A least squares based finite volume method for the Cahn-Hilliard and Cahn-Hilliard-reaction equations

摘要: A vertex-centred finite volume method (FVM) for the Cahn-Hilliard (CH) and recently proposed Singh et?al. (2008) Burch (2009) Cahn-Hilliard-reaction (CHR) equations is presented. Information at control faces computed using a high-order least-squares approach based on Taylor series approximations. This problem explicitly includes variational boundary condition (VBC) that ensures discrete satisfy all of conditions. We use this to solve CH CHR in one two dimensions show our scheme satisfies VBC least second order. For equation we evidence conservative, gradient stable solutions, however equation, strict gradient-stability more challenging achieve.