A New Approach for a Nonlocal, Nonlinear Conservation Law
A New Approach for a Nonlocal, Nonlinear Conservation Law
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DOI：
10.1137/110833233
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发表时间：
2012-02
期刊：
影响因子：
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通讯作者：
Q. Du;J. Kamm;R. Lehoucq;M. Parks
中科院分区：
文献类型：
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作者：
Q. Du;J. Kamm;R. Lehoucq;M. Parks
我们描述了一种方法，非本地，非线性平流在一维扩展通常的逐点概念，占非本地贡献的通量。我们考虑的空间非局部算子不涉及导数。相反，空间运营商涉及的积分，在分布意义上，减少到一个传统的非线性平流运营商。特别是，我们研究了一个非局部无粘Burgers方程，它给出了一个基本形式，与适定性相关的特性的特征，并检查特定情况下的数值结果。我们描述了连接到一个非局部粘性正则化，它模仿粘性Burgers方程在适当的限制。我们提出的数值结果比较的非本地的Burgers制定的标准的本地情况下的行为。本文提出的发展形成了初步的积木上建立一个理论的非本地平流现象内的peridadic理论一致…
We describe an approach to nonlocal, nonlinear advection in one dimension that extends the usual pointwise concepts to account for nonlocal contributions to the flux. The spatially nonlocal operators we consider do not involve derivatives. Instead, the spatial operator involves an integral that, in a distributional sense, reduces to a conventional nonlinear advective operator. In particular, we examine a nonlocal inviscid Burgers equation, which gives a basic form with which to characterize properties associated with well-posedness, and to examine numerical results for specific cases. We describe the connection to a nonlocal viscous regularization, which mimics the viscous Burgers equation in an appropriate limit. We present numerical results that compare the behavior of the nonlocal Burgers formulation to the standard local case. The developments presented in this paper form the preliminary building blocks upon which to build a theory of nonlocal advection phenomena consistent within the peridynamic theo...