一维标量守恒律的精确守恒粒子方法
An exactly conservative particle method for one dimensional scalar conservation laws
AI总结：
提出一种基于特征速度移动粒子、局部解析相互作用实现精确守恒的粒子方法，用于一维标量守恒律，具有变差减小、熵减、无数值耗散和二阶精度等特性。
摘要：
提出了一种用于一维标量守恒律的粒子格式。代表解的粒子根据其特征速度移动。粒子相互作用被局部解析，满足面积的精确守恒。激波保持尖锐并以正确速度传播，而稀疏波在适当位置产生。该方法具有变差减小、熵减、精确守恒的特性，并且在远离激波处没有数值耗散。解（包括激波位置）以二阶精度逼近。可以包含源项。在各种例子中，该方法与CLAWPACK进行了比较，发现在类似分辨率下，其精度相当或更优。
英文摘要：
A particle scheme for scalar conservation laws in one space dimension is presented. Particles representing the solution are moved according to their characteristic velocities. Particle interaction is resolved locally, satisfying exact conservation of area. Shocks stay sharp and propagate at correct speeds, while rarefaction waves are created where appropriate. The method is variation diminishing, entropy decreasing, exactly conservative, and has no numerical dissipation away from shocks. Solutions, including the location of shocks, are approximated with second order accuracy. Source terms can be included. The method is compared to CLAWPACK in various examples, and found to yield a comparable or better accuracy for similar resolutions.
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