ladd, A. J. C. }, citeulike-article-id = {2599477}, doi = {10.1103/PhysRevE.68.036704}, journal = {Physical Review E}, keywords = {boundary\_condition, flow, pde, stochastic}, number = {3}, pages = {036704+}, posted-at = {2008-03-26 18:49:25}, priority = {3}, publisher = {American Physical Society}, title = {Boundary conditions for stochastic solutions of the convection-diffusion equation}, url = {http://dx.doi.org/10.1103/PhysRevE.68.036704}, volume = {68}, year = {2003} }

RIS record

TY - JOUR ID - citeulike:2599477 L3 - citeulike-article-id:2599477 TI - Boundary conditions for stochastic solutions of the convection-diffusion equation JF - Physical Review E VL - 68 IS - 3 SP - 036704 PB - American Physical Society N2 - 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. KW - boundary_condition KW - flow KW - pde KW - stochastic AU - Szymczak, P AU - Ladd, AJC PY - 2003//11/ UR - http://dx.doi.org/10.1103/PhysRevE.68.036704 ER -

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