Arbitrary order finite volume well-balanced schemes for the Euler equations with gravity
It provides a general framework for constructing well-balanced schemes for moving equilibria, benefiting computational fluid dynamics simulations involving gravity.
This work develops arbitrary high order well-balanced finite volume schemes for the Euler equations with gravity, achieving exact preservation of a prescribed equilibrium and demonstrating up to fifth-order accuracy in 1D and third-order in 2D.
This work presents arbitrary high order well balanced finite volume schemes for the Euler equations with a prescribed gravitational field. It is assumed that the desired equilibrium solution is known, and we construct a scheme which is exactly well balanced for that particular equilibrium. The scheme is based on high order reconstructions of the fluctuations from equilibrium of density, momentum and pressure, and on a well balanced integration of the source terms, while no assumptions are needed on the numerical flux, beside consistency. This technique allows to construct well balanced methods also for a class of moving equilibria. Several numerical tests demonstrate the performance of the scheme on different scenarios, from equilibrium solutions to non steady problems involving shocks. The numerical tests are carried out with methods up to fifth order in one dimension, and third order accuracy in 2D.