4 papers
Fast Jacobi Spectral Methods and Closure Approximations for the Homogeneous FENE Model of Complex Fluids
Runkai Feng, Jie Shen, Haijun Yu
The Finitely Extensible Nonlinear Elastic (FENE) dumbbell model is a widely used mathematical model for complex fluids. Direct simulation of the FENE Fokker--Planck equation is com…
Phase-Field Modeling and Energy-Stable Schemes for Osmotic Flow through Semi-Permeable
Ruihan Guo, Jie Shen, Shixin Xu +1
We present a thermodynamically consistent phase-field model for simulating fluid transport across semi-permeable membranes, with a particular focus on osmotic pressure effects. The…
Numerical analysis of a semi-implicit Euler scheme for the Keller-Segel model
Xueling Huang, Olivier Goubet, Jie Shen
We study the properties of a semi-implicit Euler scheme that is widely used in time discretization of Keller-Segel equations both in the parabolic-elliptic form and the parabolic-p…
Higher-Order Energy-Decreasing Exponential Time Differencing Runge-Kutta methods for Gradient Flows
Zhaohui Fu, Jie Shen, Jiang Yang
In this paper, we develop a general framework for constructing higher-order, unconditionally energy-stable exponential time differencing Runge-Kutta methods applicable to a range o…