  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.
