Abstract
SummaryWe present a well‐balanced finite volume scheme for the compressible Euler equations with gravity, where the approximate Riemann solver is derived using a Suliciu relaxation approach. Besides the well‐balanced property, the scheme is robust with respect to the physical admissible states. General hydrostatic solutions are captured up to machine precision by deriving, for a given initial value problem, suitable time‐independent functions and using them in the discretization of the source term. The first‐order scheme is extended to a second‐order scheme by reconstructing in equilibrium variables while preserving the well‐balanced and robustness properties. Numerical examples are performed to demonstrate the accuracy, well‐balanced, and robustness properties of the presented scheme for up to three space dimensions.
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