Numerical Simulations of Stably Stratified Fluid Flow Using Compact Finite-Difference Schemes

The aim of this paper is to present the class of high order compact schemes in the context of numerical simulation of stratified flow. The numerical schemes presented here are based on the approach outlined in Lele [1]. The numerical model presented in this contribution is based on the solution of the Boussinesq approximation by a finite-difference scheme. The numerical scheme itself follows the principle of semi-discretization, with high order compact discretization in space, while the time integration is carried out by suitable Runge-Kutta time-stepping scheme. In the case presented here the steady flow was considered and thus the artificial compressibility method was used to resolve the pressure from the modified continuity equation. The test case used to demonstrate the capabilities of the selected model consists of the flow of stably stratified fluid over low, smooth hill.