SIAM Journal on Scientific Computing, Volume 43, Issue 2, Page A828-A858, January 2021.
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 and also elucidate some of our analytical results.

中文翻译：

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具有非局部自由能的流体动力学方程的高阶平衡均衡方案

SIAM杂志上的科学计算，第43卷，第2期，第A828-A858，2021年一月
，我们建议高位均衡的有限体积方案的一大类流体动力系统的有吸引力，排斥相互作用力和线性和非线性阻尼。我们的方案适用于包含相互作用势与密度的卷积的自由能，这对于诸如Keller-Segel模型，更通用的Euler-Poisson系统或动态密度泛函理论等应用至关重要。我们的方案还配备了非负密度重构，可以在仿真过程中实现真空区域。我们提供了一些来自相关应用的原型示例，突出了我们算法的优势，并阐明了一些分析结果。