In this paper a noniterative method for the numerical generation of orthogonal curvilinear coordinates for plane annular regions between two arbitrary smooth closed curves has been developed. The basic generating equation is the Gaussian equation for a Euclidean space under the constraint of orthogonality. The resulting equation has been solved analytically for the case of isothermic coordinate...

A sharp interface LES methodology on orthogonal curvilinear grid for breaking waves produced by an interface-piercing body at high Reynolds number is presented. Both gas and liquid phases are considered for the strong interactions between two phases, such as spray dispersion and bubble entrainment. The level-set based ghost fluid method is adopted for sharp interface treatment and a volume-of-f...

One-way wave equations conveniently describe wave propagation in media with discontinuous and/or rapid variations in one direction, but with smooth and slow variations in the complementary transverse directions. In the past, reciprocity theorems have been developed in terms of one-way wave fields. The boundaries of the integration volumes and the variations of the medium parameters must adhere ...

A computationally efficient numerical method for the solution of nonlinear sea ice dynamics models employing viscous-plastic rheologies is presented. The method is based on a semi-implicit decoupling of the x and y ice momentum equations into a form having better convergence properties than the coupled equations. While this decoupled form also speeds up solutions employing point relaxation meth...

The 'tHooft's 5N-parametric multiinstanton solution is generalized to curvilinear coordinates. Expressions can be simplified by the gauge transformation that makes η-symbols constant in the vierbein formalism. This generates the compensating addition to the gauge potential of pseudoparticles. Typical examples (4-spherical, 2 + 2-and 3 + 1-cylindrical coordinates) are studied and explicit formul...