The use of curvilinear coordinates is sometimes indicated by the inherent geometry a fluid dynamics problem, but this introduces fictitious forces into momentum equations that spoil strict conservative form. If one willing to work in three dimensions, these can be eliminated solving for rectangular (Cartesian) components on mesh. A thoroughly geometric approach spacetime demonstrates transparen...

The Hamiltonian based on curvilinear normal modes and local modes (CNLM) is discussed using Wilson’s exact vibrational Hamiltonian as basis, the CNLM representation diagonalizing only the normal mode block of FG matrix in curvilinear internal coordinates. Using CNLM the kinetic and potential energy operators for benzene are given, including cubic and quartic anharmonicity in the potential energ...

In this paper, three-dimensional two phase turbulent free surface flow is solved by an in-house code. The incompressible Reynolds average Navier-Stocks equations (RANS) with k-ε turbulence model are solved by the finite volume method in the non-orthogonal curvilinear coordinates. For the modeling of the free surface effect, Lagrangian propagation volume tracking method (VOF-PLIC) is used. The c...

While you have probably used tensors of rank 1, i.e vectors, in special relativity, relativity is most efficiently expressed in terms of tensor algebra. General relativity, however, requires tensor algebra in a general curvilinear coordinate system. Before discussing special relativity, it will be useful to introduce some of the mathematics of differential forms in a general curvilinear set of ...

In 1994 B erenger showed how to construct a perfectly matched absorbing layer for the Maxwell system in rectilinear coordinates. This layer absorbs waves of any wavelength and any frequency without reeection and thus can be used to artiicially terminate the domain of scattering calculations. In this paper we show how to derive and implement the B erenger layer in curvilinear coordinates (in two...