报告题目: A positivity preserving, energy stable finite difference scheme for the Flory-Huggins-Cahn-Hilliard-Navier-Stokes system
报告人:王成 教授(University of Massachusetts Dartmouth)
邀请人:宋怀玲
时间:12月24日上午10:30-11:30
地点:数学院207
报告摘要:A finite difference numerical scheme is proposed and analyzed for the Cahn-Hilliard-Navier-Stokes system, with logarithmic Flory-Huggins energy potential. In the numerical approximation to the singular chemical potential, the logarithmic term and the surface diffusion term are implicitly updated, while an explicit computation is applied to the concave expansive term. Moreover, the convective term in the phase field evolutionary equation is approximated in a semi-implicit manner. Similarly, the fluid momentum equation is computed by a semi-implicit algorithm: implicit treatment for the kinematic diffusion term, explicit update for the pressure gradient, combined with semi-implicit approximations to the fluid convection and the phase field coupled term, respectively. Such a semi-implicit method gives an intermediate velocity field. Subsequently, a Helmholtz projection into the divergence-free vector field yields the velocity vector and the pressure variable at the next time step. This approach decouples the Stokes solver, which in turn drastically improves the numerical efficiency. The positivity-preserving property and the unique solvability of the proposed numerical scheme is theoretically justified, i.e., the phase variable is always between -1 and 1, following the singular nature of the logarithmic term as the phase variable approaches the singular limit values. In addition, an iteration construction technique is applied in the positivity-preserving and unique solvability analysis, motivated by the non-symmetric nature of the fluid convection term. The energy stability of the proposed numerical scheme could be derived by a careful estimate. A few numerical results are presented to validate the robustness of the proposed numerical scheme.
报告人简介:
王成教授,1993年于中国科学技术大学数学系获得学士学位,2000年于坦普尔大学获得博士学位。2000年至2003年于印第安纳大学担任博士后,2003年至2008年于田纳西大学担任助理教授。 2008年至2012年于University of Massachusetts Dartmouth担任助理教授, 2012年至2019年于University of Massachusetts Dartmouth担任副教授, 2019年至今于University of Massachusetts Dartmouth担任教授。王教授的研究兴趣为针对流体力学、电磁力学、 材料科学中涉及的偏微分方程的数值方法研究。在SIAM、JCP、JSC等发表了百余篇论文, 被引用超过5000次。