We study the convergence of a novel family of thermodynamically compatible schemes for hyperbolic systems (HTC schemes) in the framework of dissipative weak solutions, applied to the Euler equations of compressible gas dynamics. Two key novelties of our method are i) entropy is treated as one of the main field quantities and ii) the total energy conservation is a consequence of compatible discretization and application of the Abgrall flux.

翻译：本文在耗散弱解框架下研究了一类新型双曲系统热力学相容格式（HTC格式）应用于可压缩气体动力学欧拉方程的收敛性问题。本方法的两个关键创新点在于：i) 将熵作为主要场变量之一进行处理；ii) 总能量守恒是相容离散化与Abgrall通量应用的自然结果。