The Equations of Mean Motion of an Incompressible Viscous Fluid in Orthogonal Curvilinear Coordinates

Motion of an Elastic Solid inside an Incompressible Viscous Fluid

The motion of an elastic solid inside an incompressible viscous fluid is ubiquitous in nature. Mathematically, such motion is described by a PDE system that couples the parabolic and hyperbolic phases, the latter inducing a loss of regularity which has left the basic question of existence open until now. In this paper, we prove the existence and uniqueness of such motions (locally in time), whe...

The Solution of Laminar Incompressible Flow Equation with Free Surfaces in Curvilinear Coordinates

In this paper a novel numerical approach is presented for solving the transient incompressible fluid flow problems with free surfaces in generalized two-dimensional curvilinear coordinate systems. Solution algorithm is a combination of implicit real-time steps and explicit pseudo-time steps. Governing fluid flow equations are discretized using a collocated finite-volume mesh. Convective terms a...

The Solution of Laminar Incompressible Flow Equation with Free Surfaces in Curvilinear Coordinates

In this paper a novel numerical approach is presented for solving the transient incompressible fluid flow problems with free surfaces in generalized two-dimensional curvilinear coordinate systems. Solution algorithm is a combination of implicit real-time steps and explicit pseudo-time steps. Governing fluid flow equations are discretized using a collocated finite-volume mesh. Convective terms a...

Mathematical models of turbulent motion of an incompressible viscous fluid

From Ramond Fermions to Lamé Equations for Orthogonal Curvilinear Coordinates

We show how Ramond free neutral Fermi fields lead to a τ -function theory of BKP type which describes iso-orthogonal deformations of systems of ortogonal curvilinear coordinates. We also provide a vertex operator representation for the classical Ribaucour transformation.