A modified fluxwave formula for the solution of onedimensional Euler equations with gravitational source term

In this paper a novel Godunovtype finite volume technique is presented for the solution of onedimensional Euler equations. The numerical scheme defined herein in is wellbalanced and approximates the solution by propa gating a set of jump discontinuities from each Riemann cell interface. The corresponding source terms are then treated within the fluxdifferencing of the finite volume computational cells. First, the capability of the numerical solver under gravitational source term is examined and the results are val dated with reference solution and higherorder WENO scheme. Then, the wellbalanced property of the scheme for the steadystate is tested and finally the proposed method is employed for the modeling small and large amplitude perturbation imposed to the polytropic atmosphere. It is found out that the defined wellbalanced solver provides sensible prediction for all of the given test cases.