Systems of hyperbolic partial differential equations with source terms (balance laws) arise in many applications where it is important to compute accurate time-dependent solutions modeling small perturbations of equilibrium solutions in which the source terms balance the hyperbolic part. The f-wave version of the wave-propagation algorithm is one approach, but requires the use of a particular averaged value of the source terms at each cell interface in order to be "well balanced" and exactly maintain steady states. A general approach to choosing this average is developed using the theory of path conservative methods. A scalar advection equation with a decay or growth term is introduced as a model problem for numerical experiments.

中文翻译：

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具有源项的双曲问题的平衡路径积分 f 波方法。

具有源项（平衡定律）的双曲偏微分方程组出现在许多应用中，在这些应用中，计算精确的瞬态解对平衡解的小扰动建模很重要，其中源项平衡双曲部分。波传播算法的 f 波版本是一种方法，但需要在每个单元界面使用源项的特定平均值，以便“良好平衡”并准确保持稳定状态。使用路径保守方法的理论开发了选择该平均值的一般方法。一个带有衰减或增长项的标量平流方程被引入作为数值实验的模型问题。