Numerical simulation of three-dimensional lee waves behind an isolated hill

•Newly developed numerical code for high-resolution simulation of 3D stably stratified fluid flows is presented.•The code and underlying numerical discretization and stabilization methods are explained in detail.•Numerical results of stably stratified flows over a hill are presented for a wide range of Reynolds and Froude numbers.•It is shown how the change of velocity and stratification affects the structure of the flow field.•Problems arising in mathematical modeling and numerical solution of stratified flows are discussed.