SIAM Journal on Scientific Computing, Volume 43, Issue 3, Page B539-B569, January 2021.
In this paper, we consider a nonlinear and nonlocal parabolic model for multispecies ionic fluids and introduce a semi-implicit finite volume scheme, which is second-order accurate in space, is first-order in time, and satisfies the positivity preserving and mass conservation properties. The scheme also satisfies an energy dissipation relation at the semidiscrete level. In addition, our scheme involves a fast algorithm on the convolution terms with singular but integrable kernels on the uniform grid, 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, the 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, concentration of ions at the boundary, and blowup phenomenon of Keller--Segel equations.

中文翻译：

---

具有奇异核的梯度流结构和非局部相互作用的多物种模型的统一结构保留方案

SIAM科学计算杂志，第43卷，第3期，第B539-​​B569页，2021年1月。
在本文中，我们考虑了一种多物种离子流体的非线性非局部抛物线模型，并提出了一种半隐式有限体积方案，该方案在空间上是二阶精确的，在时间上是一阶的，并且满足正性守恒和质量守恒特性。该方案还满足半离散级别的能量耗散关系。另外，我们的方案涉及在卷积项上具有在统一网格上具有奇异但可积分的快速算法，否则会妨碍整个方案的准确性和效率。接下来显示了快速卷积算法的误差估计。提供了许多数值测试来证明这些特性，例如无条件稳定性，收敛阶数，能量耗散以及快速卷积算法的复杂性。此外，