Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6929097 | Journal of Computational Physics | 2018 | 17 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Alina Chertock, Shumo Cui, Alexander Kurganov, Åeyma Nur Ãzcan, Eitan Tadmor,