@article{chertock_cui_kurganov_ozcan_tadmor_2018, title={Well-balanced schemes for the Euler equations with gravitation: Conservative formulation using global fluxes}, volume={358}, ISSN={["1090-2716"]}, url={https://doi-org.prox.lib.ncsu.edu/10.1016/j.jcp.2017.12.026}, DOI={10.1016/j.jcp.2017.12.026}, abstractNote={We develop a second-order well-balanced central-upwind scheme for the compressible Euler equations with gravitational source term. Here, we advocate a new paradigm based on a purely conservative reformulation of the equations using global fluxes. The proposed scheme is capable of exactly preserving steady-state solutions expressed in terms of a nonlocal equilibrium variable. A crucial step in the construction of the second-order scheme is a well-balanced piecewise linear reconstruction of equilibrium variables combined with a well-balanced central-upwind evolution in time, which is adapted to reduce the amount of numerical viscosity when the flow is at (near) steady-state regime. We show the performance of our newly developed central-upwind scheme and demonstrate importance of perfect balance between the fluxes and gravitational forces in a series of one- and two-dimensional examples.}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Chertock, Alina and Cui, Shumo and Kurganov, Alexander and Ozcan, Seyma Nur and Tadmor, Eitan}, year={2018}, month={Apr}, pages={36–52} }