论文标题
具有非本地自由能的流体动力方程的高阶均衡有限体积方案
High-order well-balanced finite volume schemes for hydrodynamic equations with nonlocal free energy
论文作者
论文摘要
我们建议使用具有吸引力的抑制性相互作用力以及线性和非线性阻尼的广泛流体动力系统的高阶有限体积方案。我们的方案适用于包含与密度相互作用电位的卷积的自由能，这对于诸如Keller-Segel模型，更一般的Euler-Poisson Systems或动态密度功能理论等应用至关重要。我们的方案还配备了非负密度重建，该重建允许在模拟过程中进行真空区域。我们从相关应用中提供了几个典型的示例，这些应用突出了我们算法的好处，也阐明了我们的一些分析结果。
We propose high-order well-balanced finite-volume schemes for a broad class of hydrodynamic systems with attractive-repulsive interaction forces and linear and nonlinear damping. Our schemes are suitable for free energies containing convolutions of an interaction potential with the density, which are essential for applications such as the Keller-Segel model, more general Euler-Poisson systems, or dynamic-density functional theory. Our schemes are also equipped with a nonnegative-density reconstruction which allows for vacuum regions during the simulation. We provide several prototypical examples from relevant applications highlighting the benefit of our algorithms elucidate also some of our analytical results.
