ON A DIFFUSIVELY CORRECTED KINEMATIC-WAVE TRAFFIC FLOW MODEL WITH CHANGING ROAD SURFACE CONDITIONS
ON A DIFFUSIVELY CORRECTED KINEMATIC-WAVE TRAFFIC FLOW MODEL WITH CHANGING ROAD SURFACE CONDITIONS
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变化路面条件下的扩散修正运动波交通流模型
DOI：
10.1142/s0218202503003112
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
K. Karlsen
中科院分区：
文献类型：
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作者：
R. Bürger;K. Karlsen
将单车道公路单向交通流的Lighthill-Whitham-理查兹运动学交通流模型扩展到包含路面条件突变和驾驶员反应时间及预期长度的情况。结果是一个强退化的对流扩散方程，其中的扩散项，占司机的行为，是有效的，只有当当地的汽车密度超过一个临界值，对流通量函数不连续地依赖于位置。结果表明，所提出的交通模型的有效性得到了最近的数学适定性（存在性和唯一性）理论的支持，拟线性退化抛物对流扩散方程的不连续系数。20，22该理论包括一个收敛证明的单调有限差分格式，这是用于模拟各种情况下的交通流模型。
The well-known Lighthill–Whitham–Richards kinematic traffic flow model for unidirectional flow on a single-lane highway is extended to include both abruptly changing road surface conditions and drivers' reaction time and anticipation length. The result is a strongly degenerate convection–diffusion equation, where the diffusion term, accounting for the drivers' behavior, is effective only where the local car density exceeds a critical value, and the convective flux function depends discontinuously on the location. It is shown that the validity of the proposed traffic model is supported by a recent mathematical well-posedness (existence and uniqueness) theory for quasilinear degenerate parabolic convection–diffusion equations with discontinuous coefficients.20,22 This theory includes a convergence proof for a monotone finite-difference scheme, which is used herein to simulate the traffic flow model for a variety of situations.