Application of compact finite-difference schemes to simulations of stably stratified fluid flows

This paper presents a comparison of the results of numerical simulations obtained by two different numerical methods for one specific case of stably stratified incompressible flow. The focus in this paper is on the numerical results obtained using some of the compact finite-difference discretizations introduced in the paper [1]. The numerical scheme itself follows the principle of semi-discretisation, with high order compact discretisation in space, while the time integration is carried out by the Strong Stability Preserving Runge–Kutta scheme. Results are compared against the reference solution obtained by the AUSM finite volume method. The test case used to demonstrate the capabilities of selected numerical methods represents the flow of stably stratified fluid over low, smooth, hill-like wall mounted obstacle.