We introduce local characteristic decomposition based path-conservative central-upwind schemes for (nonconservative) hyperbolic systems of balance laws. The proposed schemes are made to be well-balanced via a flux globalization approach, in which source terms are incorporated into the fluxes: This helps to enforce the well-balanced property when the resulting quasi-conservative system is solved using the local characteristic decomposition based central-upwind scheme recently introduced in [{\sc A. Chertock, S. Chu, M. Herty, A. Kurganov, and M. Luk\'{a}\v{c}ov\'{a}-Medvi{\softd}ov\'{a}}, J. Comput. Phys., 473 (2023), Paper No. 111718]. Nonconservative product terms are also incorporated into the global fluxes using a path-conservative technique. We illustrate the performance of the developed schemes by applying them to one- and two-dimensional compressible multifluid systems and thermal rotating shallow water equations.

翻译：本文针对（非守恒）双曲型平衡律系统，提出了一种基于局部特征分解的路径守恒中心迎风格式。所提格式通过通量全局化方法实现平衡保持，即将源项纳入通量：当使用近期文献[{\sc A. Chertock, S. Chu, M. Herty, A. Kurganov, and M. Luk\'{a}\v{c}ov\'{a}-Medvi{\softd}ov\'{a}}, J. Comput. Phys., 473 (2023), Paper No. 111718]中介绍的基于局部特征分解的中心迎风格式求解所得准守恒系统时，这有助于强制执行平衡保持性质。非守恒乘积项也通过路径保守技术纳入全局通量。通过将所发展的格式应用于一维和二维可压缩多流体系统以及热旋转浅水方程，我们展示了其性能。