Towards a geometric variational discretization of compressible fluids: The rotating shallow water equations
Towards a geometric variational discretization of compressible fluids: The rotating shallow water equations
This paper presents a geometric variational discretization of compressible fluid dynamics. The numerical scheme is obtained by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups and the associated variational principles. Our framework applies to irregular mesh discretizations in 2D and 3D. It …