论文标题
具有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存方案通过奇异内核
A unified structure preserving scheme for a multi-species model with a gradient flow structure and nonlocal interactions via singular kernels
论文作者
论文摘要
在本文中，我们考虑了用于多种物种离子流体的非线性和非局部抛物线模型，并引入了半无限量的有限体积方案，该方案是空间上准确的二阶阶段，一阶，时间阶段并满足以下特性：阳性保留，质量保护和能量。此外，我们的方案涉及与单数但可集成的内核的卷积术语的快速算法，否则否则会阻碍整个方案的准确性和效率。接下来显示了快速卷积算法上的错误估计。提供了许多数值测试来证明属性，例如无条件的稳定性，收敛顺序，能量耗散和快速卷积算法的复杂性。此外，进行了广泛的数值实验，以探索特定示例中的建模效果，例如空间排斥，边界处的离子浓度以及凯勒 - 隔离方程的爆炸现象。
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.
