通过粒子管理求解一维标量守恒律
Solving One Dimensional Scalar Conservation Laws by Particle Management
AI总结：
提出一种基于粒子管理的无网格数值方法，用于求解一维标量守恒律，通过特征速度移动粒子并局部管理粒子交互，实现无数值耗散的TVD、熵减、精确守恒格式，在激波处保持一阶精度，远离激波处达到二阶精度。
摘要：
我们提出了一种用于一维空间中标量守恒律的无网格数值求解器。代表解的点根据其特征速度移动。粒子相互作用通过纯局部粒子管理来解决。由于不需要全局重网格化，激波保持尖锐并以正确速度传播，同时稀散波在适当位置产生。该方法具有TVD、熵减、精确守恒且无数值耗散。涉及跨音速点的困难不会出现，但通量函数的拐点带来轻微挑战，可通过特殊处理克服。远离激波时，方法具有二阶精度，而激波以一阶精度解析。后处理步骤可恢复二阶精度。在测试案例中与CLAWPACK进行比较，发现在相同分辨率下精度有所提高。
英文摘要：
We present a meshfree numerical solver for scalar conservation laws in one space dimension. Points representing the solution are moved according to their characteristic velocities. Particle interaction is resolved by purely local particle management. Since no global remeshing is required, shocks stay sharp and propagate at the correct speed, while rarefaction waves are created where appropriate. The method is TVD, entropy decreasing, exactly conservative, and has no numerical dissipation. Difficulties involving transonic points do not occur, however inflection points of the flux function pose a slight challenge, which can be overcome by a special treatment. Away from shocks the method is second order accurate, while shocks are resolved with first order accuracy. A postprocessing step can recover the second order accuracy. The method is compared to CLAWPACK in test cases and is found to yield an increase in accuracy for comparable resolutions.
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