%0 Journal Article %1 citeulike:3718639 %A Xu, Jian-Jun %A Zhao, Hong-Kai %D 2003 %J Journal of Scientific Computing %K surfactant-transport-equation %N 1 %P 573--594 %R 10.1023/a:1025336916176 %T An Eulerian Formulation for Solving Partial Differential Equations Along a Moving Interface %U http://math.uci.edu/\~zhao/publication/mypapers/pdf/surface\_diffusion.pdf %V 19 %X In this paper we study an Eulerian formulation for solving partial differential equations (PDE) on a moving interface. A level set function is used to represent and capture the moving interface. A dual function orthogonal to the level set function defined in a neighborhood of the interface is used to represent some associated quantity on the interface and evolves according to a PDE on the moving interface. In particular we use a convection diffusion equation for surfactant concentration on an interface passively convected in an incompressible flow as a model problem. We develop a stable and efficient semi-implicit scheme to remove the stiffness caused by surface diffusion.

@article{citeulike:3718639, abstract = {{In this paper we study an Eulerian formulation for solving partial differential equations (PDE) on a moving interface. A level set function is used to represent and capture the moving interface. A dual function orthogonal to the level set function defined in a neighborhood of the interface is used to represent some associated quantity on the interface and evolves according to a PDE on the moving interface. In particular we use a convection diffusion equation for surfactant concentration on an interface passively convected in an incompressible flow as a model problem. We develop a stable and efficient semi-implicit scheme to remove the stiffness caused by surface diffusion.}}, added-at = {2017-06-29T07:13:07.000+0200}, author = {Xu, Jian-Jun and Zhao, Hong-Kai}, biburl = {https://www.bibsonomy.org/bibtex/291c457f1cf5dce6fae5bc05af8c8cafe/gdmcbain}, citeulike-article-id = {3718639}, citeulike-attachment-1 = {xu_03_eulerian_33620.pdf; /pdf/user/gdmcbain/article/3718639/33620/xu_03_eulerian_33620.pdf; acffe277a11f8e69dd78c13111f582fb91a590b4}, citeulike-linkout-0 = {http://math.uci.edu/\~{}zhao/publication/mypapers/pdf/surface\_diffusion.pdf}, citeulike-linkout-1 = {http://dx.doi.org/10.1023/a:1025336916176}, citeulike-linkout-2 = {http://www.springerlink.com/content/j35624v6458tkw38}, day = 1, doi = {10.1023/a:1025336916176}, file = {xu_03_eulerian_33620.pdf}, interhash = {a5f5d98fc763c63806fd179d7200a449}, intrahash = {91c457f1cf5dce6fae5bc05af8c8cafe}, journal = {Journal of Scientific Computing}, keywords = {surfactant-transport-equation}, month = dec, number = 1, pages = {573--594}, posted-at = {2008-11-27 23:45:35}, priority = {2}, timestamp = {2017-06-29T07:13:07.000+0200}, title = {{An Eulerian Formulation for Solving Partial Differential Equations Along a Moving Interface}}, url = {http://math.uci.edu/\~{}zhao/publication/mypapers/pdf/surface\_diffusion.pdf}, volume = 19, year = 2003 }