论文标题
非线性动力学方程的渐近保留方案，导致在扩散极限内导致体积排斥趋化性
Asymptotic preserving schemes for nonlinear kinetic equations leading to volume-exclusion chemotaxis in the diffusive limit
论文作者
论文摘要
在这项工作中，我们首先通过正式论证证明了非线性动力学方程的扩散极限，其中传输项和转弯算子均取决于密度依赖性，从而导致体积 - 排斥趋化方程。我们概括了基于微麦克罗分解的这种非线性动力学方程的渐近保留方案。通过以上风的方式正确地将非线性项置于隐式阐明的情况下，在强烈的化学敏感性的情况下，该方案也会产生准确的近似值。我们通过详细的计算表明，该方案列出了以下属性：渐近保存，阳性保存和能量耗散，这对于实际应用至关重要。我们将该方案扩展到二维动力学模型，并通过生物系统中模式形成的1D和2D数值实验来验证其效率。
In this work we first prove, by formal arguments, that the diffusion limit of nonlinear kinetic equations, where both the transport term and the turning operator are density-dependent, leads to volume-exclusion chemotactic equations. We generalise an asymptotic preserving scheme for such nonlinear kinetic equations based on a micro-macro decomposition. By properly discretizing the nonlinear term implicitly-explicitly in an upwind manner, the scheme produces accurate approximations also in the case of strong chemosensitivity. We show, via detailed calculations, that the scheme presents the following properties: asymptotic preserving, positivity preserving and energy dissipation, which are essential for practical applications. We extend this scheme to two dimensional kinetic models and we validate its efficiency by means of 1D and 2D numerical experiments of pattern formation in biological systems.
