We investigate the numerical artifact known as a carbuncle, in the solution of the shallow water equations. We propose a new Riemann solver that is based on a local measure of the entropy residual and aims to avoid carbuncles while maintaining high accuracy. We propose a new challenging test problem for shallow water codes, consisting of a steady circular hydraulic jump that can be physically unstable. We show that numerical methods are prone to either suppress the instability completely or form carbuncles. We test existing cures for the carbuncle. In our experiments, only the proposed method is able to avoid unphysical carbuncles without suppressing the physical instability.

翻译：我们用浅水方程式来调查被称为碳球球体的数字工艺品。 我们提出一个新的Riemann解答器,该解答器基于对碳球体残留物的局部测量,目的是避免碳球体,同时保持高度准确性。 我们提出浅水代码的一个新的具有挑战性的测试问题,即由稳定的循环液压跳跃构成,这种跳跃在物理上可能不稳定。 我们表明数字方法很容易完全抑制不稳定性,或者形成碳球体。 我们测试目前对碳球体的治疗方法。 在我们的实验中,只有建议的方法能够在不抑制物理不稳定的情况下避免非物理碳球体。