In this work we develop a new framework to deal numerically with discontinuous solutions in nonconservative hyperbolic systems. First an extension of the MOOD methodology to nonconservative systems based on Taylor expansions is presented. This extension combined with an in-cell discontinuous reconstruction operator are the key points to develop a new family of high-order methods that are able to capture exactly isolated shocks. Several test cases are proposed to validate these methods for the Modified Shallow Water equations and the Two-Layer Shallow Water system.

翻译：本文提出了一种新的数值框架，用于处理非守恒双曲系统中的间断解。首先，我们基于泰勒展开将 MOOD 方法推广至非守恒系统。该推广与单元内间断重构算子相结合，构成了能够精确捕捉孤立激波的新一族高阶方法的核心。我们通过多个测试算例验证了这些方法在修正浅水方程和双层浅水系统上的有效性。