Precise computations of chemotactic collapse using moving mesh methods
Precise computations of chemotactic collapse using moving mesh methods
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DOI：
10.1016/j.jcp.2004.07.010
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发表时间：
2005-01
影响因子：
4.1
通讯作者：
C. Budd;R. Carretero-González;R. Russell
中科院分区：
文献类型：
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作者：
C. Budd;R. Carretero-González;R. Russell
我们考虑趋化系统的爆破解的计算问题，即所谓的趋化崩溃问题。在两个空间维度中，这种解可能具有近似的自相似行为，这在数值模拟中可能很难验证[参见。贝特顿和布伦纳，坍塌的细菌圆柱体，物理。(2001年)061904版[J].分析了一种基于均匀分布进行空间网格移动的动态(比例不变)网格划分方法。利用适当选择的监视函数，数值解解决了渐近解结构中的细节问题，使得计算结果与Herrero和Velázquez[趋化模型中的奇点模式，数学]对崩塌现象的渐近描述完全一致。安。306(1996)583-623]。我们相信，我们构造的方法非常适合于数学生物学中的大量问题，对于这些问题，预计会出现崩溃现象。
We consider the problem of computing blow-up solutions of chemotaxis systems, or the so-called chemotactic collapse. In two spatial dimensions, such solutions can have approximate self-similar behaviour, which can be very challenging to verify in numerical simulations [cf. Betterton and Brenner, Collapsing bacterial cylinders, Phys. Rev. E 64 (2001) 061904]. We analyse a dynamic (scale-invariant) remeshing method which performs spatial mesh movement based upon equidistribution. Using a suitably chosen monitor function, the numerical solution resolves the fine detail in the asymptotic solution structure, such that the computations are seen to be fully consistent with the asymptotic description of the collapse phenomenon given by Herrero and Velázquez [Singularity patterns in a chemotaxis model, Math. Ann. 306 (1996) 583–623]. We believe that the methods we construct are ideally suited to a large number of problems in mathematical biology for which collapse phenomena are expected.