-
Field model for complex ionic fluids
In this paper, we consider the field model for complex ionic fluids with...
read it
-
Mass-preserving approximation of a chemotaxis multi-domain transmission model for microfluidic chips
The present work was inspired by the recent developments in laboratory e...
read it
-
Field model for complex ionic fluids: analytical properties and numerical investigation
In this paper, we consider the field model for complex ionic fluids with...
read it
-
A Positive and Energy Stable Numerical Scheme for the Poisson-Nernst-Planck-Cahn-Hilliard Equations with Steric Interactions
We consider numerical methods for the Poisson-Nernst-Planck-Cahn-Hilliar...
read it
-
Structure-Preserving and Efficient Numerical Methods for Ion Transport
Ion transport, often described by the Poisson–Nernst–Planck (PNP) equati...
read it
-
A structure preserving numerical scheme for Fokker-Planck equations of neuron networks: numerical analysis and exploration
In this work, we are concerned with the Fokker-Planck equations associat...
read it
-
A Finite-Volume Method for Fluctuating Dynamical Density Functional Theory
In this work we introduce a finite-volume numerical scheme for solving s...
read it
A unified structure preserving scheme for a multi-species model with a gradient flow structure and nonlocal interactions via singular kernels
In this paper, we consider a nonlinear and nonlocal parabolic model for multi-species ionic fluids and introduce a semi-implicit finite volume scheme, which is second order accurate in space, first order in time and satisfies the following properties: positivity preserving, mass conservation and energy dissipation. Besides, our scheme involves a fast algorithm on the convolution terms with singular but integrable kernels, which otherwise impedes the accuracy and efficiency of the whole scheme. Error estimates on the fast convolution algorithm are shown next. Numerous numerical tests are provided to demonstrate the properties, such as unconditional stability, order of convergence, energy dissipation and the complexity of the fast convolution algorithm. Furthermore, extensive numerical experiments are carried out to explore the modeling effects in specific examples, such as, the steric repulsion, the concentration of ions at the boundary and the blowup phenomenon of the Keller-Segel equations.
READ FULL TEXT
Comments
There are no comments yet.