In this article, numerical schemes are proposed for approximating the solutions, possibly measure-valued with concentration (delta shocks), for a class of nonstrictly hyperbolic systems. These systems are known to model physical phenomena such as the collision of clouds and dynamics of sticky particles, for example. The scheme is constructed by extending the theory of discontinuous flux for scalar conservation laws, to capture measure-valued solutions with concentration. The numerical approximations are analytically shown to be entropy stable in the framework of Bouchut (Adv Kinet Theory Comput 22:171–190, 1994), satisfy the physical properties of the state variables, and converge to the weak solution. The construction allows natural extensions of the scheme to its higher-order and multi-dimensional versions. The scheme is also extended for some more classes of fluxes, which admit delta shocks and are also known to model physical phenomena. Various physical systems are simulated both in one dimension and multi-dimensions to display the performance of the numerical scheme, and comparisons are made with the test problems available in the literature.

在本文中，提出了数值方案来逼近一类非严格双曲线系统的解，可能是用浓度（增量冲击）测量值。众所周知，这些系统可以模拟物理现象，例如云的碰撞和粘性粒子的动力学。该方案是通过扩展标量守恒定律的不连续通量理论来构建的，以捕获具有浓度的测量值解。数值近似在 Bouchut (Adv Kinet Theory Comput 22:171–190, 1994) 的框架中被分析证明是熵稳定的，满足状态变量的物理特性，并收敛到弱解。该结构允许该方案自然扩展到其高阶和多维版本。该方案还扩展到更多类别的通量，这些通量允许 delta 冲击并且也已知用于模拟物理现象。在一维和多维上模拟各种物理系统以显示数值方案的性能，并与文献中可用的测试问题进行比较。